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Half-bakery reaction with glider

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

Re: Half-bakery reaction with glider

Postby codeholic » June 9th, 2014, 8:02 pm

dvgrn wrote:This looks good, especially if the two gliders can be killed off by one guard somehow...

I've tried different scenarios, but now I'm out of ideas. 12 gliders is worse than 10, but still okay. Cleaning up two last gliders with one 'guard' per glider is of course trivial, here is one of many ways to do it.
x = 169, y = 172, rule = B3/S23
156b2o$155bo2bo$155bobo$153b2obo$152bo2bo$152bobo$153bo3$139b2o$138bo
2bo$138bobo$136b2obo$135bo2bo$135bobo$136bo2$166bo$166bobo$166b2o3$
151bo$149b2o$150b2o$133b2o$132bo2bo$132bobo$130b2obo$129bo2bo$129bobo$
130bo3$116b2o$115bo2bo$115bobo$113b2obo$112bo2bo$112bobo$113bo5$123bob
o$123b2o$124bo9$113b2o$112bo2bo$102bo9bobo$101bo8b2obo$101b3o5bo2bo$
109bobo$110bo3$96b2o$95bo2bo$95bobo$93b2obo$92bo2bo$92bobo$93bo10$90b
2o$89bo2bo$89bobo$87b2obo$86bo2bo$86bobo$87bo3$73b2o$72bo2bo$72bobo$
70b2obo$69bo2bo$69bobo$70bo19$50b2o$49bo2bo$49bobo$47b2obo$46bo2bo$46b
obo$47bo19$27b2o$26bo2bo$26bobo$24b2obo$23bo2bo$23bobo$24bo19$4b2o$3bo
2bo$3bobo$b2obo$o2bo$obo$bo!
Last edited by codeholic on June 10th, 2014, 2:01 am, edited 1 time in total.
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Re: Half-bakery reaction with glider

Postby dvgrn » June 9th, 2014, 10:28 pm

codeholic wrote:Cleaning up two last gliders with one 'guard' per glider is of course trivial, here is one of many ways to do it.

Looks like this is generation T>0 of the pattern I'd like to see, since there are only two gliders left in it...?

Another question: is it worth asking gencols if there are any possibilities for one SEward glider plus three NWward gliders making a clean 90-degree output? That would be only nine half-bakery chains instead of ten, plus a guard or two.

The search range details are a bit painful. The first NW glider is [-6..6] from the SE glider lane; the next NW glider can be [-6,-5,-4,-3,0,1,2,3] from the first one, but allowable lanes for the third glider depend on the first and second glider lanes and where those gliders are constructed. Again it's better if the three NW gliders don't have to be synchronized, but a recipe where two of them are synchronized might still be worth knowing about.
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Re: Half-bakery reaction with glider

Postby codeholic » June 10th, 2014, 2:06 am

dvgrn wrote:Looks like this is generation T>0 of the pattern I'd like to see, since there are only two gliders left in it...?

I've updated the pattern. If you're interested, here are raw gencols results: https://www.dropbox.com/s/gyjpdw46obsun ... ard.col.gz
dvgrn wrote:Another question: is it worth asking gencols if there are any possibilities for one SEward glider plus three NWward gliders making a clean 90-degree output? That would be only nine half-bakery chains instead of ten, plus a guard or two.

I'll try, but that's not really the task, that gencols is well-suited for.
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Re: Half-bakery reaction with glider

Postby codeholic » June 10th, 2014, 2:55 am

I've been making a database of 3sL seeds and invariants of glider pairs they emit.

Just playing around for now, a 9sL seed for the SE track pair:
x = 168, y = 217, rule = B3/S23
143bo$141bobo$142b2o24$159bo$158bobo$158bo2bo$159b2o5b2o$166b2o2$159bo
$158bobo$158bobo$159bo36$131b2o$131b2o2$101b2o$101b2o3$138b2o$137bo2bo
$138bobo$108b2o29bo$107bo2bo$108bobo$109bo$136bo$135bobo$134bo2bo$106b
o28b2o$105bobo$104bo2bo$105b2o33$106b2o$105bo2bo$105bobo$76b2o25b2obo$
75bo2bo23bo2bo$75bobo24bobo$73b2obo26bo$72bo2bo$72bobo$73bo30$42b2o$
41bo2bo$41bobo$39b2obo$38bo2bo$38bobo$39bo2$26b2o$25bo2bo$25bobo$23b2o
bo$22bo2bo$22bobo$23bo$54b2o$53bo2bo$53bobo$51b2obo$50bo2bo$50bobo$51b
o2$38b2o$20b2o15bo2bo$19bo2bo14bobo$19bobo13b2obo$17b2obo13bo2bo$16bo
2bo14bobo$16bobo16bo$17bo2$4b2o$3bo2bo$3bobo$b2obo$o2bo$obo$bo$32b2o$
31bo2bo$31bobo$29b2obo$28bo2bo$28bobo$29bo2$16b2o$15bo2bo$15bobo$13b2o
bo$12bo2bo$12bobo$13bo!

I've just thought, that instead of blindly enumerating all 3sL collisions it would make sense to check invariants for p2 syntheses of glider pairs in the order of their weight measured in simultaneous half-bakery transformations (i. e. if there are several HB-transformations on different trails in the same time, they're counted as one).

Have you compiled a set of operations for monochromatic single-parity slow salvo synthesis yet? The first step would be to measure their weight in half-bakeries. (Weights for operations reflected over SW-NE axis will be different.)
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Re: Half-bakery reaction with glider

Postby dvgrn » June 10th, 2014, 9:02 am

codeholic wrote:
dvgrn wrote:Another question: is it worth asking gencols if there are any possibilities for one SEward glider plus three NWward gliders making a clean 90-degree output? That would be only nine half-bakery chains instead of ten, plus a guard or two.

I'll try, but that's not really the task, that gencols is well-suited for.

Well, don't worry about it, then -- I can just as easily modify my silly Python script for that task. Here's the script as of this morning; I added labels for the recipes to make them easier to review. To change search parameters you have to edit lines 18-21 manually. Hit 'q' to quit the search and see partial results. FAIR WARNING: This script has no safety features to protect half-finished editing projects; it clobbers both the current universe and the clipboard.

# FindHBGliders.py, version 0.21
# Find HB-compatible NE glider recipes
#
#  A
#   [timeAB, offsetAB]
#    B
#
#  -6 >= offsetBC => +6 (possible collision lanes)
#
#       C
#        [timeCD, offsetCD]
#         D

import golly as g
from time import sleep
from glife.text import make_text

minABlane, maxABlane = 0, 3
minBClane, maxBClane = -6, 6 # all offsets where initial two gliders can interact
minCDlane, maxCDlane = -6,-3
minABtime, maxABtime = 0, 64


g.setrule("Life")
g.setalgo("QuickLife")

count, numsol, solutions, data = 0, 0, [], ""
for phase in range(0,1):# a number higher than 1 would check more phases --
                        # but this would give lots of duplicates.
                        # I think the only unique results would be cases where
                        #   the intermediate target is not stable.
for offsetCD in range(minCDlane,maxCDlane+1): # horizontal adjustment between gliders C and D
  for offsetBC in range(minBClane,maxBClane+1):
    for timeBC in range(0,8): # try all relative phases between B and C

      g.new("Test2glider"+str(count))
      g.putcells(g.parse("bo$2bo$3o!"))                       # glider B
      g.run(timeBC)
      g.putcells(g.parse("3o$o$bo!"),60+offsetBC,60)          # glider C
      g.run(1024)
      if int(g.getpop())==0:
        continue              # skip the vanish reactions --
                              # 180-degree sparks don't last long enough

      for timeAB in range(minABtime, maxABtime+1):
        for offsetAB in range(minABlane, maxABlane+1):
          count+=1
          if count<0:
            continue
          g.new("Test"+str(count))
          g.putcells(g.parse("3o$o$bo!"),86+offsetBC-offsetCD,86) # glider D: 86 = arbitrary distance for asynchronous collisions
          g.run(phase)
          g.putcells(g.parse("bo$2bo$3o!"))                       # glider B
          g.run(timeBC)
          g.putcells(g.parse("3o$o$bo!"),60+offsetBC,60)          # glider C
          g.run(timeAB)
          g.putcells(g.parse("bo$2bo$3o!"),-8+offsetAB,-8)        # glider A always in same phase
                               # -8 magic constant is small enough that most of the valid
                               # potentially synchronous positions for glider A are also tested,
                               # along with a few invalid ones.
          sav=g.getcells(g.getrect())
          g.fit()
          g.run(1024)
          if int(g.getpop())==5: # test for existence of one clean glider
            r=g.getrect()
            test=g.getcells(r)
            g.run(1)
            if test!=g.getcells(r): 
              if (r[0]<200 or r[1]<200) and (r[0]>-100 or r[1]>-100): # not NW or SE gliders
                vert=0 if (r[0]<200 and r[1]>-100) else 200
                params="#"+str(numsol)+": X="+str(offsetAB)+","+str(offsetBC)+","+str(offsetCD)+", T="+str(timeAB)+","+str(timeBC)+","+str(phase)
                data+=params+"\n"
                t = make_text(params, "mono")
                solutions=g.join(solutions,g.transform(t,numsol*200,phase*500-20+vert))
                solutions=g.join(solutions,g.transform(sav,numsol*200,phase*500+vert))
                numsol+=1
                g.new("Found " + str(numsol))
                g.putcells(sav)
               
          if count%100==1:
            g.putcells(sav) # just overlap trial gliders with result to show an occasional sample
            g.update()
            if g.getevent()=="key q none":
              if numsol:
                g.new("Partial Results")
                g.putcells(solutions)
                g.setclipstr(data)
                g.note("Parameters for results so far:\n"+ data)
              else:
                g.note("No solutions found yet.")
              g.exit()
        g.show("Found " + str(numsol) + " glider recipes.  offsetAB, offsetBC, offsetCD = " + str([offsetAB,offsetBC,offsetCD]) \
             + "; timeAB, timeBC, phase = " +str([timeAB,timeBC, phase]))
             
g.new("Results")
g.putcells(solutions)
g.setclipstr("Parameters for results:\n"+data)
g.note(data)

This version 0.1 is really stupidly slow and brute-force. The next obvious optimization is to check the B+C glider collision and skip all the vanish reactions. I'll probably add that this morning, along with any other fixes I think of during this next test run. EDIT: Updated to version 0.2. Here's a stamp collection of the recipes v0.2 found for NW-bound gliders in the -6..-3 range:

x = 7143, y = 325, rule = LifeHistory
7.D.D3.3D14.D3.D8.3D17.D15.3D14.5D8.3D3.3D8.5D8.3D65.D.D4.D15.D3.D8.
3D10.D16.3D14.5D8.3D3.3D9.3D9.3D271.D.D3.3D14.D3.D8.3D9.3D15.3D14.5D
10.D3.3D8.5D8.3D71.D.D5.D14.D3.D8.3D9.3D15.3D14.5D10.D5.D8.5D8.3D71.D
.D2.5D13.D3.D8.3D9.3D15.3D14.5D10.D3.3D8.5D8.3D71.D.D3.3D14.D3.D8.3D
9.3D15.3D14.5D10.D3.3D8.5D8.3D71.D.D2.5D13.D3.D8.3D9.3D15.3D14.5D7.5D
2.3D8.5D8.3D71.D.D3.3D14.D3.D8.3D9.3D15.3D14.5D7.5D2.3D8.5D8.3D71.D.D
3.3D14.D3.D8.3D9.3D15.3D14.5D7.5D4.D8.5D8.3D71.D.D4.D4.3D14.D3.D8.3D
9.3D15.3D14.5D7.5D2.3D8.5D8.3D65.D.D4.D5.D15.D3.D8.3D9.3D15.3D14.5D7.
5D2.3D8.5D8.3D65.D.D4.D4.3D14.D3.D8.3D9.3D15.3D14.5D8.3D3.3D8.5D8.3D
65.D.D4.D4.3D14.D3.D8.3D9.3D15.3D14.5D8.3D3.3D8.5D8.3D465.D.D4.D4.3D
14.D3.D8.3D9.3D14.5D13.5D9.D4.3D9.3D9.3D65.D.D4.D3.5D13.D3.D8.3D9.3D
14.5D13.5D9.D4.3D9.3D9.3D65.D.D4.D4.3D14.D3.D9.D11.D15.5D13.5D7.5D.5D
8.3D9.3D65.D.D4.D4.3D14.D3.D9.D10.3D14.5D13.5D9.D4.3D9.3D9.3D65.D.D3.
3D3.3D14.D3.D8.3D9.3D14.5D13.5D7.5D2.3D8.5D8.3D665.D.D3.3D5.D14.D3.D
9.D16.3D17.D14.5D7.5D.5D8.3D9.3D59.D.D3.3D2.5D13.D3.D8.3D15.3D17.D14.
5D9.D4.3D9.3D9.3D259.D.D3.3D2.5D13.D3.D8.3D9.3D17.D14.5D8.3D3.3D9.3D
9.3D65.D.D3.3D3.3D14.D3.D9.D10.3D17.D14.5D7.5D.5D8.3D9.3D265.D.D3.3D
3.3D14.D3.D8.3D15.3D15.3D14.5D8.3D3.3D9.3D9.3D259.D.D3.3D3.3D14.D3.D
9.D10.3D15.3D14.5D10.D2.5D9.D10.3D65.D.D3.3D3.3D14.D3.D8.3D11.D15.3D
14.5D7.5D.5D9.D10.3D$7.D.D2.D3.D13.D3.D7.D3.D15.2D14.D19.D9.D3.D.D11.
D11.D3.D64.D.D3.2D15.D3.D7.D3.D8.2D15.D19.D9.D5.D3.D7.D11.D3.D270.D.D
2.D3.D13.D3.D7.D3.D7.D3.D13.D19.D11.2D2.D3.D11.D7.D3.D70.D.D4.2D14.D
3.D7.D3.D7.D3.D13.D19.D11.2D4.2D12.D7.D3.D70.D.D2.D17.D3.D7.D3.D7.D3.
D13.D19.D11.2D2.D15.D7.D3.D70.D.D2.D17.D3.D7.D3.D7.D3.D13.D19.D11.2D
2.D3.D11.D7.D3.D70.D.D6.D13.D3.D7.D3.D7.D3.D13.D19.D9.D5.D3.D11.D7.D
3.D70.D.D2.D3.D13.D3.D7.D3.D7.D3.D13.D19.D9.D5.D3.D11.D7.D3.D70.D.D2.
D3.D13.D3.D7.D3.D7.D3.D13.D19.D9.D7.2D12.D7.D3.D70.D.D3.2D3.D3.D13.D
3.D7.D3.D7.D3.D13.D19.D9.D5.D15.D7.D3.D64.D.D3.2D4.2D15.D3.D7.D3.D7.D
3.D13.D19.D9.D5.D3.D11.D7.D3.D64.D.D3.2D3.D3.D13.D3.D7.D3.D7.D3.D13.D
19.D9.D5.D3.D11.D7.D3.D64.D.D3.2D3.D3.D13.D3.D7.D3.D7.D3.D13.D19.D9.D
5.D3.D11.D7.D3.D464.D.D3.2D3.D17.D3.D7.D3.D7.D3.D13.D19.D10.2D3.D11.D
11.D3.D64.D.D3.2D7.D13.D3.D7.D3.D7.D3.D13.D19.D10.2D3.D3.D7.D11.D3.D
64.D.D3.2D3.D3.D13.D3.D8.2D10.2D15.D19.D9.D5.D11.D11.D3.D64.D.D3.2D3.
D3.D13.D3.D8.2D9.D3.D13.D19.D10.2D3.D3.D7.D3.D7.D3.D64.D.D2.D3.D.D3.D
13.D3.D7.D3.D7.D3.D13.D19.D9.D5.D15.D7.D3.D664.D.D2.D3.D3.2D14.D3.D8.
2D15.D3.D15.2D16.D9.D5.D11.D11.D3.D58.D.D2.D3.D.D17.D3.D7.D3.D13.D3.D
15.2D16.D10.2D3.D3.D7.D3.D7.D3.D258.D.D2.D3.D5.D13.D3.D7.D3.D7.D3.D
15.2D16.D9.D3.D.D3.D7.D11.D3.D64.D.D2.D3.D.D3.D13.D3.D8.2D9.D3.D15.2D
16.D9.D9.D7.D11.D3.D264.D.D2.D3.D.D3.D13.D3.D7.D3.D13.D3.D13.D3.D15.D
9.D5.D3.D7.D11.D3.D258.D.D2.D3.D.D3.D13.D3.D8.2D9.D3.D13.D3.D15.D11.
2D2.D12.2D9.D3.D64.D.D2.D3.D.D3.D13.D3.D7.D3.D9.2D14.D3.D15.D9.D9.D8.
2D9.D3.D$6.5D.D2.2D3.D10.D.D2.5D5.D14.D.D14.D19.D3.5D5.D.D11.D11.D2.
2D63.5D3.D5.D10.D.D2.5D5.D9.D15.D19.D3.5D.D9.D7.D11.D2.2D269.5D5.D3.D
10.D.D2.5D5.D11.D13.D19.D3.5D2.D.D6.D10.D8.D2.2D69.5D2.D.D4.D10.D.D2.
5D5.D11.D13.D19.D3.5D2.D.D3.D.D11.D8.D2.2D69.5D.D7.D10.D.D2.5D5.D11.D
13.D19.D3.5D2.D.D2.D14.D8.D2.2D69.5D.D7.D10.D.D2.5D5.D11.D13.D19.D3.
5D2.D.D2.D3.D10.D8.D2.2D69.5D4.D4.D10.D.D2.5D5.D11.D13.D19.D3.5D.D5.D
2.2D10.D8.D2.2D69.5D.D3.D3.D10.D.D2.5D5.D11.D13.D19.D3.5D.D9.D10.D8.D
2.2D69.5D.D3.D3.D10.D.D2.5D5.D11.D13.D19.D3.5D.D6.D.D11.D8.D2.2D69.5D
3.D3.D2.2D3.D10.D.D2.5D5.D11.D13.D19.D3.5D.D5.D14.D8.D2.2D63.5D3.D5.D
5.D10.D.D2.5D5.D11.D13.D19.D3.5D.D5.D3.D10.D8.D2.2D63.5D3.D7.D3.D10.D
.D2.5D5.D11.D13.D19.D3.5D.D5.D2.2D10.D8.D2.2D63.5D3.D7.D3.D10.D.D2.5D
5.D11.D13.D19.D3.5D.D9.D10.D8.D2.2D463.5D3.D3.D7.D10.D.D2.5D5.D7.D2.
2D13.D19.D3.5D3.D3.D11.D11.D2.2D63.5D3.D6.D4.D10.D.D2.5D5.D7.D2.2D13.
D19.D3.5D3.D3.D3.D7.D11.D2.2D63.5D3.D3.D3.D3.D10.D.D2.5D3.D11.D15.D
19.D3.5D.D5.D11.D11.D2.2D63.5D3.D3.D3.D3.D10.D.D2.5D3.D13.D13.D19.D3.
5D3.D3.D3.D11.D7.D2.2D63.5D5.D.D2.2D3.D10.D.D2.5D5.D11.D13.D19.D3.5D.
D5.D14.D8.D2.2D663.5D5.D2.D.D4.D10.D.D2.5D3.D19.D14.D.D16.D3.5D.D5.D
11.D11.D2.2D57.5D5.D.D7.D10.D.D2.5D5.D17.D14.D.D16.D3.5D3.D3.D2.2D11.
D7.D2.2D257.5D5.D4.D4.D10.D.D2.5D5.D11.D14.D.D16.D3.5D5.D.D2.2D7.D11.
D2.2D63.5D5.D.D3.D3.D10.D.D2.5D3.D13.D14.D.D16.D3.5D.D8.D8.D11.D2.2D
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196.4B196.4B196.4B196.4B596.4B196.4B195.4B196.4B198.4B794.4B195.B2C4B
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195.CBC2B195.4B195.B2C2B198.4B794.4B195.7B395.4B195.4B397.4B395.4B
198.4B$14.4B197.4B395.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B
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196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B594.6B
194.6B195.4B195.5B198.4B794.4B195.7B394.2BC2B195.4B397.4B395.4B198.4B
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196.4B196.4B594.6B194.6B195.4B195.5B198.4B794.4B195.7B393.3C3B195.4B
397.4B395.4B198.4B$16.B2C3B197.4B395.4B196.4B196.4B196.4B196.4B196.4B
196.4B196.4B196.4B196.4B196.4B594.6B194.6B195.4B195.5B198.4B794.4B
195.7B393.6B195.4B397.4B395.2BCB198.4B$17.C5B197.4B394.CBC2B196.C3B
196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B594.6B194.6B
195.4B195.5B198.4B794.4B195.7B393.6B195.4B397.4B394.CBC2B198.4B$18.6B
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4B196.4B196.4B594.6B194.6B195.4B195.5B198.4B794.4B195.7B393.6B195.4B
397.4B394.2C3B198.4B$19.6B197.4B393.C5B194.2C4B194.B2C3B195.B2C2B195.
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198.4B794.4B195.7B393.6B195.4B397.4B394.5B197.BC3B$20.6B197.4B393.6B
194.6B194.C5B194.2C4B194.B2C3B195.B2C2B195.CBC2B196.C3B196.4B196.4B
196.4B594.6B194.6B195.CBCB195.5B197.C4B794.CBCB195.7B393.6B195.BC2B
397.4B394.5B195.CBC4B$21.6B197.4B393.6B194.6B194.6B194.6B194.C5B194.
2C4B194.B2C3B195.B2C2B195.CBC2B196.C3B196.4B594.6B194.6B194.B2C2B195.
5B196.B2C3B793.B2C2B195.7B393.6B195.B2CB397.BC2B394.5B195.2C5B$22.6B
195.CBC3B393.6B194.6B194.6B194.6B194.6B194.6B194.C5B194.2C4B194.B2C3B
195.B2C2B195.CBC2B594.6B194.6B194.C4B195.5B195.2C5B793.C4B195.7B393.
6B194.2C3B396.2BC2B394.5B195.7B$23.6B194.B2C4B393.6B194.6B194.6B194.
6B194.6B194.6B194.6B194.6B194.C5B194.2C4B194.B2C3B594.6B194.6B194.5B
195.5B195.7B793.5B195.7B393.6B194.5B395.3C3B394.5B195.7B$24.6B194.C6B
393.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.C5B
594.6B194.6B194.5B195.5B195.7B793.5B195.7B393.6B194.5B395.6B394.5B
195.7B$25.6B194.7B393.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B
194.6B194.6B194.6B594.6B194.6B194.5B195.5B195.7B793.5B195.7B393.6B
194.5B395.6B394.5B195.7B$26.6B194.7B393.6B194.6B194.6B194.6B194.6B
194.6B194.6B194.6B194.6B194.6B194.6B594.6B194.6B194.5B195.5B195.7B
793.5B195.7B393.6B194.5B395.6B394.5B195.7B$27.6B194.7B393.6B194.6B
194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B594.6B194.6B
194.5B195.5B195.7B793.5B195.7B393.6B194.5B395.6B394.5B195.7B$28.6B
194.7B393.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B
194.6B594.6B194.6B194.5B195.5B195.7B793.5B195.7B393.6B194.5B395.6B
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194.6B194.6B194.6B194.6B594.6B194.6B194.5B195.5B195.7B793.5B195.7B
393.6B194.5B395.6B394.5B195.7B$30.6B194.7B393.6B194.6B194.6B194.6B
194.6B194.6B194.6B194.6B194.6B194.6B194.6B594.6B194.6B194.5B195.5B
195.7B793.5B195.7B393.6B194.5B395.6B394.5B195.7B$31.6B194.7B393.6B
194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B594.6B
194.6B194.5B195.5B195.7B793.5B195.7B393.6B194.5B395.6B394.5B195.7B$
32.6B194.7B393.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.
6B194.6B594.6B194.6B194.5B195.5B195.7B793.5B195.7B8.4B381.6B194.5B
395.6B394.5B195.7B$33.6B194.7B393.6B194.6B194.6B194.6B194.6B194.6B
194.6B194.6B194.6B194.6B194.6B594.6B194.6B194.5B195.5B195.7B793.5B
195.7B7.5B381.6B194.5B395.6B394.5B195.7B$34.6B194.7B393.6B194.6B194.
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195.5B195.7B793.5B195.7B.B3.6B382.6B194.5B395.6B394.5B195.7B$35.6B
194.7B393.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B194.6B
194.6B594.6B194.6B194.5B195.5B195.7B793.5B195.9B2.6B383.6B194.5B395.
6B394.5B195.7B$36.6B194.7B393.6B194.6B194.6B194.6B194.6B194.6B194.6B
194.6B194.6B194.6B194.6B594.6B194.6B194.5B195.5B195.7B793.5B195.17B
383.6B194.5B395.6B394.5B195.7B$37.6B194.7B393.6B4.B3.B185.6B4.B3.B
185.6B4.B3.B185.6B4.B3.B185.6B4.B3.B185.6B4.B3.B185.6B4.B3.B185.6B4.B
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190.7B793.5B195.9BD6B384.6B194.5B395.6B394.5B195.7B$38.6B194.7B393.6B
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395.6B394.5B195.7B3.4B$39.8B192.7B393.16B184.16B184.16B184.16B184.16B
184.16B184.16B184.16B184.16B184.16B184.16B584.6B194.6B194.5B188.17B
190.10B6.B783.5B195.6BDBD5B386.6B194.5B395.6B394.5B.B193.7B.6B$40.8B
192.7B392.17B183.17B183.17B183.17B183.17B183.17B183.17B183.17B183.17B
183.17B183.17B584.6B194.7B193.5B187.18B190.17B783.5B194.7BD5B388.6B
194.5B395.6B394.7B3.D189.13B$41.7B193.8B389.19B181.19B181.19B181.19B
181.19B181.19B181.19B181.19B181.19B181.19B181.19B584.6B193.7B194.5B
186.19B190.16B784.5B192.15B388.6B194.5B395.6B394.9BDB189.15B$42.7B
193.8B387.19B181.19B181.19B181.19B181.19B181.19B181.19B181.19B181.19B
181.19B181.19B584.9B190.10B193.5B.B182.20B191.14B786.6B190.3B2D7B2D2B
388.6B194.5B395.6B394.8BD2B189.15B$41.9B193.8B385.20B180.20B180.20B
180.20B180.20B180.20B180.20B180.20B180.20B180.20B180.12BD7B583.5BDBD
4B188.7BD4B192.7B181.20B192.5BD8B786.6B190.BD2BD5BD2BDB389.6B194.5B
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7B178.12B3D7B178.12B3D7B178.12B3D7B178.12B3D7B178.12B3D7B178.12B3D7B
178.12B3D7B178.13BD8B582.6B2D4B188.8BD3B193.7B180.21B191.5BD7B788.6B
190.B2D7B2DB391.6B194.5B395.5B395.2B3D3B3D189.6BD2BD4B$40.5BDBD2B193.
3B2D3B383.22B178.22B178.22B178.22B178.22B178.22B178.22B178.22B178.22B
178.22B178.14BD7B581.8BD9B182.8B3D7B190.B2D3B181.13B3D5B191.4BD7B787.
7B190.11B394.7B193.7B391.6B394.11B191.5BD2BD4B$41.5B2D3B191.3BD2BD3B
381.4B2.6BD5BD3B178.4B2.6BD5BD3B178.4B2.6BD5BD3B178.4B2.6BD5BD3B178.
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6BD5BD3B178.4B2.6BD5BD3B178.4B2.16B581.20B180.13B2D5B189.D2BD3B180.
13BD8B191.11B786.3B2D3B191.5BD2B397.7B193.7B389.3B2D2B394.7BD3B192.5B
2D4B$42.9B190.5BDBD4B379.4B3.6BD5BD3B177.4B3.6BD5BD3B177.4B3.6BD5BD3B
177.4B3.6BD5BD3B177.4B3.6BD5BD3B177.4B3.6BD5BD3B177.4B3.6BD5BD3B177.
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13B783.5BDBD3B192.2BDBD6B392.9B191.9B386.4BDBD2B396.4BD5B189.12B$41.
9B189.4B2.10B375.4B8.8B.6B173.4B8.8B.6B173.4B8.8B.6B173.4B8.8B.6B173.
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782.4B.2BD4B192.3BD7B392.5B.4B191.BD7B386.4BD4B396.10B187.14B$40.11B
187.4B3.5B2.4B373.4B10.4B3DB3.4B171.4B10.4B3DB3.4B171.4B10.4B3DB3.4B
171.4B10.4B3DB3.4B171.4B10.4B3DB3.4B171.4B10.4B3DB3.4B171.4B10.4B3DB
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D2B3.4B574.4B3.16B177.4B3.16B189.12B178.24B184.6BD9B780.4B2.8B192.10B
391.2B3D2B.4B190.BD8B384.11B394.12B185.4B3.9B$39.7B2.4B185.4B6.4B2.4B
371.4B15.6B2.4B169.4B15.6B2.4B169.4B15.6B2.4B169.4B15.6B2.4B169.4B15.
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169.4B15.6B2.4B169.4B15.BD4B2.4B572.4B5.16B175.4B5.16B187.9B.4B178.
19B.4B182.7BD10B778.4B3.9B193.8B390.5B2.7B190.D9B382.13B392.4B2.8B
183.4B4.10B$38.4B.4B2.4B183.4B8.4B2.4B369.4B17.6B2.4B167.4B17.6B2.4B
167.4B17.6B2.4B167.4B17.6B2.4B167.4B17.6B2.4B167.4B17.6B2.4B167.4B17.
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570.4B7.6B.9B173.4B7.6B.9B185.4B3.4B.4B176.4B4.13B.4B180.4B2.14B776.
4B6.8B193.8B388.4B4.8B189.11B380.4B4.7B390.4B4.8B181.4B6.10B$37.4B3.
4B2.4B181.4B10.4B2.4B367.4B21.4B2.4B165.4B21.4B2.4B165.4B21.4B2.4B
165.4B21.4B2.4B165.4B21.4B2.4B165.4B21.4B2.4B165.4B21.4B2.4B165.4B21.
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171.4B10.3B3.4B.4B183.4B5.4B.4B174.4B5.14B.4B178.4B4.9B.4B774.4B8.8B
193.8B386.4B6.8B189.11B378.4B6.7B388.4B7.7B179.4B7.11B$36.4B5.4B2.4B
179.4B12.4B2.4B365.4B23.4B2.4B163.4B23.4B2.4B163.4B23.4B2.4B163.4B23.
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163.4B23.4B2.4B163.4B23.4B2.4B163.4B23.4B2.4B566.4B18.4B.4B169.4B18.
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384.4B8.8B187.13B376.4B8.7B386.4B9.7B177.4B9.B.9B$35.4B7.4B2.4B177.4B
14.4B2.4B363.4B25.4B2.4B161.4B25.4B2.4B161.4B25.4B2.4B161.4B25.4B2.4B
161.4B25.4B2.4B161.4B25.4B2.4B161.4B25.4B2.4B161.4B25.4B2.4B161.4B25.
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10.8B186.14B374.4B10.7B384.4B11.7B175.4B15.7B$34.4B9.4B2.4B175.4B16.
4B2.4B361.4B27.4B2.4B159.4B27.4B2.4B159.4B27.4B2.4B159.4B27.4B2.4B
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4B11.4B.4B168.4B5.11B5.4B.4B172.4B15.4B.4B768.4B14.8B187.4B2.8B380.4B
12.8B184.16B372.4B12.7B382.4B13.7B173.4B17.7B$33.4B11.4B2.4B173.4B18.
4B2.4B359.4B29.4B2.4B157.4B29.4B2.4B157.4B29.4B2.4B157.4B29.4B2.4B
157.4B29.4B2.4B157.4B29.4B2.4B157.4B29.4B2.4B157.4B29.4B2.4B157.4B29.
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4B13.4B.4B166.4B7.8B8.4B.4B170.4B17.4B.4B766.4B16.8B185.4B4.8B378.4B
14.8B182.7B3.8B370.4B14.7B380.4B15.7B171.4B19.7B$32.4B13.4B2.4B171.4B
20.4B2.4B357.4B31.4B2.4B155.4B31.4B2.4B155.4B31.4B2.4B155.4B31.4B2.4B
155.4B31.4B2.4B155.4B31.4B2.4B155.4B31.4B2.4B155.4B31.4B2.4B155.4B31.
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4B15.4B.4B164.4B9.6B10.4B.4B168.4B19.4B.4B764.4B18.8B183.4B6.8B376.4B
16.8B180.4B2.B5.8B368.4B16.7B378.4B17.7B169.4B21.7B$31.4B15.4B2.4B
169.4B22.4B2.4B355.4B33.4B2.4B153.4B33.4B2.4B153.4B33.4B2.4B153.4B33.
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153.4B33.4B2.4B153.4B33.4B2.4B153.4B33.4B2.4B556.4B28.4B.4B159.4B28.
4B.4B171.4B17.4B.4B162.4B11.3B13.4B.4B166.4B21.4B.4B762.4B20.8B181.4B
8.8B374.4B18.8B178.4B10.8B366.4B18.7B376.4B19.7B167.4B23.7B$30.4B17.
4B2.4B167.4B24.4B2.4B353.4B35.4B2.4B151.4B35.4B2.4B151.4B35.4B2.4B
151.4B35.4B2.4B151.4B35.4B2.4B151.4B35.4B2.4B151.4B35.4B2.4B151.4B35.
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4B30.4B.4B169.4B19.4B.4B160.4B13.B15.4B.4B164.4B23.4B.4B760.4B22.8B
179.4B10.8B372.4B20.8B176.4B12.8B364.4B20.7B374.4B21.7B165.4B25.7B$
29.4B19.4B2.4B165.4B26.4B2.4B351.4B37.4B2.4B149.4B37.4B2.4B149.4B37.
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149.4B37.4B2.4B149.4B37.4B2.4B149.4B37.4B2.4B149.4B37.4B2.4B552.4B32.
4B.4B155.4B32.4B.4B167.4B21.4B.4B158.4B31.4B.4B162.4B25.4B.4B758.4B
24.8B177.4B12.8B370.4B22.8B174.4B14.8B362.4B22.7B372.4B23.7B163.4B27.
7B$28.4B21.4B2.4B163.4B28.4B2.4B349.4B39.4B2.4B147.4B39.4B2.4B147.4B
39.4B2.4B147.4B39.4B2.4B147.4B39.4B2.4B147.4B39.4B2.4B147.4B39.4B2.4B
147.4B39.4B2.4B147.4B39.4B2.4B147.4B39.4B2.4B147.4B39.4B2.4B550.4B34.
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26.8B175.4B14.8B368.4B24.8B172.4B16.8B360.4B24.7B370.4B25.7B161.4B29.
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28.8B173.4B16.8B366.4B26.8B170.4B18.8B358.4B26.7B368.4B27.7B159.4B31.
7B$26.4B25.4B2.4B159.4B32.4B2.4B345.DBDB43.4B2.4B143.DBDB43.4B2.4B
143.DBDB43.4B2.4B143.DBDB43.4B2.4B143.DBDB43.4B2.4B143.DBDB43.4B2.4B
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4B.4B156.D3B31.4B.4B752.4B30.8B171.4B18.8B364.4B28.8B168.4B20.8B356.
4B28.7B366.4B29.7B157.4B33.7B$25.4B27.4B2.4B157.4B34.4B2.4B344.2DB45.
4B2.4B142.2DB45.4B2.4B142.2DB45.4B2.4B142.2DB45.4B2.4B142.2DB45.4B2.
4B142.2DB45.4B2.4B142.2DB45.4B2.4B142.2DB45.4B2.4B142.2DB45.4B2.4B
142.2DB45.4B2.4B142.2DB45.4B2.4B544.4B40.4B.4B147.4B40.4B.4B159.4B29.
4B.4B150.4B39.4B.4B155.3D33.4B.4B750.4B32.8B169.4B20.8B362.4B30.8B
166.4B22.8B354.4B30.7B364.4B31.7B155.4B35.7B$24.4B29.4B2.4B155.4B36.
4B2.4B344.D47.4B2.4B142.D47.4B2.4B142.D47.4B2.4B142.D47.4B2.4B142.D
47.4B2.4B142.D47.4B2.4B142.D47.4B2.4B142.D47.4B2.4B142.D47.4B2.4B142.
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148.4B41.4B.4B191.4B.4B748.4B34.8B167.4B22.8B360.4B32.8B164.4B24.8B
352.4B32.7B362.4B33.7B153.4B37.7B$23.4B31.4B2.4B153.4B38.4B2.4B392.4B
2.4B190.4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B190.
4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B540.4B44.4B.4B143.4B44.4B.4B155.
4B33.4B.4B146.4B43.4B.4B191.4B.4B746.4B36.8B165.4B24.8B358.4B34.8B
162.4B26.8B350.4B34.7B360.4B35.7B151.4B39.7B$22.4B33.4B2.4B151.4B40.
4B2.2B2C392.4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B
190.4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B190.4B2.2B2C538.4B46.4B.4B
141.4B46.4B.4B153.4B35.4B.4B144.4B45.4B.4B191.4B.4B744.4B38.8B163.4B
26.8B356.4B36.8B160.4B28.8B348.4B36.5B2C358.4B37.7B149.4B41.7B$21.4B
35.4B2.4B149.4B42.4B2.2CB393.4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B190.
4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B190.4B2.2B2C190.4B2.B3C190.4B2.BC
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742.4B40.8B161.4B28.8B354.4B38.8B158.4B30.7BC346.4B38.4BCBC356.4B39.
7B147.4B43.6BC$20.4B37.4B2.4B147.4B44.4B2.BC394.4B2.4B190.4B2.4B190.
4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B190.4B2.2B2C190.4B2.B3C190.4B2.BC
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140.4B49.4B.4B191.4B.B3C740.4B42.6B2C159.4B30.8B352.4B40.8B156.4B32.
5B2CB344.4B40.3BCB356.4B41.7B145.4B45.4B2CB$19.4B39.4B2.4B145.4B46.4B
398.4B2.4B190.4B2.4B190.4B2.4B190.4B2.4B190.4B2.2B2C190.4B2.B3C190.4B
2.BCBC190.4B2.C2B191.4B2.CB192.4B2.C193.4B538.4B52.4B.4B135.4B52.4B.
4B147.4B41.4B.2CB139.4B51.4B.4B191.4B.C2B739.4B44.4B2CB158.DBDB32.8B
350.4B42.8B154.4B34.4BCBC343.4B42.4B355.4B43.7B143.4B47.3BCBC$18.D3B
41.4B2.4B143.4B48.4B398.4B2.4B190.4B2.4B190.4B2.2B2C190.4B2.B3C190.4B
2.BCBC190.4B2.C2B191.4B2.CB192.4B2.C193.4B196.4B196.4B536.4B54.4B.4B
133.4B54.4B.4B145.4B43.4B.BC138.4B53.4B.4B191.4B.C739.4B46.5BC158.2DB
34.8B348.4B44.8B152.4B36.4B344.4B44.4B353.4B45.6BC141.DBDB49.4B$18.DB
D43.4B2.4B141.4B50.4B398.4B2.2B2C190.4B2.B3C190.4B2.BCBC190.4B2.C2B
191.4B2.CB192.4B2.C193.4B196.4B196.4B196.4B196.4B534.4B56.4B.4B131.4B
56.4B.4B143.4B45.4B139.4B55.4B.4B191.4B739.4B48.4B160.D36.8B346.4B46.
8B150.4B38.4B342.4B46.4B351.4B47.4B2CB140.2DB51.4B$18.2D45.4B2.4B139.
4B52.4B398.4B2.BCBC190.4B2.C2B191.4B2.CB192.4B2.C193.4B196.4B196.4B
196.4B196.4B196.4B196.4B532.4B58.4B.4B129.4B58.4B.4B141.4B47.4B137.4B
57.4B.4B191.4B737.4B50.4B197.8B344.4B48.8B148.4B40.4B340.4B48.4B349.
4B49.3BCBC141.D53.4B$66.4B2.B3C137.4B54.4B398.4B2.CB192.4B2.C193.4B
196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B530.4B60.4B.4B127.4B
60.4B.4B139.4B49.4B135.4B59.4B.4B191.4B735.4B52.4B197.8B342.4B50.8B
146.4B42.4B338.4B50.4B347.4B51.4B197.4B$67.4B2.C2B136.4B56.4B398.4B
196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B528.4B62.
4B.4B125.4B62.4B.4B137.4B51.4B133.4B61.4B.4B191.4B733.4B54.4B197.8B
340.4B52.6B2C144.4B44.4B336.4B52.4B345.4B53.4B197.4B$68.4B2.C136.D3B
58.4B398.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.
4B526.4B64.4B.4B123.4B64.4B.4B135.4B53.4B131.4B63.4B.4B191.4B731.D3B
56.4B197.8B338.DBDB54.5BCBC142.4B46.4B334.4B54.4B343.4B55.4B197.4B$
69.4B137.D3B60.4B398.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.
4B196.4B196.4B524.4B66.4B.4B121.4B66.4B.4B133.4B55.4B129.4B65.4B.4B
191.4B729.D3B58.4B197.8B337.2DB56.4BCB142.4B48.4B332.4B56.4B341.DBDB
57.4B197.4B$70.4B136.3D62.4B398.4B196.4B196.4B196.4B196.4B196.4B196.
4B196.4B196.4B196.4B196.4B522.4B68.4B.4B119.4B68.4B.2B2C131.4B57.4B
127.4B67.4B.2B2C191.4B728.3D60.4B197.8B337.D58.4B142.4B50.4B330.4B58.
4B340.2DB59.4B197.4B$71.4B201.4B398.4B196.4B196.4B196.4B196.4B196.4B
196.4B196.4B196.4B196.4B196.4B520.D3B70.4B.B3C117.4B70.4B.2CB130.4B
59.4B125.DBDB69.4B.2CB192.4B791.4B197.8B396.4B140.4B52.4B328.4B60.4B
340.D61.4B197.4B$72.4B201.4B398.4B196.4B196.4B196.4B196.4B196.4B196.
4B196.4B196.4B196.4B196.4B519.DBD72.4B.C2B116.DBDB72.4B.BC129.DBDB61.
4B124.2DB71.4B.BC193.4B791.4B197.6B2C396.4B138.4B54.4B326.4B62.4B402.
4B197.4B$73.4B201.4B398.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B
196.4B196.4B196.4B518.2D74.4B.C117.2DB74.4B131.2DB63.4B124.D73.4B196.
4B791.4B197.5BCBC396.4B136.4B56.4B324.4B64.4B402.4B197.4B$74.4B201.4B
398.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B
594.4B119.D76.4B131.D65.4B198.4B196.4B791.4B197.4BCB398.4B134.D3B58.
4B322.DBDB66.4B402.4B197.4B$75.4B201.4B398.4B196.4B196.4B196.4B196.4B
196.4B196.4B196.4B196.4B196.4B196.4B594.4B196.4B197.4B198.4B196.4B
791.4B197.4B400.4B133.DBD60.4B321.2DB68.4B402.4B197.4B$76.4B201.4B
398.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B
594.4B196.4B197.4B198.4B196.4B791.4B197.4B400.4B132.2D62.4B321.D70.4B
402.4B197.4B$77.4B201.4B398.4B196.4B196.4B196.4B196.4B196.4B196.4B
196.4B196.4B196.4B196.4B594.4B196.4B197.4B198.4B196.4B791.4B197.4B
400.4B196.4B392.4B402.4B197.4B$78.4B201.4B398.4B196.4B196.4B196.4B
196.4B196.4B196.4B196.4B196.4B196.4B196.4B594.4B196.4B197.4B198.4B
196.4B791.4B197.4B400.4B196.4B392.4B402.4B197.4B$79.4B201.4B398.4B
196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B594.4B
196.4B197.4B198.4B196.4B791.4B197.4B400.4B196.4B392.4B402.4B197.4B$
80.4B201.4B398.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.
4B196.4B594.4B196.4B197.4B198.4B196.4B791.4B197.4B400.4B196.4B392.4B
402.4B197.4B$81.4B201.4B398.4B196.4B196.4B196.4B196.4B196.4B196.4B
196.4B196.4B196.4B196.4B594.4B196.4B197.4B198.4B196.4B791.4B197.4B
400.4B196.4B392.4B402.4B197.4B$82.4B201.4B398.4B196.4B196.4B196.4B
196.4B196.4B196.4B196.4B196.4B196.4B196.4B594.4B196.4B197.4B198.4B
196.4B791.4B197.4B400.4B196.4B392.4B402.4B197.4B$83.4B201.3BC398.4B
196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.3BC594.4B
196.4B197.4B198.4B196.4B791.4B197.4B400.4B196.4B392.4B402.4B197.4B$
84.4B201.B2CB398.4B196.4B196.4B196.4B196.4B196.4B196.4B196.4B196.3BC
196.2B2C196.B2CB594.4B196.4B197.4B198.4B196.4B791.4B197.4B400.4B196.
4B392.B3C402.4B197.4B$85.4B201.CBC399.4B196.4B196.4B196.4B196.4B196.
4B196.3BC196.2B2C196.B2CB196.2CB197.CBC595.4B196.4B197.3BC198.4B196.
2B2C791.3BC197.4B400.4B196.2B2C392.C2B403.4B197.4B$86.4B603.4B196.4B
196.4B196.4B196.3BC196.2B2C196.B2CB196.2CB197.CBC197.BC796.4B196.4B
197.B2CB198.4B196.2CB792.B2CB197.4B400.4B196.2CB393.C405.4B197.2B2C$
87.4B603.4B196.4B196.3BC196.2B2C196.B2CB196.2CB197.CBC197.BC1196.4B
196.4B197.CBC199.4B196.BC793.CBC198.4B400.4B196.BC800.4B197.BCBC$88.
4B603.3BC196.2B2C196.B2CB196.2CB197.CBC197.BC1596.4B196.4B399.4B1192.
4B400.4B998.4B197.CB$89.4B603.B2CB196.2CB197.CBC197.BC1996.4B196.4B
399.4B1192.4B400.4B998.2B2C$90.3BC603.CBC197.BC2396.4B196.4B399.4B
1192.4B400.4B998.BCBC$91.B2CB3201.4B196.4B399.4B1192.4B400.4B998.CB$
92.CBC3202.4B196.4B399.4B1192.4B400.B3C$3298.4B196.4B399.4B1192.4B
400.C2B$3299.4B196.3BC399.4B1192.4B400.C$3300.2B2C196.B2CB399.3BC
1192.4B$3301.BCBC196.CBC400.B2CB1192.4B$3302.CB601.CBC1193.3BC$5102.B
2CB$5103.CBC76$407.D.D3.3D14.D3.D8.3D9.3D15.3D14.5D10.D3.3D8.5D8.3D
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9.D3.D7.5D3.D4.3D4.D10.3D4.D11.D10.3D3.3D4.D3.5D3.D4.3D$450.D11.D17.D
35.D11.D2327.D11.D17.D35.D11.D121.D17.D17.D35.D11.D1115.D11.D17.D35.D
11.D121.D11.D17.D35.D11.D121.D17.D17.D35.D11.D515.D11.D17.D35.D11.D
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11.D17.D35.D11.D$449.D11.D17.D35.D11.D2327.D11.D17.D35.D11.D121.D17.D
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11.D521.D11.D17.D35.D11.D121.D11.D17.D35.D11.D4$402.C2398.C200.C1198.
C199.C198.C599.C600.C400.C596.C201.C$401.2BC2396.2BC198.2BC1196.2BC
197.2BC81.2D113.2BC597.2BC598.2BC81.2D315.2BC594.2BC199.2BC81.2D$401.
3CB2395.3CB197.3CB1195.3CB196.3CB79.DBD113.3CB596.3CB597.3CB79.DBD
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114.4B596.4B597.4B77.3BD316.4B593.4B198.4B77.3BD$403.4B2395.4B197.4B
1195.4B196.4B75.4B116.4B596.4B597.4B75.4B318.4B593.4B198.4B75.4B$404.
4B2395.4B197.4B1195.4B196.4B73.4B118.4B596.4B597.4B73.4B320.4B593.4B
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71.4B322.4B593.4B198.4B71.4B$406.4B2395.4B197.4B1195.4B196.4B69.4B
122.4B596.4B597.4B69.4B324.4B593.4B198.4B69.4B$407.4B2395.4B197.4B
1195.4B196.4B67.4B124.4B596.4B597.4B67.4B326.4B593.4B198.4B67.4B$408.
4B2395.4B197.4B1195.4B196.4B65.4B126.4B596.4B597.4B65.4B328.4B593.4B
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63.4B330.4B593.4B198.4B63.4B$410.4B2395.4B197.4B1195.4B196.4B61.4B
130.4B596.4B597.4B61.4B332.4B593.4B198.4B61.4B$411.4B2395.4B197.4B
1195.4B196.C3B59.4B132.4B596.4B597.C3B59.4B334.4B593.4B198.C3B59.4B$
412.4B2395.4B197.4B1195.4B195.B2C2B57.4B134.4B596.4B596.B2C2B57.4B
336.4B593.4B197.B2C2B57.4B$413.4B2395.4B197.4B1195.4B194.2C4B55.4B
136.4B596.4B595.2C4B55.4B338.4B593.4B196.2C4B55.4B$414.4B2395.4B197.
4B1195.4B194.6B53.4B138.4B596.4B595.6B53.4B340.4B593.4B196.6B53.4B$
415.4B59.2D2334.4B197.4B1195.4B194.6B51.4B140.4B596.4B595.6B51.4B342.
4B593.4B64.2D130.6B51.4B$416.4B57.DBD2335.4B197.4B1195.4B63.3D128.6B
49.4B142.BC2B56.2D538.4B595.6B49.4B344.4B593.4B62.2B2D130.6B49.4B$
417.4B55.3BD2336.4B197.4B1195.4B61.3BD129.6B47.4B144.B2CB54.2B2D538.
4B595.6B47.4B346.4B593.4B60.2BDB132.6B47.4B$418.4B53.4B2338.4B59.2D
136.4B58.2D1135.4B59.3BD131.6B45.4B145.2C3B52.2BDB540.BC2B595.6B45.4B
348.4B593.4B58.4B134.6B45.4B$419.4B51.4B2340.4B57.DBD137.4B56.2B2D
1135.4B57.4B133.6B43.4B147.5B50.4B542.B2CB595.6B43.4B348.CBC3B593.4B
56.4B136.6B43.4B$420.4B49.4B2342.4B55.3BD137.BC3B54.2BDB1137.4B55.4B
135.6B41.4B149.5B48.4B543.2C3B595.6B41.4B349.B2C4B593.4B54.4B138.6B
41.4B$420.BC3B47.4B2344.4B53.4B137.CBC4B52.4B1139.4B53.4B137.6B39.4B
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4B45.4B2346.C3B51.4B139.2C5B50.4B1141.4B51.4B139.6B37.4B153.5B44.4B
547.5B595.6B37.4B353.7B52.B2D538.4B50.4B142.6B37.4B$420.2C5B43.4B
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56.2D537.6B35.4B355.7B50.BDBD539.2BCB48.4B144.6B35.4B$421.7B41.4B
2348.2C4B47.4B143.7B46.4B1143.B2C3B47.4B143.6B33.4B157.5B40.4B551.5B
54.2B2D537.6B33.4B357.7B48.4B541.2B2C46.4B146.6B33.4B$422.7B39.4B
2350.6B45.4B145.7B44.4B1145.C5B45.4B145.6B31.4B159.5B38.4B553.5B52.2B
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43.4B147.7B42.4B1147.6B43.4B147.6B29.4B161.5B36.4B555.5B50.4B541.6B
29.4B361.7B44.4B545.4B42.4B150.6B29.4B$424.7B35.4B2354.6B41.4B149.7B
40.4B1149.6B41.4B149.6B27.4B163.5B34.4B557.5B48.4B543.6B27.4B363.7B
42.4B547.4B40.4B152.6B27.4B$425.7B33.4B2356.6B39.4B151.7B38.4B1151.6B
39.4B151.6B25.4B165.5B32.4B559.5B46.4B545.6B25.4B365.7B40.4B549.4B38.
4B154.6B25.4B$426.7B31.4B2358.6B37.4B153.7B36.4B1153.6B37.4B153.6B23.
4B167.5B30.4B561.5B44.4B547.6B23.4B367.7B38.4B551.4B36.4B156.6B23.4B$
427.7B29.4B2360.6B35.4B155.7B34.4B1155.6B35.4B155.6B21.4B169.5B28.4B
563.5B42.4B549.6B21.4B369.7B36.4B553.4B34.4B158.6B21.4B$428.7B27.4B
2362.6B33.4B157.7B32.4B1157.6B33.4B157.6B19.4B171.5B26.4B565.5B40.4B
551.6B19.4B371.7B34.4B555.4B32.4B160.6B19.4B$429.7B25.4B2364.6B31.4B
159.7B30.4B1159.6B31.4B159.6B17.4B173.5B24.4B567.5B38.4B553.6B17.4B
373.7B32.4B557.4B30.4B162.6B17.4B$430.7B23.4B2366.6B29.4B161.7B28.4B
1161.6B29.4B161.6B15.4B175.5B22.4B569.5B36.4B555.6B15.4B375.7B30.4B
559.4B28.4B164.6B15.4B$431.7B21.4B2368.6B27.4B163.7B26.4B1163.6B27.4B
163.6B13.4B177.5B20.4B571.5B34.4B557.6B13.4B377.7B28.4B561.4B26.4B
166.6B13.4B$432.7B19.4B2370.6B25.4B165.7B24.4B1165.6B25.4B165.6B11.3D
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$433.7B17.4B2372.6B23.4B167.7B22.4B1167.6B23.4B167.6B10.BDB181.5B16.
4B575.5B30.4B561.6B10.BDB381.7B24.4B565.4B22.4B170.6B10.BDB$434.7B15.
4B2374.6B21.4B169.7B20.4B1169.6B21.4B169.6B8.2B3D181.5B14.4B577.5B28.
4B563.6B8.2B3D381.7B22.4B567.4B20.4B172.6B8.2B3D$435.7B13.4B2376.6B
19.4B171.7B18.4B1171.6B19.4B171.6B7.5B182.5B12.4B579.5B26.4B565.6B7.
5B382.7B20.4B569.4B18.4B174.6B7.5B$436.7B11.4B2378.6B17.4B173.7B16.4B
1173.6B17.4B173.6B6.6B182.5B10.4B581.5B24.4B567.6B6.6B382.7B18.4B571.
4B16.4B176.6B6.6B$437.7B9.4B2380.6B15.4B175.7B14.4B1175.6B15.4B175.6B
5.6B183.5B5.B2.4B583.5B22.4B569.6B5.6B383.7B16.4B573.4B14.4B178.6B5.
6B$438.7B7.4B2382.6B13.4B177.8B11.4B1177.6B13.4B177.6B2.8B184.5B3.7B
585.5B20.4B571.6B2.8B384.7B14.4B575.4B12.4B180.6B2.8B$439.7B5.4B2384.
6B11.4B179.9B8.4B1179.6B11.4B179.14B186.13B587.5B18.4B573.14B386.7B
12.4B577.4B10.4B182.14B$440.7B3.4B2386.6B9.4B181.9B6.4B1181.6B9.4B
181.14B186.11B589.5B16.4B575.14B386.7B10.4B579.4B8.4B184.14B$441.7B.
4B2388.6B7.4B183.8B5.4B1183.6B7.4B183.13B187.10B590.5B14.4B577.13B
387.7B8.4B581.4B6.4B186.13B$442.10B2390.6B3.B.4B185.3B2D2B4.4B1185.6B
5.4B185.4B.6B189.8B592.5B12.4B579.4B.6B389.8B5.4B583.4B4.4B188.4B.6B$
443.8B2392.8B2D3B187.BD2BD2B2.4B1187.6B3.4B187.10B190.8B592.4B.3B7.4B
581.10B390.8B3.4B585.4B2.4B190.10B$444.8B2392.7B2D2B189.D2BD2B.4B
1189.11B189.5B2D3B189.7BD590.10B6.4B583.5B2D3B390.8B.4B587.9B191.5B2D
3B$445.3BD3B2393.9B190.B2D7B1191.9B191.4B2D4B187.8BDB587.7B2D4B4.4B
585.4B2D4B390.3BD7B589.9B191.4B2D4B$445.2BDBD3B2391.11B189.10B1192.9B
191.10B186.8BD587.7BD2BD4B2.4B587.10B388.3BDBD5B590.10B191.10B$446.2B
2D4B2391.11B188.10B1193.2D7B190.11B186.6B590.7BDBD4B.4B589.10B386.5B
2D4B593.2D7B191.10B$446.9B2390.6B2.4B186.12B1192.2DB.B.4B188.13B185.
6B592.6BD9B590.11B386.11B592.2D8B190.11B$447.9B2391.5B2.4B186.10B
1194.5B.4B188.8B.4B185.6B594.12B594.9B387.10B592.B2.7B192.9B$446.5B2.
4B2392.4B2.4B185.8B1197.5B.4B188.8B.4B183.8B594.11B596.8B388.2B.6B
595.7B194.7B$447.5B2.4B2392.4B2.4B182.8B1201.4B.4B189.7B.4B183.8B594.
11B596.8B390.7B595.7B194.7B$449.4B2.4B2392.4B2.4B181.4B.4B1201.4B.4B
188.8B.4B183.8B594.11B596.8B390.7B595.7B194.7B$450.4B2.4B2392.4B2.4B
181.4B.4B1201.4B.4B188.2B2.4B.4B183.8B596.9B596.8B390.7B595.7B194.7B$
451.4B2.4B2392.4B2.4B181.4B.4B1201.4B.4B192.4B.4B183.8B597.8B596.8B
390.7B595.7B194.7B$452.4B2.4B2392.4B2.4B181.4B.4B1201.4B.4B192.4B.4B
183.8B597.8B596.8B390.7B595.7B194.7B$453.4B2.4B2392.4B2.4B181.4B.4B
1201.4B.4B192.4B.4B183.8B597.8B596.8B390.7B595.7B194.7B$454.4B2.4B
2392.4B2.4B181.4B.4B1201.4B.4B192.4B.4B183.8B597.8B596.8B390.7B595.7B
194.7B$455.4B2.4B2392.4B2.4B181.4B.4B1201.4B.4B192.4B.4B183.8B597.8B
596.8B390.7B595.7B194.7B$456.4B2.4B2392.4B2.4B181.4B.4B1201.4B.4B192.
4B.4B183.8B597.8B596.8B390.7B595.7B194.7B$457.4B2.4B2392.4B2.4B181.4B
.4B1201.4B.4B192.4B.4B183.8B597.8B596.8B390.7B595.7B194.7B$458.4B2.4B
2392.4B2.4B181.4B.4B1201.4B.4B192.4B.4B183.8B597.8B596.8B390.7B595.7B
194.7B$459.4B2.4B2392.4B2.4B181.4B.4B1201.4B.4B192.4B.4B183.8B597.8B
596.8B390.7B595.7B194.7B$460.4B2.4B2392.4B2.4B181.4B.4B1201.4B.4B192.
4B.4B183.8B597.8B596.8B390.7B595.7B194.7B$461.4B2.4B2392.4B2.4B181.4B
.4B1201.4B.4B192.4B.4B183.8B597.8B596.8B390.7B595.7B194.7B$462.4B2.4B
2392.4B2.4B181.4B.4B1201.4B.4B192.4B.4B183.8B597.8B596.8B390.7B595.7B
194.7B$463.4B2.4B2392.4B2.4B181.4B.4B1201.4B.4B192.4B.4B183.8B597.8B
596.8B390.7B595.7B194.7B$464.4B2.4B2392.4B2.4B181.4B.4B1201.4B.4B192.
4B.4B183.8B597.8B596.8B390.7B595.7B194.7B$465.4B2.4B2392.4B2.4B181.4B
.4B1201.4B.4B192.4B.4B183.8B597.8B596.8B390.7B595.7B194.7B$466.4B2.4B
2392.4B2.4B181.4B.4B1201.4B.4B192.4B.4B183.8B597.8B596.8B390.7B595.5B
2C194.7B$467.4B2.4B2392.4B2.B3C181.4B.4B1201.4B.B3C192.4B.4B183.8B
597.8B596.8B390.7B595.4BCBC194.7B$468.4B2.3BC2392.4B2.C2B182.4B.4B
1201.4B.C2B193.4B.4B183.8B597.8B596.8B390.7B595.3BCB196.7B$469.4B2.B
2CB2392.4B2.C184.4B.4B1201.4B.C195.4B.4B183.8B597.8B596.8B390.7B595.
4B197.7B$470.4B2.CBC2393.4B187.4B.2B2C1201.4B197.4B.4B183.8B597.8B
596.8B390.7B595.4B197.7B$471.4B2398.4B187.4B.2CB1202.4B197.4B.4B183.
8B597.7BC596.8B390.4B3C595.4B197.7B$472.4B2398.4B187.4B.BC1203.4B197.
4B.4B183.8B597.5B2CB596.8B390.3BC2B596.4B197.7B$473.4B2398.4B187.4B
1206.4B197.4B.4B183.7BC597.4BCBC597.8B390.3BC598.4B197.7B$474.4B2398.
4B187.4B1206.4B197.4B.4B183.5B2CB597.4B600.8B390.4B598.4B197.7B$475.
4B2398.4B187.4B1206.4B197.4B.4B183.4BCBC598.4B600.8B390.4B598.4B197.
7B$476.4B2398.4B187.4B1206.4B197.4B.4B183.4B601.4B600.8B390.4B598.4B
197.7B$477.4B2398.4B187.4B1206.4B197.4B.3BC183.4B601.4B600.7BC390.4B
598.4B197.6BC$478.4B2398.4B187.4B1206.4B197.4B.B2CB183.4B601.4B600.5B
2CB390.4B598.4B197.4B2CB$479.4B2398.4B187.4B1206.4B197.4B.CBC184.4B
601.4B600.4BCBC391.4B598.4B197.3BCBC$480.4B2398.4B187.4B1206.4B197.4B
188.4B601.4B600.4B394.4B598.4B197.4B$481.4B2398.4B187.4B1206.4B197.4B
188.4B601.4B600.4B394.4B598.4B197.4B$482.4B2398.4B187.4B1206.4B197.4B
188.4B601.4B600.4B394.4B598.4B197.4B$483.4B2398.4B187.4B1206.4B197.4B
188.4B601.4B600.4B394.4B598.4B197.4B$484.4B2398.4B187.4B1206.4B197.4B
188.4B601.4B600.4B394.4B598.4B197.4B$485.4B2398.4B187.4B1206.4B197.4B
188.4B601.4B600.4B394.4B598.4B197.4B$486.4B2398.4B187.4B1206.4B197.4B
188.4B601.4B600.4B394.4B598.4B197.4B$487.4B2398.4B187.4B1206.4B197.4B
188.4B601.4B600.4B394.4B598.4B197.4B$488.4B2398.4B187.4B1206.4B197.4B
188.4B601.4B600.4B394.4B598.4B197.4B$489.4B2398.4B187.4B1206.4B197.4B
188.4B601.4B600.4B394.4B598.4B197.4B$490.4B2398.4B187.4B1206.4B197.4B
188.4B601.4B600.4B394.4B598.4B197.4B$491.4B2398.4B187.4B1206.3BC197.
4B188.4B601.4B600.4B394.4B598.2B2C197.4B$492.4B2398.2B2C187.4B1206.B
2CB197.4B188.4B601.4B600.4B394.4B598.2CB198.4B$493.2B2C2398.2CB188.4B
1206.CBC198.4B188.4B601.4B600.4B394.4B598.BC199.4B$494.BCBC2398.BC
189.2B2C1407.4B188.4B601.4B600.4B394.4B799.4B$495.CB2591.BCBC1407.4B
188.4B601.4B600.4B394.3BC799.4B$3089.CB1409.4B188.4B601.2B2C600.4B
394.B2CB799.4B$4501.4B188.4B601.2CB601.4B394.CBC800.4B$4502.4B188.2B
2C601.BC602.4B1197.4B$4503.4B188.2CB1206.4B1197.4B$4504.4B188.BC1207.
4B1197.4B$4505.4B1397.4B1197.4B$4506.4B1397.4B1197.4B$4507.2B2C1397.
2B2C1197.2B2C$4508.2CB1398.2CB1198.2CB$4509.BC1399.BC1199.BC!

Now I have to check whether the inverted-rakes trick works for the SEward gliders as well. (It didn't work last time I tried it, but it was late at night and I'm easily confused by this kind of thing.) If it does work, then maybe the SW outputs can be rotated into possible NE outputs.

codeholic wrote:Have you compiled a set of operations for monochromatic single-parity slow salvo synthesis yet? The first step would be to measure their weight in half-bakeries. (Weights for operations reflected over SW-NE axis will be different.)

Not yet. I should really modify oblique's sscs search utility to look for these, but I might start out by just digging up a minimal universal set. Maybe next weekend I'll have enough time to tackle that, if someone else doesn't get to it first.

EDIT 2: Drat, a parity error: none of the above recipes are any good, because version 0.2 calculated the ranges wrong for the D glider. I've changed a + to a - in the code above and called it version 0.21. Revised recipes will be coming along eventually.
dvgrn
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Re: Half-bakery reaction with glider

Postby codeholic » June 10th, 2014, 5:51 pm

I've written a Python version of the script for computing invariants, so you can borrow code from it, if you want: https://github.com/codeholic/hbk/blob/m ... ariants.py

(That was my first attempt to write Python code for Golly. It was fun. Maybe I'll do it more frequently from now on to practice my Python programming skills.)
Ivan Fomichev
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codeholic
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Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby dvgrn » June 10th, 2014, 7:05 pm

I'll keep all the workable NE glider recipe data in this post. Here's the revised v0.21 output in the -6 to -3 range for the D glider:

#C inverted SE rakes
x = 2200, y = 309, rule = LifeHistory
1870.D.D5.D2.5D13.D3.D8.3D9.3D15.3D14.5D10.D3.3D8.5D8.3D65.D.D5.D3.3D
14.D3.D8.3D8.5D14.3D14.5D8.3D9.3D9.3D$1870.D.D4.2D6.D13.D3.D7.D3.D7.D
3.D13.D3.D15.D11.2D2.D15.D7.D3.D64.D.D4.2D2.D3.D13.D3.D7.D3.D7.D17.D
3.D15.D9.D3.D7.D3.D7.D3.D$1869.5D2.D.D5.D4.D10.D.D2.5D5.D11.D17.D15.D
3.5D2.D.D2.D14.D8.D2.2D63.5D2.D.D2.D3.D3.D10.D.D2.5D5.D7.D21.D15.D3.
5D.D3.D11.D7.D2.2D$1870.D.D2.D2.D4.D17.D12.D10.2D8.5D3.2D16.D9.D2.D2.
4D10.D9.D.D.D64.D.D2.D2.D3.4D15.D12.D9.3D8.5D3.2D16.D10.4D10.D8.D.D.D
$1869.5D.5D2.D17.D.D2.5D3.D13.D17.D15.D3.5D.5D.D3.D8.D10.2D2.D63.5D.
5D5.D14.D.D2.5D3.D13.D17.D15.D3.5D5.D9.D9.2D2.D$1870.D.D5.D2.D17.D3.D
8.D10.D3.D13.D3.D15.D12.D2.D3.D7.D11.D3.D64.D.D5.D6.D13.D3.D8.D10.D3.
D13.D3.D15.D13.D8.D10.D3.D$6.D.D3.3D14.D3.D8.3D17.D15.3D14.5D8.3D5.D
9.3D9.3D65.D.D4.D15.D3.D9.D10.3D15.3D14.5D8.3D2.5D8.3D9.3D71.D.D3.3D
14.D3.D8.3D8.5D13.5D13.5D8.3D9.3D9.3D77.D.D5.D14.D3.D8.3D14.5D16.D14.
5D8.3D8.5D8.3D71.D.D2.5D13.D3.D8.3D9.3D17.D14.5D10.D3.3D8.5D8.3D71.D.
D3.3D14.D3.D8.3D8.5D16.D14.5D8.3D9.3D9.3D77.D.D4.D5.D15.D3.D8.3D14.5D
14.3D14.5D8.3D8.5D8.3D65.D.D4.D4.3D14.D3.D8.3D17.D15.3D14.5D7.5D.5D7.
5D8.3D59.D.D4.D6.D10.D.D5.D3.3D14.D3.D8.3D9.3D15.3D14.5D8.3D10.3D5.D
3.4D.D3.D.4D2.D3.D9.D10.3D67.D.D5.D2.D7.D9.D3.D7.5D3.D4.3D4.D10.3D4.D
11.D12.D3.3D4.D3.D7.D4.3D65.D.D5.D3.3D4.D9.D3.D7.5D3.D4.3D4.D10.3D4.D
11.D10.3D4.D3.5D3.D4.3D$6.D.D2.D3.D13.D3.D7.D3.D15.2D14.D19.D9.D7.2D
8.D11.D3.D64.D.D3.2D15.D3.D8.2D9.D3.D13.D19.D9.D3.D.D11.D11.D3.D70.D.
D2.D3.D13.D3.D7.D3.D7.D17.D19.D9.D3.D7.D3.D7.D3.D76.D.D4.2D14.D3.D7.D
3.D13.D19.2D16.D9.D3.D11.D7.D3.D70.D.D6.D13.D3.D7.D3.D7.D3.D15.2D16.D
11.2D2.D3.D11.D7.D3.D70.D.D2.D3.D13.D3.D7.D3.D7.D19.2D16.D9.D3.D7.D3.
D7.D3.D76.D.D3.2D4.2D15.D3.D7.D3.D13.D17.D3.D15.D9.D3.D11.D7.D3.D64.D
.D3.2D3.D3.D13.D3.D7.D3.D15.2D14.D3.D15.D9.D5.D15.D7.D3.D58.D.D3.2D5.
2D10.D.D4.2D2.D17.D3.D7.D3.D7.D3.D13.D3.D15.D9.D3.D8.D7.2D3.D4.D3.D.D
5.2D2.D8.2D9.D3.D115.D11.D17.D35.D11.D121.D11.D17.D29.D11.D$5.5D.D2.
2D3.D10.D.D2.5D5.D14.D.D14.D19.D3.5D.D6.D.D8.D11.D2.2D63.5D3.D5.D10.D
.D2.5D3.D13.D13.D19.D3.5D5.D.D11.D11.D2.2D69.5D5.D3.D10.D.D2.5D5.D7.D
17.D19.D3.5D.D3.D11.D7.D2.2D75.5D2.D.D4.D10.D.D2.5D5.D13.D18.D.D16.D
3.5D.D3.D10.D8.D2.2D69.5D4.D4.D10.D.D2.5D5.D11.D14.D.D16.D3.5D2.D.D2.
D3.D10.D8.D2.2D69.5D.D3.D3.D10.D.D2.5D5.D7.D18.D.D16.D3.5D.D3.D11.D7.
D2.2D75.5D3.D5.D5.D10.D.D2.5D5.D13.D21.D15.D3.5D.D3.D10.D8.D2.2D63.5D
3.D7.D3.D10.D.D2.5D5.D14.D.D18.D15.D3.5D.D5.D14.D8.D2.2D57.5D3.D4.D.D
9.5D2.D.D2.D7.D10.D.D2.5D5.D11.D17.D15.D3.5D.D2.2D8.D6.D.D3.D4.D3.D.D
5.2D2.D9.D9.D2.2D114.D11.D17.D35.D11.D121.D11.D17.D29.D11.D$6.D.D2.D.
D.D15.D11.2D8.5D.D2.D8.5D.4D16.D9.4D2.D2.D8.4D8.D.D.D64.D.D4.D17.D11.
D12.D8.5D.4D16.D11.2D3.3D8.4D8.D.D.D70.D.D4.2D16.D12.D9.3D8.5D2.3D16.
D10.4D10.D8.D.D.D76.D.D2.D2.D16.D11.2D8.5D2.3D8.5D.D2.D16.D10.4D9.D9.
D.D.D70.D.D4.D17.D12.D10.2D8.5D.D2.D16.D9.D2.D3.3D10.D9.D.D.D70.D.D3.
4D15.D12.D9.3D8.5D.D2.D16.D10.4D10.D8.D.D.D76.D.D4.D5.D17.D11.2D8.5D
2.3D8.5D3.2D16.D10.4D9.D9.D.D.D64.D.D4.D5.2D16.D11.2D8.5D.D2.D8.5D3.
2D16.D10.3D3.3D10.D9.D.D.D58.D.D4.D3.D2.D3.4D3.D.D2.D2.D2.4D16.D11.2D
10.2D8.5D3.2D16.D9.D.D.D8.4D2.D2.D3.3D2.D3.D.3D3.D.D.D9.D9.D.D.D$5.5D
.2D2.D14.D.D2.5D5.D13.5D13.D3.D15.D3.5D.D3.D.5D7.D3.D7.2D2.D63.5D3.D
16.D.D2.5D3.D11.D15.D3.D15.D3.5D5.D5.D7.D3.D7.2D2.D69.5D5.D14.D.D2.5D
3.D13.D17.D15.D3.5D5.D9.D9.2D2.D75.5D.5D14.D.D2.5D5.D17.D13.5D15.D3.
5D5.D8.D10.2D2.D69.5D2.D17.D.D2.5D3.D13.D13.5D15.D3.5D.5D.D3.D8.D10.
2D2.D69.5D5.D14.D.D2.5D3.D13.D13.5D15.D3.5D5.D9.D9.2D2.D75.5D3.D5.D
16.D.D2.5D5.D17.D17.D15.D3.5D5.D8.D10.2D2.D63.5D3.D7.D14.D.D2.5D5.D
13.5D17.D15.D3.5D5.D5.D8.D10.2D2.D57.5D3.D3.5D8.5D.5D.D3.D14.D.D2.5D
5.D11.D17.D15.D3.5D.2D2.D8.D3.D.5D2.D5.D.D2.D5.D.D.D9.D9.2D2.D$6.D.D
2.D3.D13.D3.D7.D3.D16.D14.D3.D15.D9.D3.D4.D8.D3.D7.D3.D64.D.D4.D15.D
3.D9.D10.D16.D3.D15.D9.D3.D.D3.D7.D3.D7.D3.D70.D.D2.D3.D13.D3.D8.D10.
D3.D13.D3.D15.D13.D8.D10.D3.D76.D.D5.D14.D3.D7.D3.D13.D3.D16.D16.D13.
D7.D11.D3.D70.D.D2.D17.D3.D8.D10.D3.D16.D16.D12.D2.D3.D7.D11.D3.D70.D
.D6.D13.D3.D8.D10.D3.D16.D16.D13.D8.D10.D3.D76.D.D4.D5.D15.D3.D7.D3.D
13.D3.D13.D3.D15.D13.D7.D11.D3.D64.D.D4.D3.D3.D13.D3.D7.D3.D16.D14.D
3.D15.D9.D3.D.D3.D7.D11.D3.D58.D.D4.D6.D10.D.D5.D2.D3.D13.D3.D7.D3.D
7.D3.D13.D3.D15.D9.D3.D8.D3.D4.D3.D5.D.D2.D5.D2.2D9.D9.D3.D$6.D.D3.3D
4.D9.D3.D8.3D4.D12.D4.D10.3D4.D11.D10.3D5.D4.D4.3D4.D4.3D65.D.D3.3D4.
D9.D3.D8.3D4.D3.5D3.D10.3D4.D11.D10.3D3.3D4.D4.3D4.D4.3D71.D.D3.3D4.D
9.D3.D7.5D3.D4.3D4.D10.3D4.D11.D10.3D4.D3.5D3.D4.3D77.D.D5.D4.D9.D3.D
8.3D4.D10.3D4.D12.D4.D11.D10.3D4.D3.D7.D4.3D71.D.D2.D7.D9.D3.D7.5D3.D
4.3D4.D12.D4.D11.D12.D3.3D4.D3.D7.D4.3D71.D.D3.3D4.D9.D3.D7.5D3.D4.3D
4.D12.D4.D11.D10.3D4.D3.5D3.D4.3D77.D.D3.3D3.3D4.D9.D3.D8.3D4.D10.3D
4.D10.3D4.D11.D10.3D4.D3.D7.D4.3D65.D.D3.3D3.3D4.D9.D3.D8.3D4.D12.D4.
D10.3D4.D11.D10.3D3.3D4.D3.D7.D4.3D59.D.D3.3D5.D10.D.D5.D3.3D4.D9.D3.
D8.3D4.D4.3D4.D10.3D4.D11.D10.3D3.D2.D3.3D5.D3.4D3.D3.4D2.D3.D3.D4.3D
4.D4.3D61.C199.C$49.D17.D17.D35.D11.D115.D11.D17.D35.D11.D121.D11.D
17.D29.D11.D127.D17.D17.D29.D11.D121.D11.D17.D35.D11.D121.D11.D17.D
29.D11.D133.D17.D17.D29.D11.D121.D17.D17.D35.D11.D140.D11.D17.D72.D
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199.4B159.C26.4B167.6B15.4B271.4B$20.2C34.4B159.6B13.4B211.4B165.C33.
4B161.2C23.4B169.6B13.4B271.4B$20.C34.4B161.6B7.8B211.4B164.C.C32.4B
161.2C23.4B171.6B7.8B271.4B$54.4B163.6B5.8B211.4B166.2C31.4B186.4B
173.6B5.8B251.6B14.4B$53.4B165.6B3.8B211.4B199.4B186.4B175.6B3.8B253.
6B12.4B$52.4B167.6B2.7B185.7B19.4B199.4B167.6B13.4B177.6B2.7B255.6B
10.4B$51.4B169.6B.3B3DB186.7B17.4B199.4B169.6B11.4B179.6B.3B3DB256.7B
2.2B3.4B$25.7B18.4B171.6B.3BD2B187.7B6.B8.4B199.4B171.6B9.4B181.6B.3B
D2B257.16B$26.7B16.4B173.7B3D2B188.7B4.3B6.4B176.7B16.4B173.6B7.4B
183.7B3D2B258.14B$27.7B14.4B175.11B189.7B.6B4.4B178.7B14.4B175.6B5.4B
185.11B259.12B$28.7B12.4B177.10B190.14B2.4B180.7B12.4B177.6B3.4B187.
10B260.2B2D8B$29.7B10.4B179.9B191.18B182.7B4.B5.4B179.6B.4B189.9B260.
BD2BD8B$30.7B8.4B181.8B192.16B184.12B3.4B181.9B191.8B261.D2BD9B$31.8B
5.4B183.8B192.14B186.11B2.4B183.7B193.8B260.B2D3B.7B$32.7B4.4B185.6B.
B192.12B188.8B2D5B185.6B194.6B262.6B.7B$33.6B3.4B186.9B192.6BD4B189.
6BD2BD3B186.7B193.7B261.5B3.7B$34.11B188.9B191.6BD4B189.6BD2BD3B186.
3B.4B193.6B260.7B3.7B$33.B2D8B189.9B192.5BD4B189.7B2D6B183.B2D2B.3B
193.6B260.6B5.7B$32.BD2BD7B190.B2D7B190.9B189.17B181.BD2BD2B.B195.B2D
B262.4B7.7B$33.BDBD7B189.2B2D8B189.10B188.18B180.BD2BD4B194.2B2DB.B
272.7B$33.2BD9B189.11B190.10B187.10B.8B179.2B2D6B194.7B$34.12B189.9B
192.8B189.8B3.8B179.10B194.7B$35.12B189.8B193.8B189.7B4.8B182.7B194.
7B$38.5B.4B189.8B193.8B188.5B7.8B182.7B194.7B274.2C$38.6B.4B189.8B
193.8B200.8B182.7B194.7B273.C.C$39.6B.4B189.8B193.8B200.8B182.7B194.
7B272.C$39.2B.4B.4B189.8B193.8B200.8B182.7B194.7B$43.4B.4B189.8B193.
8B200.8B182.7B194.7B2$655.C$654.2C189.2C$654.C.C188.C.C$50.2C793.C$
49.2C$51.C$452.2C$451.2C$453.C4$256.3C797.3C$256.C799.C$257.C799.C4$
1346.C$1345.2C$1345.C.C6$684.2C$80.C603.C.C187.2C$79.2C603.C188.2C$
79.C.C793.C$481.C$480.2C$480.C.C4$285.2C797.2C$284.2C797.2C$286.C798.
C!

-- but they can't be inverted to make NEward recipes, because the HB transformation would have to be inverted as well.

I suppose with this blueprint you could perfectly well build a growing knightship where the two halves travel in mirror-image directions, but let's not go there just now... The equivalent rake-inversion trick for the NE rakes leaves just a -3..0 window to shoot through, which is the same range you get if you don't invert the rakes, so there are no new options there.

Here are the standard rakes, according to v0.21:
#C standard SE rakes
x = 3940, y = 307, rule = LifeHistory
10.D.D3.3D14.D3.D8.3D14.5D8.3D14.5D8.3D8.5D8.3D77.D.D2.5D13.D3.D9.D
12.D9.3D14.5D8.3D4.D9.5D8.3D77.D.D3.3D14.D3.D8.3D14.5D9.D15.5D8.3D8.
5D8.3D77.D.D4.D5.D15.D3.D9.D18.D10.D15.5D9.D4.3D9.3D9.3D65.D.D4.D4.3D
14.D3.D9.D16.3D10.D15.5D8.3D3.3D8.5D8.3D65.D.D4.D3.5D13.D3.D8.3D9.3D
10.D15.5D10.D3.3D8.5D8.3D71.D.D4.D4.3D14.D3.D8.3D9.3D10.D15.5D10.D3.
3D8.5D8.3D71.D.D4.D4.3D14.D3.D8.3D8.5D9.D15.5D7.5D2.3D8.5D8.3D71.D.D
3.3D4.D15.D3.D8.3D9.3D9.3D14.5D7.5D2.3D9.3D9.3D71.D.D3.3D3.3D14.D3.D
9.D10.3D9.3D14.5D10.D3.3D10.D10.3D71.D.D3.3D3.3D14.D3.D8.3D9.3D9.3D
14.5D10.D3.3D8.5D8.3D71.D.D3.3D3.3D14.D3.D8.3D15.3D9.3D14.5D8.3D3.3D
9.3D9.3D65.D.D3.3D3.3D14.D3.D9.D10.3D9.3D14.5D10.D2.5D9.D10.3D71.D.D
3.3D4.D15.D3.D8.3D11.D9.3D14.5D7.5D.5D9.D10.3D$10.D.D2.D3.D13.D3.D7.D
3.D13.D11.D3.D15.D9.D3.D11.D7.D3.D76.D.D2.D17.D3.D8.2D11.2D8.D3.D15.D
9.D6.2D9.D11.D3.D76.D.D2.D3.D13.D3.D7.D3.D13.D12.2D17.D9.D3.D11.D7.D
3.D76.D.D3.2D4.2D15.D3.D8.2D17.2D9.2D17.D10.2D3.D3.D7.D11.D3.D64.D.D
3.2D3.D3.D13.D3.D8.2D15.D3.D8.2D17.D9.D3.D.D3.D7.D11.D3.D64.D.D3.2D3.
D17.D3.D7.D3.D7.D3.D8.2D17.D11.2D2.D3.D11.D7.D3.D70.D.D3.2D3.D17.D3.D
7.D3.D7.D3.D8.2D17.D11.2D2.D3.D11.D7.D3.D70.D.D3.2D3.D3.D13.D3.D7.D3.
D7.D12.2D17.D9.D5.D3.D11.D7.D3.D70.D.D2.D3.D2.2D15.D3.D7.D3.D7.D3.D7.
D3.D15.D9.D5.D3.D7.D3.D7.D3.D70.D.D2.D3.D.D3.D13.D3.D8.2D9.D3.D7.D3.D
15.D11.2D2.D3.D8.2D9.D3.D70.D.D2.D3.D.D3.D13.D3.D7.D3.D7.D3.D7.D3.D
15.D11.2D2.D3.D11.D7.D3.D70.D.D2.D3.D.D3.D13.D3.D7.D3.D13.D3.D7.D3.D
15.D9.D5.D3.D7.D11.D3.D64.D.D2.D3.D.D3.D13.D3.D8.2D9.D3.D7.D3.D15.D
11.2D2.D12.2D9.D3.D70.D.D2.D3.D2.2D15.D3.D7.D3.D9.2D8.D3.D15.D9.D9.D
8.2D9.D3.D$9.5D.D2.2D3.D10.D.D2.5D5.D13.D11.D2.2D15.D3.5D.D3.D10.D8.D
2.2D75.5D.D7.D10.D.D2.5D3.D10.D.D8.D2.2D15.D3.5D.D7.D9.D11.D2.2D75.5D
.D3.D3.D10.D.D2.5D5.D13.D13.D17.D3.5D.D3.D10.D8.D2.2D75.5D3.D5.D5.D
10.D.D2.5D3.D16.D.D10.D17.D3.5D3.D7.D7.D11.D2.2D63.5D3.D7.D3.D10.D.D
2.5D3.D19.D9.D17.D3.5D5.D5.D7.D11.D2.2D63.5D3.D3.D7.D10.D.D2.5D5.D11.
D9.D17.D3.5D2.D.D2.D2.2D10.D8.D2.2D69.5D3.D3.D7.D10.D.D2.5D5.D11.D9.D
17.D3.5D2.D.D6.D10.D8.D2.2D69.5D3.D3.D3.D3.D10.D.D2.5D5.D7.D13.D17.D
3.5D.D5.D2.2D10.D8.D2.2D69.5D5.D3.D5.D10.D.D2.5D5.D7.D2.2D11.D15.D3.
5D.D5.D3.D11.D7.D2.2D69.5D5.D5.D3.D10.D.D2.5D3.D13.D11.D15.D3.5D2.D.D
6.D9.D9.D2.2D69.5D5.D5.D3.D10.D.D2.5D5.D11.D11.D15.D3.5D2.D.D2.D2.2D
10.D8.D2.2D69.5D5.D.D3.D3.D10.D.D2.5D5.D17.D11.D15.D3.5D.D9.D7.D11.D
2.2D63.5D5.D.D2.2D3.D10.D.D2.5D3.D13.D11.D15.D3.5D2.D.D2.D13.D9.D2.2D
69.5D5.D3.D5.D10.D.D2.5D5.D8.D.D12.D15.D3.5D.D8.D10.D9.D2.2D$10.D.D2.
D.D.D15.D11.2D8.5D2.3D8.D.D.D15.D10.4D9.D9.D.D.D76.D.D3.3D16.D11.D9.D
2.D8.D.D.D15.D9.4D4.D10.3D8.D.D.D76.D.D3.3D16.D11.2D8.5D2.3D10.D17.D
10.4D9.D9.D.D.D76.D.D4.D5.D17.D11.D9.5D.D2.D10.D17.D11.D5.2D8.4D8.D.D
.D64.D.D4.D6.D16.D11.D9.5D4.D10.D17.D11.2D4.2D9.3D8.D.D.D64.D.D4.D4.
3D16.D11.2D10.2D10.D17.D9.D2.D2.D.D.D9.D9.D.D.D70.D.D4.D3.4D16.D11.2D
10.2D10.D17.D9.D2.D5.D10.D9.D.D.D70.D.D4.D4.4D15.D11.2D9.3D10.D17.D
10.3D2.D.D.D9.D9.D.D.D70.D.D5.D4.D17.D12.D8.D.D.D10.D16.D10.3D3.4D9.
2D8.D.D.D70.D.D5.D5.D16.D11.D11.2D11.D16.D9.D2.D4.2D10.D9.D.D.D70.D.D
5.D4.2D16.D11.2D10.2D11.D16.D9.D2.D2.D.D.D9.D9.D.D.D70.D.D5.D3.3D16.D
12.D8.5D3.2D10.2D16.D9.4D5.D8.4D8.D.D.D64.D.D4.2D2.D.D.D15.D11.D11.2D
10.2D16.D9.D2.D3.3D10.D9.D.D.D70.D.D4.2D4.D17.D11.2D8.D2.D10.2D16.D
10.3D4.D11.D9.D.D.D$9.5D.2D2.D14.D.D2.5D5.D17.D7.2D2.D15.D3.5D5.D8.D
10.2D2.D75.5D5.D14.D.D2.5D3.D9.5D7.2D2.D15.D3.5D.D3.D3.D13.D7.2D2.D
75.5D.D3.D14.D.D2.5D5.D17.D9.D17.D3.5D5.D8.D10.2D2.D75.5D3.D5.D16.D.D
2.5D3.D15.5D9.D17.D3.5D3.D7.D7.D3.D7.2D2.D63.5D3.D5.D16.D.D2.5D3.D17.
D11.D17.D3.5D5.D5.D11.D7.2D2.D63.5D3.D7.D14.D.D2.5D5.D11.D9.D17.D3.5D
.5D.2D2.D8.D10.2D2.D69.5D3.D3.D3.D14.D.D2.5D5.D11.D9.D17.D3.5D.5D3.D
10.D10.2D2.D69.5D3.D7.D14.D.D2.5D5.D11.D9.D17.D3.5D5.D.2D2.D8.D10.2D
2.D69.5D3.D5.D16.D.D2.5D3.D9.2D2.D9.D17.D3.5D5.D5.D11.D7.2D2.D69.5D3.
D5.D16.D.D2.5D3.D13.D9.D17.D3.5D.5D5.D9.D9.2D2.D69.5D3.D7.D14.D.D2.5D
5.D11.D9.D17.D3.5D.5D.2D2.D8.D10.2D2.D69.5D3.D3.D3.D14.D.D2.5D3.D19.D
11.D15.D3.5D.D3.D3.D9.D3.D7.2D2.D63.5D5.D.2D2.D14.D.D2.5D3.D13.D11.D
15.D3.5D.5D5.D9.D9.2D2.D69.5D5.D3.D16.D.D2.5D5.D7.5D11.D15.D3.5D5.D2.
D12.D9.2D2.D$10.D.D2.D3.D13.D3.D7.D3.D13.D3.D7.D3.D15.D13.D7.D11.D3.D
76.D.D2.D3.D13.D3.D9.D12.D8.D3.D15.D9.D3.D3.D9.D3.D7.D3.D76.D.D2.D3.D
13.D3.D7.D3.D13.D3.D9.D17.D13.D7.D11.D3.D76.D.D4.D5.D15.D3.D9.D18.D
10.D17.D11.D3.D3.D7.D3.D7.D3.D64.D.D4.D4.D16.D3.D9.D16.D12.D17.D9.D3.
D.D3.D7.D3.D7.D3.D64.D.D4.D3.D3.D13.D3.D7.D3.D7.D3.D9.D17.D12.D2.D3.D
7.D11.D3.D70.D.D4.D3.D3.D13.D3.D7.D3.D7.D3.D9.D17.D12.D3.D10.D11.D3.D
70.D.D4.D7.D13.D3.D7.D3.D7.D3.D9.D17.D9.D3.D.D3.D7.D11.D3.D70.D.D3.D
6.D15.D3.D8.D10.D3.D8.D18.D9.D3.D5.D7.D3.D7.D3.D70.D.D3.D5.D16.D3.D9.
D9.D3.D8.D18.D12.D2.D3.D9.D9.D3.D70.D.D3.D4.D3.D13.D3.D7.D3.D7.D3.D8.
D18.D12.D2.D3.D7.D11.D3.D70.D.D3.D4.D3.D13.D3.D8.D16.D3.D7.D3.D15.D9.
D3.D2.D10.D3.D7.D3.D64.D.D2.D3.D.D3.D13.D3.D9.D9.D3.D7.D3.D15.D12.D2.
D3.D9.D9.D3.D70.D.D2.D3.D3.D15.D3.D7.D3.D10.D8.D3.D15.D9.D3.D.D13.D9.
D3.D$10.D.D3.3D4.D9.D3.D8.3D4.D10.3D4.D4.3D4.D11.D10.3D4.D3.D7.D4.3D
77.D.D3.3D4.D9.D3.D8.3D4.D6.D4.D4.3D4.D11.D10.3D3.3D4.D4.3D4.D4.3D77.
D.D3.3D4.D9.D3.D8.3D4.D10.3D4.D4.3D4.D11.D10.3D4.D3.D7.D4.3D77.D.D3.
3D3.3D4.D9.D3.D8.3D4.D12.D4.D4.3D4.D11.D10.3D3.3D4.D4.3D4.D4.3D65.D.D
3.3D2.5D3.D9.D3.D8.3D4.D9.5D3.D4.3D4.D11.D10.3D3.3D4.D4.3D4.D4.3D65.D
.D3.3D3.3D4.D9.D3.D8.3D4.D4.3D4.D4.3D4.D11.D12.D3.3D4.D3.D7.D4.3D71.D
.D3.3D3.3D4.D9.D3.D8.3D4.D4.3D4.D4.3D4.D11.D12.D2.5D3.D3.D7.D4.3D71.D
.D3.3D3.3D4.D9.D3.D8.3D4.D4.3D4.D4.3D4.D11.D10.3D3.3D4.D3.D7.D4.3D71.
D.D2.5D2.3D4.D9.D3.D7.5D3.D4.3D4.D3.5D3.D11.D10.3D3.3D4.D4.3D4.D4.3D
71.D.D2.5D.5D3.D9.D3.D8.3D4.D4.3D4.D3.5D3.D11.D12.D3.3D4.D4.3D4.D4.3D
71.D.D2.5D2.3D4.D9.D3.D8.3D4.D4.3D4.D3.5D3.D11.D12.D3.3D4.D3.D7.D4.3D
71.D.D2.5D2.3D4.D9.D3.D7.5D3.D10.3D4.D4.3D4.D11.D10.3D2.5D3.D4.3D4.D
4.3D65.D.D3.3D3.3D4.D9.D3.D8.3D4.D4.3D4.D4.3D4.D11.D12.D3.3D4.D4.3D4.
D4.3D71.D.D3.3D3.3D4.D9.D3.D8.3D4.D6.D4.D4.3D4.D11.D10.3D2.D7.D4.3D4.
D4.3D$53.D17.D11.D29.D11.D127.D11.D11.D35.D11.D127.D17.D11.D29.D11.D
133.D17.D11.D35.D11.D121.D17.D11.D35.D11.D121.D11.D11.D35.D11.D127.D
11.D11.D35.D11.D127.D11.D11.D35.D11.D127.D11.D11.D35.D11.D127.D11.D
11.D35.D11.D127.D11.D11.D35.D11.D127.D17.D11.D35.D11.D121.D11.D11.D
35.D11.D127.D11.D11.D35.D11.D$52.D17.D11.D29.D11.D127.D11.D11.D35.D
11.D127.D17.D11.D29.D11.D133.D17.D11.D35.D11.D121.D17.D11.D35.D11.D
121.D11.D11.D35.D11.D127.D11.D11.D35.D11.D127.D11.D11.D35.D11.D127.D
11.D11.D35.D11.D127.D11.D11.D35.D11.D127.D11.D11.D35.D11.D127.D17.D
11.D35.D11.D121.D11.D11.D35.D11.D127.D11.D11.D35.D11.D4$5.A197.A201.A
197.A199.A201.A199.A199.A198.A198.A201.A198.A198.A201.A$6.A197.A201.A
197.A199.A201.A199.A199.A198.A198.A201.A198.A198.A201.A$4.3A195.3A
199.3A195.3A197.3A199.3A197.3A197.3A196.3A196.3A199.3A196.3A196.3A
199.3A10$14.A399.A$15.A399.A198.A$13.3A397.3A199.2A$614.2A3$820.A$
818.A.A1000.A$819.2A200.A800.A198.A400.A$1022.2A197.A.A596.3A199.2A
396.A.A$1021.2A199.2A797.2A398.2A$1222.A200.A.A1199.A$1424.2A200.A
996.A.A$227.A1196.A199.A.A600.A396.2A$225.A.A1397.2A601.A$226.2A1998.
3A$27.7B5.B187.5B195.7B5.B187.5B195.5B195.7B193.7B193.7B193.6B194.5B
195.7B193.6B194.5B195.7B$28.7B3.3D187.5B5.B189.7B3.3D187.5B195.5B195.
7B193.7B193.7B193.6B.2B191.5B195.7B193.6B194.5B195.7B$29.7B.2BDB188.
12B188.7B.2BDB188.5B195.5B195.7B193.7B193.7B193.10B190.5B195.7B193.6B
194.5B195.7B$30.7B3D2B188.12B188.7B3D2B188.5B5.B189.5B195.7B193.7B
193.7B193.10B190.5B195.7B193.6B194.5B195.7B$31.4B2.5B189.10B.B188.4B
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193.6BD2B191.5B.B193.7B193.6B194.5B.B193.7B.6B$29.13B190.13B184.13B
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193.8BD2B189.5B.4B190.6B194.8BD2B189.15B$26.4B6.6B188.15B181.4B6.6B
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193.4BD4B191.4BD4B191.11B181.4B2D7B2DB192.2B3D3B3D189.4BD4B191.5B195.
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24.4B165.6B13.4B177.6B6.6B182.4B196.7B18.4B171.4B16.4B176.6B6.6B$30.
7B3D2B181.4B3.6B194.6B2.8B184.7B22.4B167.6B5.6B183.6B5.6B183.7B3D2B
188.6B7.4B183.7B2.8B183.4B10.AB5.4B175.7B17.4B172.6B5.6B183.5B5.B3.4B
182.7B22.4B167.6B11.4B179.6B5.6B183.4B196.7B16.4B173.4B14.4B178.6B5.
6B$31.11B180.4B5.6B194.6B.7B186.7B20.4B169.6B2.8B184.6B4.6B184.11B
189.6B5.4B185.7B.7B185.4B7.BA3B3.4B177.7B15.4B174.6B2.8B184.5B3.3B.4B
184.7B20.4B169.6B9.4B181.6B2.8B184.4B196.7B14.4B175.4B12.4B180.6B2.8B
$32.10B179.4B7.6B194.12B188.7B18.4B171.14B186.6B2.6B186.10B190.6B3.4B
187.13B187.4B3.4B3A2B.4B179.7B13.4B176.14B186.14B186.7B18.4B171.6B7.
4B183.14B186.4B196.7B12.4B177.4B10.4B182.14B$33.9B178.4B9.6B.2B191.
10B190.7B2.2B12.4B173.14B186.14B186.9B191.6B.4B189.11B189.4B.5BC2A6B
181.7B11.4B178.14B186.12B188.7B2.2B12.4B173.6B5.4B185.14B186.4B25.3D
168.7B10.4B179.4B8.4B184.14B$34.8B177.4B11.8B192.8B192.11B10.4B175.
14B186.14B186.8B192.9B191.9B191.9BCA6B183.7B9.4B180.13B187.10B190.11B
10.4B175.13B187.13B187.4B23.3BD169.7B8.4B181.4B6.4B186.13B$35.8B176.
6B9.9B192.6B194.5B.4B9.4B177.4B.9B186.4B.9B186.8B192.7B193.7B193.8BD
7B184.5B.3B5.4B182.4B.6B189.9B191.5B.4B9.4B177.11B189.4B.6B189.4B11.
2B8.3BD171.8B5.4B183.4B4.4B188.4B.6B$36.6B176.13B.11B193.6B194.5BD4B
7.4B179.13B187.13B187.6B194.5B195.7B193.15B185.5BD3B3.4B184.10B189.
10B191.5BD4B7.4B177.12B190.10B190.4B4.3B2.3B7.4B173.8B3.4B185.4B2.4B
190.10B$36.7B175.25B193.6B195.4BD4B6.4B181.5B2D7B186.5B2D7B185.7B193.
3BDB196.6B194.2B3D3B3D3B186.4BD3B2.4B186.5B2D3B187.9BD193.4BD4B6.4B
178.12B191.5B2D3B190.4B.11B5.4B175.8B.4B187.9B191.5B2D3B$37.6B176.24B
194.2B2DB196.3BD5B4.4B183.4B2D8B186.4B2D8B185.6B193.2BDBDB196.2B2DB
194.14B187.3BD8B188.4B2D4B185.10BDB193.3BD5B4.4B179.6B2D6B190.4B2D4B
190.8B2D5B4.4B177.3BD7B189.9B191.4B2D4B$37.6B176.19B2D6B192.B2D2B195.
10B2.4B185.13B187.13B185.6B193.3B2D3B195.B2D2B193.6BD5B189.11B190.10B
185.9BD194.10B2.4B180.5BD2BD7B189.10B190.7B2D12B177.3BDBD5B190.10B
191.10B$38.B2DB176.19BD2BD6B191.5B194.3D3B3D2B.4B187.11B189.11B187.B
2DB194.9B194.6B192.6BD6B187.3D3B3D2B192.10B186.8B193.3D3B3D2B.4B182.
4BD2BD8B189.10B190.19B177.5B2D4B193.2D7B191.10B$37.2B2D175.22BDBD6B
193.4B194.14B188.11B189.11B186.2B2D3B193.7B197.5B192.5BD7B187.11B191.
11B185.7B195.14B185.3B2D8B190.11B190.17B179.11B192.2D8B190.11B$38.5B
173.23BD7B194.4B194.2BD9B192.4B.4B191.4B.4B184.9B192.6B199.5B191.14B
188.BD2B2.4B193.2B2.5B185.6B196.2BD9B186.14B192.2B.6B190.17B180.10B
192.B2.7B192.9B$39.4B173.31B195.4B194.BD3B2.4B198.4B196.4B183.9B193.
6B199.5B190.14B188.BD2B2.5B197.5B183.8B196.BD9B186.15B195.6B190.15B
183.2B.6B195.7B194.7B$40.4B173.29B197.4B194.D5.5B198.4B196.4B181.10B
195.5B199.5B190.13B189.DB4.5B197.5B181.10B196.D4.6B186.15B195.6B189.
15B186.7B195.7B194.7B$41.4B174.28B197.4B201.4B198.4B196.4B181.9B196.
5B199.5B191.12B195.5B197.5B180.11B201.6B187.2B.B.9B195.6B188.14B188.
7B195.7B194.7B$42.4B173.29B197.4B201.4B198.4B196.4B181.9B196.5B199.5B
190.6B2.5B195.5B197.5B179.12B201.6B195.6B195.6B187.13B190.7B195.7B
194.7B$43.4B172.6B.23B197.4B201.4B198.4B196.4B182.8B196.5B199.5B190.
4B4.5B195.5B197.5B180.11B201.6B195.6B195.6B187.13B190.7B195.7B194.7B$
44.4B171.22B5.4B402.4B198.4B196.4B181.9B196.5B199.5B190.B7.5B195.5B
197.5B185.6B201.6B195.6B195.6B187.B.11B190.7B195.7B194.7B$45.4B171.
21B6.4B402.4B198.4B196.4B181.2B2.5B196.5B199.5B198.5B195.5B197.5B185.
6B201.6B195.6B195.6B187.13B190.7B195.7B194.7B$46.4B170.15B.B2.B8.4B
402.4B198.4B196.4B185.5B603.5B195.5B197.5B185.6B201.6B195.6B195.6B
187.13B190.7B195.7B194.7B$47.4B169.15B14.4B402.4B198.4B196.4B185.5B
603.5B397.5B185.6B201.6B195.6B195.6B188.B5.6B190.7B195.7B194.7B$48.4B
169.14B15.4B198.3A201.4B198.4B196.4B185.5B200.A201.3A198.5B198.2A197.
5B185.6B201.6B195.4B2A195.6B194.6B190.7B195.5B2A194.7B$49.4B168.3B.8B
18.4B197.A204.4B198.4B196.4B185.5B198.2A201.A403.A.A197.5B185.6B402.
2B2AB196.6B194.6B190.7B195.4BABA194.7B$50.4B168.B4.5B20.4B197.A204.4B
198.4B196.4B185.5B197.A.A201.A402.A200.5B185.6B402.3BA197.6B390.7B
195.3BAB196.7B$51.4B174.2B22.4B402.4B198.4B196.4B185.5B1005.5B185.6B
402.4B197.6B198.2A190.7B195.4B197.7B$662.2A1198.2A798.2A598.2A192.7B
195.4B197.7B$662.A.A1196.2A799.A.A599.A192.4B3A195.4B197.7B$662.A
1200.A798.A795.3BA2B196.4B197.7B$3459.3BA198.4B197.7B$3460.4B198.4B
197.7B$3461.4B198.4B197.7B$3462.4B198.4B197.7B$60.3A809.A198.2A187.3A
1009.A799.A390.4B198.4B197.6BA$60.A204.A605.2A198.A.A186.A1010.2A798.
2A391.4B198.4B197.4B2AB$61.A202.2A605.A.A197.A189.A1009.A.A797.A.A
391.4B198.4B197.3BABA$264.A.A2199.A999.4B198.4B197.4B$2465.2A1000.4B
198.4B197.4B$2465.A.A1000.4B198.4B197.4B$3469.4B198.4B197.4B$3470.4B
198.4B197.4B$3471.4B198.4B197.4B$3472.4B198.4B197.4B$3473.4B198.4B
197.4B$3474.4B198.4B197.4B$3475.4B198.4B197.4B$2082.A798.2A593.4B198.
4B197.4B$477.3A995.2A201.3A400.2A798.A.A593.4B198.2B2A197.4B$477.A
997.A.A200.A402.A.A797.A596.4B198.2AB198.4B$478.A996.A203.A1605.2A
192.4B198.BA199.4B$687.A1997.A599.A.A192.4B399.4B$686.2A1996.2A599.A
195.3BA399.4B$686.A.A1197.3A795.A.A795.B2AB399.4B$1886.A1596.ABA400.
4B$1887.A1999.4B$3888.4B$3889.4B$85.2A1197.2A2604.4B$84.2A1197.2A
2606.4B$86.A202.2A606.2A197.3A186.A1010.2A797.2A795.2B2A$288.2A606.2A
198.A1198.2A797.2A797.2AB$290.A607.A198.A1199.A190.2A606.A797.BA$
2487.2A$2489.A!

That might be all the options we get, in terms of finding a way of HB-transforming all ten gliders into absorber pairs. (Are there absorber triples, quadruples, etc.?)
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Re: Half-bakery reaction with glider

Postby Kazyan » June 10th, 2014, 11:39 pm

Large projects like this are generally over my head (I can't figure out how to operate the search programs), but from what I can gather...the HBK needs a slow salvo where all of the gliders are of the same color, so that it can liberate a glider at a right-angle to the glider stream, then reconstruct the original seed in the same position.

I've probably misinterpreted what you guys need, but, here's that. Can someone check my work?

x = 219, y = 198, rule = B3/S23
bo$2bo$3o20bo$24bo$22b3o9$36bo$37bo$35b3o11$47bo$48bo$46b3o19$64bobo$
65b2o$65bo12$71bo$72b2o$71b2o6$92bo$93bo$91b3o12$102bo$103bo$101b3o13$
111bo$112bo$110b3o10$133bo$134bo$132b3o25$158bobo$159b2o$159bo5$171bob
o$172b2o$172bo12$179bobo$180b2o$180bo17$200bo$201bo$199b3o16$213bo3b2o
$214b2ob2o$213b2o!
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Re: Half-bakery reaction with glider

Postby dvgrn » June 11th, 2014, 9:23 am

Kazyan wrote:...from what I can gather...the HBK needs a slow salvo where all of the gliders are of the same color, so that it can liberate a glider at a right-angle to the glider stream, then reconstruct the original seed in the same position.

I've probably misinterpreted what you guys need, but, here's that. Can someone check my work?

You're very close -- there's one requirement that you don't actually need. Thanks for posting: I was about to waste a lot of time on an irrelevant tangent, and this made me stop and look things over.

First, there's no requirement that the seed should go back to the same position. It will probably need to be somewhere else to produce the next sideways glider anyway. We already have recipes that can move an elbow object any (X,Y) distance we want, so if you can transform the leftover junk back into the original object, or just leave a copy of the object off to the side where it doesn't get in the way, that's plenty good enough. That means the above recipe can be shortened in various ways, such as:

#C Kazyan's monochromatic 90-degree glider recipe.
#C Output glider is the same color as the input salvo.
x = 222, y = 112, rule = B3/S23
218b2o$218b2o$108b2o$108b2o$219b3o$100b3o118bo$102bo117bo$101bo2$214b
3o$216bo$215bo11$87b3o107b3o$89bo109bo$88bo109bo17$68bo109bo$68b2o108b
2o$67bobo107bobo6$164bo$164b2o$163bobo4$60bo$60b2o$59bobo5$47bo109bo$
47b2o108b2o$46bobo107bobo25$122b3o$124bo$123bo6$20b3o$22bo$21bo6$3o$2b
o$bo2$114b3o$116bo$115bo!

The version on the right shows that the mirror image of the same recipe, plus a (2,1) block pull, will fire in the other direction. Now we just need a recipe that produces the other color of output glider, and we'll have a complete universal toolkit for a Half-Baked Knightship.

I thought there was a requirement that all salvo gliders have the same parity -- all 3o$2bo$bo! or b2o$obo$2bo!, let's say, no odd-phase gliders -- but it turns out that's not true! Please ignore anything I said in previous posts about "same-parity" or "single-parity" glider recipes; the only restriction is the single-color one.

Here's why: if you run the basic geometry pattern from a week ago, you'll notice that the gliders going northwest alternate between even and odd phases as the lane changes. For each of these gliders we have a free choice to send it or not send it. So for a given "glider scan" across the shooting range, you can only use even-parity gliders for half the lanes, and only odd-parity gliders for the other half.

But on the next pass, after the reset (the gap you see in NEward gliders when you run the basic-geometry pattern) you'll get odd-parity gliders on the lanes that got even-parity gliders last time, and vice versa. That means we can send either parity of monochromatic glider -- it might just take a little longer if we need the phase that isn't in the current scan.

Conclusion: we can build any monochromatic P2 slow salvo we want, with the tools we have already. P1 slow salvos, where you never get blinkers or anything else P2 as an intermediate target, are going to be more efficient to build than P2 slow salvos. But P2 salvos are proportionately shorter, so I think it all comes out about even.

The above glider recipes will take four and five passes, respectively -- three reset operations for the left version and four for the right. If we end up doing an exhaustive search for glider-making slow salvos, we'll probably optimize for the smallest number of scan-and-reset passes. If we're really lucky, there might be a universal toolkit with just two scans per recipe.

The efficiency measurement for these monochromatic slow salvos is very strange. After each reset, you can send as many gliders as you want at no extra cost -- as long as each new glider is to the right/southeast of the previous one, and as long as the parities happen to work out (even lanes same parity as first glider, odd lanes the other parity... for P1 targets either parity will work, of course).

It's probably good to start and end each recipe with the traditional block, though there might be good arguments for basing the toolkit on some other common target, most likely a honeyfarm but possibly a blinker or traffic light.
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Re: Half-bakery reaction with glider

Postby codeholic » June 11th, 2014, 5:13 pm

dvgrn wrote:It's probably good to start and end each recipe with the traditional block, though there might be good arguments for basing the toolkit on some other common target, most likely a honeyfarm but possibly a blinker or traffic light.

Honestly I don't see a problem to have different intermediate targets. It would increase the complexity of the search script just slightly, but can improve efficiency of slow salvo synthesis quite significantly. When I wrote the search script for building a 2c/7 rake, I also thought first about going back to a certain pi orientation after each transformation, but then I realised that you should just define the start and the end pattern for each conduit and make sure that the start pattern of the next conduit matches the end pattern of the last one.

In the meanwhile I've written a script for selecting only monochromatic recipes from gencols results: https://github.com/codeholic/hbk/blob/m ... romatic.py

Here are two variants of a recipe I found with gencols and this script. It makes clear, why having different intermediate targets might be quite useful.
x = 166, y = 154, rule = B3/S23
2bo$obo$b2o36$47bo$48bo$46b3o52$100bo$101b2o$100b2o43$148bo$146bobo$
147b2o2$159bo$158bobo$158bobo$159bo2$154b2o7b2o$153bo2bo5bo2bo$154b2o
7b2o2$159bo$158bobo$158bobo$159bo!

x = 176, y = 159, rule = B3/S23
2bo$obo$b2o41$57bo$58bo$56b3o52$110bo$111b2o$110b2o43$158bo$156bobo$
157b2o2$169bo$168bobo$168bobo$169bo2$164b2o7b2o$163bo2bo5bo2bo$164b2o
7b2o2$169bo$168bobo$168bobo$169bo!
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Re: Half-bakery reaction with glider

Postby dvgrn » June 11th, 2014, 5:29 pm

codeholic wrote:Honestly I don't see a problem to have different intermediate targets. It would increase the complexity of the search script just slightly, but can improve efficiency of slow salvo synthesis quite significantly.

Oh, I definitely agree -- I saw the exact same thing with the Life replicator project. Going back to a block after every operation is usually a huge waste of gliders. But I'm still tempted to take the easy way out and write a quick-and-dirty HBK compiler for a nice simple library of block moves and glider outputs.

I'd love to have a library of all-possible-targets plus all-possible-slow-salvos giving all-possible-outputs, don't get me wrong. But that's a lot of data to sort through, and then I'd be tempted to work on optimization algorithms for months and not actually get a Half-Baked Knightship constructed. That was what delayed the Life replicator for about a decade, you know...!
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Re: Half-bakery reaction with glider

Postby Kazyan » June 11th, 2014, 6:28 pm

dvgrn wrote:Now we just need a recipe that produces the other color of output glider, and we'll have a complete universal toolkit for a Half-Baked Knightship.


x = 270, y = 263, rule = B3/S23
o$b2o$2o38$55bobo$56b2o$56bo13$74bo$75bo$73b3o21$77bo$78bo$76b3o4$101b
o$102bo$100b3o13$114bo$115bo$113b3o16$130bo$131bo$129b3o2$144bo$145bo$
143b3o43$173bo$174bo$172b3o9$182bo$183bo$181b3o7$191bo$192bo$190b3o11$
202bobo$203b2o$203bo15$220bo$221b2o$220b2o22$244bo$245b2o$244b2o18$
264bo3b2o$265b2ob2o$264b2o!


Whacking the block until it makes a conveniently-placed boat works, but I'm sure there's a way to do it with fewer gliders.
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Re: Half-bakery reaction with glider

Postby codeholic » June 11th, 2014, 6:44 pm

Here are recipes for different starting targets. Restrictions are: 3 gliders, monochromatic, the end pattern consists of less than 30 cells (one orthogonal glider + some periodic junk up to 24 cells), intermediate steps finish stabilise in less than 180 generations, the final step stabilises in less than 280 generations. I'm sorry for duplicates.
Honey farm
x = 517, y = 532, rule = B3/S23
2bo197bobo199bo$obo198b2o197bobo$b2o198bo199b2o47$239bo199bo$240bo199b
o$49bobo186b3o197b3o$50b2o$50bo45$104bo$102bobo$103b2o$289bo199bo$287b
obo197bobo$288b2o198b2o2$301bo199bo$300bobo197bobo$110bo189bobo197bobo
$109bobo189bo199bo$109bobo$110bo185b2o7b2o189b2o7b2o$295bo2bo5bo2bo
187bo2bo5bo2bo$105b2o7b2o180b2o7b2o189b2o7b2o$104bo2bo5bo2bo$105b2o7b
2o185bo199bo$300bobo197bobo$110bo189bobo197bobo$109bobo189bo199bo$109b
obo$110bo81$2bo198bo198bo$obo199bo198b2o$b2o197b3o197b2o38$445bo$446bo
$444b3o12$46bobo205bo$47b2o206b2o$47bo206b2o38$501bo$499bobo$500b2o2$
510bo$302bo206bobo$300bobo206bobo$101bo199b2o207bo$99bobo$100b2o211bo
191b2o7b2o$312bobo189bo2bo5bo2bo$113bo198bobo190b2o7b2o$112bobo198bo$
112bobo395bo$113bo194b2o7b2o190bobo$307bo2bo5bo2bo189bobo$108b2o7b2o
189b2o7b2o191bo$107bo2bo5bo2bo$108b2o7b2o194bo$312bobo$113bo198bobo$
112bobo198bo$112bobo$113bo83$2bo197bobo$obo198b2o$b2o198bo50$50bo$48bo
bo$49b2o197bo$249bo$247b3o44$302bo$300bobo$301b2o2$314bo$313bobo$313bo
bo$314bo2$309b2o7b2o$308bo2bo5bo2bo$309b2o7b2o2$314bo$313bobo$99bo213b
obo$97bobo214bo$98b2o2$108bo$107bobo$107bobo$108bo2$103b2o7b2o$102bo2b
o5bo2bo$103b2o7b2o2$108bo$107bobo$107bobo$108bo!

Traffic light
x = 530, y = 2533, rule = B3/S23
bo199bo198bo$2bo199bo198b2o$3o197b3o197b2o46$254bo$255b2o$254b2o$49bo
404bo$50b2o400bobo$49b2o402b2o45$104bo$105b2o$104b2o396bo$299bo203b2o$
300b2o200b2o$299b2o4$512b3o$109b3o197b3o$510bo5bo$107bo5bo193bo5bo196b
o5bo$107bo5bo193bo5bo196bo5bo$107bo5bo193bo5bo$512b3o$109b3o197b3o86$b
o199bo199bo$2bo199bo199bo$3o197b3o197b3o37$463bo$61bobo199bo200b2o$62b
2o197bobo199b2o$62bo199b2o59$118bo199bo199bo$116bobo197bobo197bobo$
117b2o198b2o198b2o7$125b3o197b3o197b3o2$123bo5bo193bo5bo193bo5bo$123bo
5bo193bo5bo193bo5bo$123bo5bo193bo5bo193bo5bo2$125b3o197b3o197b3o84$bo
199bo199bo$2bo199bo199bo$3o197b3o197b3o37$64bo199bobo199bo$62bobo200b
2o197bobo$63b2o200bo199b2o60$118bo199bo199bo$116bobo197bobo197bobo$
117b2o198b2o198b2o7$125b3o197b3o197b3o2$123bo5bo193bo5bo193bo5bo$123bo
5bo193bo5bo193bo5bo$123bo5bo193bo5bo193bo5bo2$125b3o197b3o197b3o84$o
199bo199bo$b2o198b2o198b2o$2o198b2o198b2o44$242bo$243b2o$242b2o$462bo$
460bobo$461b2o4$48bobo$49b2o$49bo35$298bo$299b2o$298b2o2$106bo397bo$
107b2o396b2o$106b2o396b2o4$303b3o2$301bo5bo$301bo5bo$110b3o188bo5bo
203b3o2$108bo5bo188b3o203bo5bo$108bo5bo394bo5bo$108bo5bo394bo5bo2$110b
3o398b3o88$obo198bo198bo$b2o199bo198b2o$bo198b3o197b2o49$259bo$260b2o$
259b2o3$447bobo$448b2o$448bo2$50bo$51bo$49b3o38$504bo$505b2o$100bo403b
2o$98bobo206bo$99b2o207b2o$307b2o4$108b3o$317b3o189b3o$106bo5bo$106bo
5bo202bo5bo185bo5bo$106bo5bo202bo5bo185bo5bo$315bo5bo185bo5bo$108b3o$
317b3o189b3o84$o199bo199bobo$b2o198b2o198b2o$2o198b2o199bo46$254bo$
255b2o$54bo199b2o$55b2o$54b2o2$448bobo$449b2o$449bo39$504bo$505b2o$
504b2o4$298bo$296bobo$100bo196b2o$98bobo$99b2o409b3o2$508bo5bo$307b3o
198bo5bo$508bo5bo$109b3o193bo5bo$305bo5bo198b3o$107bo5bo191bo5bo$107bo
5bo$107bo5bo193b3o2$109b3o84$obo198bo200bo$b2o199bo197bobo$bo198b3o
198b2o46$254bo$255b2o$254b2o4$50bobo395bobo$51b2o396b2o$51bo397bo39$
504bo$505b2o$106bo397b2o$107b2o$106b2o2$298bo$296bobo$297b2o2$510b3o2$
112b3o393bo5bo$307b3o198bo5bo$110bo5bo391bo5bo$110bo5bo188bo5bo$110bo
5bo188bo5bo198b3o$305bo5bo$112b3o$307b3o86$bo200bo197bo$2bo197bobo198b
2o$3o198b2o197b2o44$42bo$43b2o202bobo$42b2o204b2o$248bo8$447bo$448b2o$
447b2o33$98bo$99b2o$98b2o2$297bo$298b2o$297b2o3$499bo$103b3o394b2o$
307b3o189b2o$101bo5bo$101bo5bo197bo5bo$101bo5bo197bo5bo$305bo5bo$103b
3o403b3o$307b3o$507bo5bo$507bo5bo$507bo5bo2$509b3o86$o199bo199bobo$b2o
198b2o198b2o$2o198b2o199bo46$253bo$254bo$252b3o2$450bo$448bobo$449b2o
3$48bo$49bo$47b3o39$303bo$301bobo196bo$302b2o197b2o$99bo400b2o$100b2o$
99b2o2$311b3o2$309bo5bo$109b3o197bo5bo$309bo5bo191b3o$107bo5bo$107bo5b
o197b3o191bo5bo$107bo5bo391bo5bo$505bo5bo$109b3o$507b3o85$2bo199bo199b
o$obo197bobo197bobo$b2o198b2o198b2o44$251bo200bo$252b2o196bobo$251b2o
198b2o4$60bo$58bobo$59b2o43$307bo199bo$305bobo197bobo$306b2o198b2o4$
110bo$111b2o$110b2o2$309b3o197b3o2$307bo5bo193bo5bo$307bo5bo193bo5bo$
307bo5bo193bo5bo2$114b3o192b3o197b3o2$112bo5bo$112bo5bo$112bo5bo2$114b
3o81$o199bobo198bo$b2o198b2o199bo$2o199bo198b3o49$52bobo$53b2o196bo$
53bo198b2o$251b2o194bobo$448b2o$448bo40$302bo$300bobo$98bo202b2o$99b2o
404bo$98b2o406b2o$505b2o2$310b3o2$308bo5bo$308bo5bo$308bo5bo$105b3o$
310b3o196b3o$103bo5bo$103bo5bo397bo5bo$103bo5bo397bo5bo$507bo5bo$105b
3o$509b3o85$bo200bo198bo$2bo197bobo199bo$3o198b2o197b3o44$457bobo$458b
2o$458bo$55bo$56b2o$55b2o4$249bobo$250b2o$250bo40$304bo$305b2o201bo$
304b2o203b2o$508b2o2$101bo$99bobo$100b2o3$311b3o$513b3o$109b3o197bo5bo
$309bo5bo195bo5bo$107bo5bo195bo5bo195bo5bo$107bo5bo397bo5bo$107bo5bo
197b3o$513b3o$109b3o85$obo199bo$b2o197bobo$bo199b2o63$35bobo197bobo$
36b2o198b2o$36bo199bo49$85bo199bo$86b2o198b2o$85b2o198b2o8$89b3o197b3o
2$87bo5bo193bo5bo$87bo5bo193bo5bo$87bo5bo193bo5bo2$89b3o197b3o!

Blinker
x = 106, y = 118, rule = B3/S23
2bo$obo$b2o50$50bo$48bobo$49b2o53$100bo$101b2o$100b2o8$103b3o!

Beehive
x = 109, y = 123, rule = B3/S23
obo$b2o$bo50$49bo$50b2o$49b2o57$99bo$97bobo$98b2o7$106b2o$105bo2bo$
106b2o!
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Re: Half-bakery reaction with glider

Postby dvgrn » June 11th, 2014, 8:11 pm

codeholic wrote:Here are recipes for different starting targets. Restrictions are: 3 gliders, monochromatic, the end pattern consists of less than 30 cells (one orthogonal glider + some periodic junk up to 24 cells), intermediate steps finish stabilise in less than 180 generations, the final step stabilises in less than 280 generations.

Looks good! It should be easy enough to register those for use in a slow-salvo compiler, and we don't really need any more than that. Might be able to get say 25% more efficient by building a much bigger database and looking for ways to build multiple OTT predecessors simultaneously in just the right places -- but that's the kind of time-sucking problem I was talking about. Interesting, but really difficult and time-consuming to get the optimization right.

The blinker and beehive searches turned up only one recipe each, so there must be only the one 2G+traffic light reaction. That might end up getting used more than any of the others, since there are so many different ways to produce traffic lights, and there's no cleanup problem afterwards -- just one beehive to continue from, so the compiler will be able to solve one easy problem at a time.

It's really nice that this HBK design doesn't require the "elbow" object to stay on the same diagonal, so the compiler can choose the cheapest recipe from a wide range of possible (X,Y) elbow moves. This knightship might not end up being as big as I thought. Any more clever ideas on how to reduce the number of half-bakery trails?

Here's a table of object conversions that I put together a few years ago -- good for quick looking up of what's possible from a given object. This will need to get fed into the compiler in a more organized way, of course:

EDIT: If I recall correctly, the lane numbers are for bo$2bo$3o! gliders heading southeast; leftward is negative, rightward is positive, and 0 is the line of symmetry (if applicable).
Glider + Block:
-11  block(-1,-2)
  -9  honeyfarm
  -7  pi
  -5  null
  -3  null
  -1  null
   1  null
   3  null
   5  null
   7  pi
   9  honeyfarm
  11  block(-1,-2)

Glider + Tub:
-11  boat
  -9  null
  -7  null
  -5  beehive
  -3  3 gliders + junk
  -1  beehive
   1  beehive
   3  3 gliders + junk
   5  beehive
   7  null
   9  null
  11  boat

Glider + Pond:
-13  tub
-11  loaf, two blinkers, and block
  -9  pi
  -7  block
  -5  null
  -3  2HF,2G big mess
  -1  ship(2o$obo$b2o!)
   1  ship(2o$obo$b2o!)
   3  2HF,2G big mess
   5  null
   7  block
   9  pi
  11  loaf, two blinkers, and block
  13  tub

Glider + Ship(2o$obo$b2o!)
-11  null
  -9  beehive (large offset)
  -7  TL, toad, 6 blocks misc. mess
  -5  TL*7/4 + barge + 1G medium mess
  -3  block
  -1  block
   1  block
   3  block
   5  TL*7/4 + barge + 1G medium mess
   7  TL, toad, 6 blocks misc. mess
   9  beehive (large offset)
  11  null

Glider + Ship(b2o$obo$2o!)
-13  null
-11  queen bee shuttle, to two mirrored centuries
  -9  pi
  -7  block
  -5  Wing/BG -- 1 90-degree glider, 1 block remains
  -3  null
  -1  null
   1  null
   3  null
   5  Wing/BG -- 1 90-degree glider, 1 block remains
   7  block
   9  pi
  11  queen bee shuttle, to two mirrored centuries
  13  null


Glider + Boat(2o$obo$bo!):
-11  null
  -9  block
  -7  blinkers, traffic light, toad, 15 still lifes
  -5  B-heptomino
  -3  blinker(phase0)
  -1  same blinker(phase0)
   1  same blinker(phase1)
   3  same blinker(phase1)
   5  B-heptomino
   7  blinkers, traffic light, toad, 15 still lifes
   9  block
  11  null
 
Glider + Boat(bo$obo$b2o!):
-11  block (boat-bit collapse)
  -9  Wing/BG
  -7  null
  -5  6 blocks, 1 beehive, 1 return glider (not a bad super-splitter)
  -3  century (b2o$obo$o$2o!)
  -1  null
   1  null
   3  century
   5  6 blocks, 1 beehive, 1 glider
   7  null
   9  Wing/BG -- 1 90-degree glider, 1 block remains
  11  block

Glider + Loaf(b2o$o2bo$obo$bo!):
-13  honeyfarm
-11  honeyfarm, beehive, block (pi plus pond)
  -9  34 still lifes, 3 gliders
  -7  beehive & block
  -5  traffic light
  -3  null
  -1  loaf (toggle)
   1  loaf (toggle)
   3  null
   5  traffic light
   7  beehive & block
   9  34 still lifes, 3 gliders
  11  honeyfarm, beehive, block
13  honeyfarm

Glider + Loaf(2bo$bobo$o2bo$b2o!):
-13  boat, 2TL, 2G, 2 blinkers, 2 blocks, 5 beehives
-11  null
  -9  honeyfarm
  -7  boat, ship, and blinker
  -5  R-pentomino + blinker mess
  -3  block
  -1  null
   1  null
   3  block
   5  R-pentomino + blinker mess
   7  boat, ship, and blinker
   9  honeyfarm
  11  null
13  boat, 2TL, 2G, 2 blinkers, 2 blocks, 5 beehives

Not diagonally symmetric in glider-lane line:

Glider + Blinker(phase0):
-11  pond
  -9  pi
  -7  blinker
  -5  R-pentomino & 4-ships mess
  -3  block
  -1  4G, 3 TL, 17 blinkers, ~31 still-life mess
   1  null
   3  null
   5  null
   7  loaf(b2o$o2bo$bobo$2bo!)
   9  ship(b2o$obo$2o!)
  11  traffic light

Glider + Blinker(phase1) -- phase0 in reverse:
-11  traffic light
  -9  ship(b2o$obo$2o!)
  -7  loaf(b2o$o2bo$bobo$2bo!)
  -5  null
  -3  null
  -1  null
   1  4G, 3 TL, 17 blinkers, ~31 still-life mess
   3  block
   5  R-pentomino & 4-ships mess
   7  blinker
   9  pi
  11  pond

Glider + Beehive:
-11  null
  -9  block + tub (Brice Due bit)
  -7  pi
  -5  B-heptomino + boat
  -3  R-pentomino
  -1  traffic light
   1  honeyfarm
   3  null
   5  R-pentomino
   7  block
   9  null
  11  null
  13  LOM

Glider + Boat(bo$obo$2o!):
-11  1 glider, 9 still lifes, 1 blinker
  -9  null
  -7  Wing/BG
  -5  blinker
  -3  B-heptomino, boat and blinker
  -1  null
   1  null
   3  90-degree glider
   5  null
   7  honeyfarm
   9  pi
  11  null
  13  honeyfarm

Glider + Loaf(b2o$o2bo$bobo$2bo!):
-11  block
  -9  TL&HF&B-hept&pond&boat&tub&blinker&blocks mess
  -7  3-glider-isolated-TL-huge-mess
  -5  block
  -3  loaf(b2o$o2bo$obo$bo!) (rotated 90 degrees)
  -1  loaf(b2o$o2bo$bobo$2bo!) (same orientation, [-3,-1]!)
   1  beehive
   3  null
   5  honeyfarm
   7  R-pentomino
   9  null
  11  honeyfarm
  13  null

Measurements are in Paul Chapman's quarter-diagonals, by the way, so "1" and "3" are different-color lanes.
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Re: Half-bakery reaction with glider

Postby codeholic » June 14th, 2014, 8:18 am

I'd like to do a weighted search for universal set of operations on the slow elbow.

Please double-check my assumption, that the basic set of operations for generating NE glider salvo with gliders coming from half-bakeries (no matter which synthesis we choose in the end) looks like this:
name hd  parity glider weight
0    +2  1      0      1
G    +2  1      1      1
R    -78 0      0      8

'parity' column means whether parity changes or not (actually this is ('weight' mod 2)). 'glider' is whether an operation emits a glider.

One could theoretically add an anti-reset operation, but practically that would be probably useless. Is there anything else I'm missing?
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Re: Half-bakery reaction with glider

Postby dvgrn » June 14th, 2014, 9:46 am

codeholic wrote:I'd like to do a weighted search for universal set of operations on the slow elbow.

Please double-check my assumption, that the basic set of operations for generating NE glider salvo with 4 gliders coming from half-bakeries (no matter which synthesis we choose in the end) looks like this:
name hd  parity glider weight
0    +2  1      0      1
G    +2  1      1      1
R    -78 0      0      8

I've been thinking about weightings in a slightly different way. It may make sense to say that the only thing that counts the number of resets.

Inevitably a HBK knightship is going to consist of a large number of glider scans and resets. So the "shooting range" width is going to be at least 39 monochromatic lanes, maybe somewhat more but 39 is probably plenty wide enough.

On each scan, we have a free choice of whether or not to send a glider on each of the 39 lanes. The parity changes with every lane, so every other scan will let us choose the other parity of glider for a given lane, in the cases where that matters.

But we have to scan past all 39 lanes to get far enough rightward to do the next reset... which means that on each scan, we could send anywhere from 1 to 39 gliders at the exact same cost (!) The "basic geometry" pattern shows one way to use dozens of gliders in a row, but normally just a few can be sent in a single scan before the next reset is needed.

I suspect there's room in a width-79 shooting range for three or four separate slow-salvo targets, at different NE/SW distances. So in a single scan, we can shoot the next glider in each of three or four construction salvos, one after the other -- all at no extra cost.

If necessary, there's no problem with the shooting range drifting left and right a little bit: as long as the last glider in one scan is no more than 39 lanes to the right (southeast) of the first glider in the next scan, there will be no need for an expensive double reset.

Does that make sense? It seems strange to not have to care about the number of gliders in the salvo, but in these monochromatic salvos, you only have to count the gliders that are not to the right/southwest of a previous glider.

That's assuming a NE-traveling salvo is the standard orientation. I've always used NW-traveling slow salvos as the standard in Geminoid search programs, but maybe these HBK salvos are different enough that a new standard orientation isn't a bad idea...?
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Re: Half-bakery reaction with glider

Postby codeholic » June 14th, 2014, 10:29 am

dvgrn wrote:I suspect there's room in a width-79 shooting range for three or four separate slow-salvo targets, at different NE/SW distances. So in a single scan, we can shoot the next glider in each of three or four construction salvos, one after the other -- all at no extra cost.

Given this brilliant idea, that I didn't think of, everything you've said perfectly makes sense. Let's consider that it's only the number of scans that matters.

dvgrn wrote:That's assuming a NE-traveling salvo is the standard orientation. I've always used NW-traveling slow salvos as the standard in Geminoid search programs, but maybe these HBK salvos are different enough that a new standard orientation isn't a bad idea...?

Well, it doesn't really matter. Though, for me, SE always seemed the most "natural" direction for a glider, because that's where coordinates in Golly grow to ;) But let's stick to the orientation in the original calcyman's design to keep consistency.
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Re: Half-bakery reaction with glider

Postby dvgrn » June 14th, 2014, 9:30 pm

dvgrn wrote:...in a single scan, we can shoot the next glider in each of three or four construction salvos, one after the other -- all at no extra cost.


codeholic wrote:Let's consider that it's only the number of scans that matters.

There's one other strange detail that I didn't describe clearly in my "no extra cost" claim: glider parity. It works perfectly well to allow P2 intermediate targets in monochromatic HBK slow salvos -- but on a given scan, the glider parity is fixed for each lane. The parity changes with each new lane, and for a given lane it also changes with each new scan.

So let's say you need to send one particular phase of glider on a particular lane to hit a P2 target. Half the time, you'll have to skip that lane and hit it on the next scan instead, to get the correct glider parity. Makes the slow-salvo search weightings a little bit more interesting...!

I think that sometimes it will turn out that you can use either parity of glider from a previous scan, so that a recipe won't cost extra after all. For example, suppose you have a blinker that has to be modified, but the key lane is on the wrong phase for the current scan. One previous glider in the slow salvo might shoot down a block, and on the next scan a glider on some other independent lane might create the blinker from a P1 target. Then if you swap scans for the block-killer and the blinker-maker, the blinker will end up in the other phase, and suddenly the key lane is in the right phase after all.

-- I guess it wouldn't really happen quite like this, because if the block-killer and blinker-maker are on independent lanes, then in one order or other they could both be sent during the same scan, one after another. The point still holds, though: changing the construction order can change a P2 intermediate target's phase, and that can easily change the recipe's total cost (measured in resets).
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Re: Half-bakery reaction with glider

Postby dvgrn » June 17th, 2014, 5:26 am

codeholic wrote:Bad news is that I took a look at invariants of absorbers and invariants of gliders in two HB-transforming tracks with minimal spacing. I haven't strictly excluded the possibility, that they're not compatible, but I have a strong feeling, that they aren't.

Good news is that I hit upon a trivial way to get rid of all gliders but two. Here is an example how...

I've started looking at this problem again, and it's very tricky to enumerate all the possible distance and delay combinations that might correspond to working absorbers. The example you gave corresponds to the glider spacing in the sample guard-glider pattern I posted earlier, which used a recipe with an intermediate Herschel.

Intermediate-Herschel recipes are bad in the northwest, because you lose a degree of freedom for the relative timing of the two SE-traveling gliders. On the other hand, they're good in the southeast, because you gain a degree of freedom in the placement of the second NW-traveling glider -- it can be on several different lanes and any timing you want, since it's just cleaning up a leftover block.

Maybe it makes sense to try all the workable Herschel-based recipes, concentrating on finding an efficient absorber for the six northwest gliders -- on the theory that the four gliders in the southeast can probably be adjusted into a good absorber, one way or another.

-- Or will the "trivial solution" get rid of N-2 gliders for any set of N gliders? I'm not seeing immediately how to make that trick work with the triplets of gliders in the northwest, even if the timing happened to work out for the two glider-producing trails in each triplet.

I just tried analyzing a recipe with a stable intermediate target, chosen more or less at random:

x = 644, y = 701, rule = LifeHistory
459.C$458.C$458.3C16$477.C$477.C.C$477.2C11$420.2D$419.D2.D32.C.C$
419.D.D33.2C$417.2D.D35.C$416.D2.D$416.D.D$417.D5.2C25.2D$422.C2.C23.
D2.D$422.C.C24.D.D$420.2C.C23.2D.D$419.C2.C23.D2.D$419.C.C24.D.D$420.
C26.D5.2C$452.C2.C$434.2D16.C.C$433.D2.D13.2C.C$433.D.D13.C2.C$431.2D
.D14.C.C50.C.C$430.D2.D16.C51.2C$430.D.D70.C$431.D5.2C$436.C2.C$436.C
.C$434.2C.C$433.C2.C$433.C.C$434.C8$522.C$520.2C$521.2C7$641.C$641.C.
C$641.2C2$464.2D$463.D2.D32.C$463.D.D33.C.C$461.2D.D34.2C$460.D2.D$
460.D.D$461.D5.2C25.2D$466.C2.C23.D2.D$466.C.C24.D.D$464.2C.C23.2D.D$
463.C2.C23.D2.D125.C.C$463.C.C24.D.D126.2C$464.C26.D5.2C101.C19.C$
496.C2.C100.C.C$478.2D16.C.C101.2C$477.D2.D13.2C.C$477.D.D13.C2.C$
358.2D115.2D.D14.C.C$357.D2.D113.D2.D16.C$357.D.D114.D.D$355.2D.D116.
D5.2C50.2D$354.D2.D32.2D88.C2.C50.2D$354.D.D32.D2.D87.C.C50.D$355.D5.
2E26.D.D86.2C.C$360.E2.E23.2D.D86.C2.C$360.E.E23.D2.D87.C.C$358.2E.E
24.D.D89.C99.C.C$357.E2.E26.D5.2E183.2C$357.E.E32.E2.E183.C$358.E33.E
.E$373.2D15.2E.E$372.D2.D13.E2.E$372.D.D14.E.E$370.2D.D16.E$369.D2.D$
369.D.D$370.D5.2E176.C$375.E2.E174.C$375.E.E175.3C$338.2D33.2E.E$337.
D2.D31.E2.E135.2D$337.D.D32.E.E135.D2.D$335.2D.D34.E136.D2.D$334.D2.D
173.2D$334.D.D$335.D5.2E25.2D$340.E2.E23.D2.D165.2D$340.E.E24.D.D165.
D2.D$338.2E.E23.2D.D166.D.D$337.E2.E23.D2.D165.2D.D$337.E.E24.D.D165.
D2.D$338.E26.D5.2E159.D.D$370.E2.E159.D5.2C$370.E.E165.C2.C$351.2D15.
2E.E166.C.C$350.D2.D13.E2.E165.2C.C$350.D.D14.E.E165.C2.C$348.2D.D16.
E166.C.C9.2D$347.D2.D185.C9.D2.D$347.D.D196.D.D$348.D5.2E188.2D.D$
353.E2.E186.D2.D$353.E.E187.D.D$316.2D33.2E.E189.D5.2C$315.D2.D31.E2.
E48.2D145.C2.C$315.D.D32.E.E48.D2.D126.2D16.C.C$313.2D.D34.E49.D.D
126.D2.D13.2C.C$312.D2.D83.2D.D127.D.D13.C2.C$312.D.D83.D2.D32.2D92.
2D.D14.C.C$313.D5.2E25.2D50.D.D32.D2.D90.D2.D16.C$318.E2.E23.D2.D50.D
5.2E26.D.D91.D.D$318.E.E24.D.D56.E2.E23.2D.D93.D5.2C22.2D$316.2E.E23.
2D.D57.E.E23.D2.D99.C2.C20.D2.D$315.E2.E23.D2.D56.2E.E24.D.D100.C.C
21.D.D$315.E.E24.D.D56.E2.E26.D5.2E92.2C.C20.2D.D$316.E26.D5.2E50.E.E
32.E2.E90.C2.C20.D2.D$348.E2.E50.E33.E.E91.C.C21.D.D$348.E.E66.2D15.
2E.E93.C23.D5.2C$329.2D15.2E.E66.D2.D13.E2.E123.C2.C$328.D2.D13.E2.E
67.D.D14.E.E106.2D16.C.C$328.D.D14.E.E66.2D.D16.E106.D2.D13.2C.C$326.
2D.D16.E66.D2.D124.D.D13.C2.C$325.D2.D84.D.D123.2D.D14.C.C$325.D.D86.
D5.2E116.D2.D16.C$326.D5.2E85.E2.E115.D.D$331.E2.E84.E.E117.D5.2C$
331.E.E48.2D33.2E.E123.C2.C$294.2D33.2E.E48.D2.D31.E2.E124.C.C$293.D
2.D31.E2.E49.D.D32.E.E123.2C.C$293.D.D32.E.E48.2D.D34.E123.C2.C$291.
2D.D34.E48.D2.D159.C.C$290.D2.D84.D.D161.C$290.D.D86.D5.2E25.2D$291.D
5.2E25.2D58.E2.E23.D2.D$296.E2.E23.D2.D57.E.E24.D.D$296.E.E24.D.D56.
2E.E23.2D.D$294.2E.E23.2D.D56.E2.E23.D2.D$293.E2.E23.D2.D57.E.E24.D.D
$293.E.E24.D.D59.E26.D5.2E$294.E26.D5.2E85.E2.E$326.E2.E84.E.E$326.E.
E66.2D15.2E.E$307.2D15.2E.E66.D2.D13.E2.E$306.D2.D13.E2.E67.D.D14.E.E
$306.D.D14.E.E66.2D.D16.E$304.2D.D16.E66.D2.D$303.D2.D84.D.D$303.D.D
86.D5.2E$304.D5.2E85.E2.E$309.E2.E84.E.E$309.E.E48.2D33.2E.E$272.2D
33.2E.E48.D2.D31.E2.E$271.D2.D31.E2.E49.D.D32.E.E$271.D.D32.E.E48.2D.
D34.E$269.2D.D34.E48.D2.D$268.D2.D84.D.D$268.D.D86.D5.2E25.2D$269.D5.
2E25.2D58.E2.E23.D2.D$274.E2.E23.D2.D57.E.E24.D.D$274.E.E24.D.D56.2E.
E23.2D.D$272.2E.E23.2D.D56.E2.E23.D2.D$271.E2.E23.D2.D57.E.E24.D.D$
271.E.E24.D.D59.E26.D5.2E$272.E26.D5.2E85.E2.E$304.E2.E84.E.E$304.E.E
66.2D15.2E.E$285.2D15.2E.E66.D2.D13.E2.E$284.D2.D13.E2.E67.D.D14.E.E$
284.D.D14.E.E66.2D.D16.E$282.2D.D16.E66.D2.D$281.D2.D84.D.D$281.D.D
86.D5.2E$282.D5.2E85.E2.E$287.E2.E84.E.E$287.E.E48.2D33.2E.E$250.2D
33.2E.E48.D2.D31.E2.E$249.D2.D31.E2.E49.D.D32.E.E$249.D.D32.E.E48.2D.
D34.E$247.2D.D34.E48.D2.D$246.D2.D84.D.D$246.D.D86.D5.2E25.2D$247.D5.
2E25.2D58.E2.E23.D2.D$252.E2.E23.D2.D57.E.E24.D.D$252.E.E24.D.D56.2E.
E23.2D.D$250.2E.E23.2D.D56.E2.E23.D2.D$249.E2.E23.D2.D57.E.E24.D.D$
249.E.E24.D.D59.E26.D5.2E$250.E26.D5.2E85.E2.E$282.E2.E84.E.E$282.E.E
66.2D15.2E.E$263.2D15.2E.E66.D2.D13.E2.E$262.D2.D13.E2.E67.D.D14.E.E$
262.D.D14.E.E66.2D.D16.E$260.2D.D16.E66.D2.D$259.D2.D84.D.D$259.D.D
86.D5.2E$260.D5.2E85.E2.E$265.E2.E84.E.E$265.E.E48.2D33.2E.E$228.2D
33.2E.E48.D2.D31.E2.E$227.D2.D31.E2.E49.D.D32.E.E$227.D.D32.E.E48.2D.
D34.E$225.2D.D34.E48.D2.D$224.D2.D84.D.D$224.D.D86.D5.2E25.2D$225.D5.
2E25.2D58.E2.E23.D2.D$230.E2.E23.D2.D57.E.E24.D.D$230.E.E24.D.D56.2E.
E23.2D.D$228.2E.E23.2D.D56.E2.E23.D2.D$227.E2.E23.D2.D57.E.E24.D.D$
227.E.E24.D.D59.E26.D5.2E$228.E26.D5.2E85.E2.E$260.E2.E84.E.E$260.E.E
66.2D15.2E.E$241.2D15.2E.E66.D2.D13.E2.E$240.D2.D13.E2.E67.D.D14.E.E$
240.D.D14.E.E66.2D.D16.E$238.2D.D16.E66.D2.D$237.D2.D84.D.D$237.D.D
86.D5.2E$238.D5.2E85.E2.E$243.E2.E84.E.E$243.E.E48.2D33.2E.E$206.2D
33.2E.E48.D2.D31.E2.E$205.D2.D31.E2.E49.D.D32.E.E$205.D.D32.E.E48.2D.
D34.E$203.2D.D34.E48.D2.D$202.D2.D84.D.D$202.D.D86.D5.2E25.2D$203.D5.
2E25.2D58.E2.E23.D2.D$208.E2.E23.D2.D57.E.E24.D.D$208.E.E24.D.D56.2E.
E23.2D.D$206.2E.E23.2D.D56.E2.E23.D2.D$205.E2.E23.D2.D57.E.E24.D.D$
205.E.E24.D.D59.E26.D5.2E$206.E26.D5.2E85.E2.E$238.E2.E84.E.E$238.E.E
66.2D15.2E.E$219.2D15.2E.E66.D2.D13.E2.E$218.D2.D13.E2.E67.D.D14.E.E$
218.D.D14.E.E66.2D.D16.E$216.2D.D16.E66.D2.D$215.D2.D84.D.D$215.D.D
86.D5.2E$216.D5.2E85.E2.E$221.E2.E84.E.E$221.E.E48.2D33.2E.E$184.2D
33.2E.E48.D2.D31.E2.E$183.D2.D31.E2.E49.D.D32.E.E$183.D.D32.E.E48.2D.
D34.E$181.2D.D34.E48.D2.D$180.D2.D84.D.D$180.D.D86.D5.2E25.2D$181.D5.
2E25.2D58.E2.E23.D2.D$186.E2.E23.D2.D57.E.E24.D.D$186.E.E24.D.D56.2E.
E23.2D.D$184.2E.E23.2D.D56.E2.E23.D2.D$183.E2.E23.D2.D57.E.E24.D.D$
183.E.E24.D.D59.E26.D5.2E$184.E26.D5.2E85.E2.E$216.E2.E84.E.E$216.E.E
66.2D15.2E.E$197.2D15.2E.E66.D2.D13.E2.E$196.D2.D13.E2.E67.D.D14.E.E$
196.D.D14.E.E66.2D.D16.E$194.2D.D16.E66.D2.D$193.D2.D84.D.D$193.D.D
86.D5.2E$194.D5.2E85.E2.E$199.E2.E84.E.E$199.E.E48.2D33.2E.E$162.2D
33.2E.E48.D2.D31.E2.E$161.D2.D31.E2.E49.D.D32.E.E$161.D.D32.E.E48.2D.
D34.E$159.2D.D34.E48.D2.D$158.D2.D84.D.D$158.D.D86.D5.2E25.2D$159.D5.
2E25.2D58.E2.E23.D2.D$164.E2.E23.D2.D57.E.E24.D.D$164.E.E24.D.D56.2E.
E23.2D.D$162.2E.E23.2D.D56.E2.E23.D2.D$161.E2.E23.D2.D57.E.E24.D.D$
161.E.E24.D.D59.E26.D5.2E$162.E26.D5.2E85.E2.E$194.E2.E84.E.E$194.E.E
66.2D15.2E.E$175.2D15.2E.E66.D2.D13.E2.E$174.D2.D13.E2.E67.D.D14.E.E$
174.D.D14.E.E66.2D.D16.E$172.2D.D16.E66.D2.D$171.D2.D84.D.D$171.D.D
86.D5.2E$172.D5.2E85.E2.E$177.E2.E84.E.E$177.E.E48.2D33.2E.E$140.2D
33.2E.E48.D2.D31.E2.E$139.D2.D31.E2.E49.D.D32.E.E$139.D.D32.E.E48.2D.
D34.E$137.2D.D34.E48.D2.D$136.D2.D84.D.D$136.D.D86.D5.2E25.2D$137.D5.
2E25.2D58.E2.E23.D2.D$142.E2.E23.D2.D57.E.E24.D.D$142.E.E24.D.D56.2E.
E23.2D.D$140.2E.E23.2D.D56.E2.E23.D2.D$139.E2.E23.D2.D57.E.E24.D.D$
139.E.E24.D.D59.E26.D5.2E$140.E26.D5.2E85.E2.E$172.E2.E84.E.E$172.E.E
66.2D15.2E.E$153.2D15.2E.E66.D2.D13.E2.E$152.D2.D13.E2.E67.D.D14.E.E$
152.D.D14.E.E66.2D.D16.E$150.2D.D16.E66.D2.D$149.D2.D84.D.D$149.D.D
86.D5.2E$150.D5.2E85.E2.E$155.E2.E84.E.E$155.E.E48.2D33.2E.E$118.2D
33.2E.E48.D2.D31.E2.E$117.D2.D31.E2.E49.D.D32.E.E$117.D.D32.E.E48.2D.
D34.E$115.2D.D34.E48.D2.D$114.D2.D84.D.D$114.D.D86.D5.2E25.2D$115.D5.
2E25.2D58.E2.E23.D2.D$120.E2.E23.D2.D57.E.E24.D.D$120.E.E24.D.D56.2E.
E23.2D.D$118.2E.E23.2D.D56.E2.E23.D2.D$117.E2.E23.D2.D57.E.E24.D.D$
117.E.E24.D.D59.E26.D5.2E$118.E26.D5.2E85.E2.E$150.E2.E84.E.E$150.E.E
66.2D15.2E.E$131.2D15.2E.E66.D2.D13.E2.E$130.D2.D13.E2.E67.D.D14.E.E$
130.D.D14.E.E66.2D.D16.E$128.2D.D16.E66.D2.D$127.D2.D84.D.D$127.D.D
86.D5.2E$128.D5.2E85.E2.E$133.E2.E84.E.E$133.E.E48.2D33.2E.E$96.2D33.
2E.E48.D2.D31.E2.E$95.D2.D31.E2.E49.D.D32.E.E$95.D.D32.E.E48.2D.D34.E
$93.2D.D34.E48.D2.D$92.D2.D84.D.D$92.D.D86.D5.2E25.2D$93.D5.2E25.2D
58.E2.E23.D2.D$98.E2.E23.D2.D57.E.E24.D.D$98.E.E24.D.D56.2E.E23.2D.D$
96.2E.E23.2D.D56.E2.E23.D2.D$95.E2.E23.D2.D57.E.E24.D.D$95.E.E24.D.D
59.E26.D5.2E$96.E26.D5.2E85.E2.E$128.E2.E84.E.E$128.E.E66.2D15.2E.E$
109.2D15.2E.E66.D2.D13.E2.E$108.D2.D13.E2.E67.D.D14.E.E$108.D.D14.E.E
66.2D.D16.E$106.2D.D16.E66.D2.D$105.D2.D84.D.D$105.D.D86.D5.2E$106.D
5.2E85.E2.E$111.E2.E84.E.E$111.E.E48.2D33.2E.E$74.2D33.2E.E48.D2.D31.
E2.E$73.D2.D31.E2.E49.D.D32.E.E$73.D.D32.E.E48.2D.D34.E$71.2D.D34.E
48.D2.D$70.D2.D84.D.D$70.D.D86.D5.2E25.2D$71.D5.2E25.2D58.E2.E23.D2.D
$76.E2.E23.D2.D57.E.E24.D.D$76.E.E24.D.D56.2E.E23.2D.D$74.2E.E23.2D.D
56.E2.E23.D2.D$73.E2.E23.D2.D57.E.E24.D.D$73.E.E24.D.D59.E26.D5.2E$
74.E26.D5.2E85.E2.E$106.E2.E84.E.E$106.E.E66.2D15.2E.E$87.2D15.2E.E
66.D2.D13.E2.E$86.D2.D13.E2.E67.D.D14.E.E$86.D.D14.E.E66.2D.D16.E$84.
2D.D16.E66.D2.D$83.D2.D84.D.D$83.D.D86.D5.2E$84.D5.2E85.E2.E$89.E2.E
84.E.E$89.E.E48.2D33.2E.E$87.2E.E48.D2.D31.E2.E$86.E2.E49.D.D32.E.E$
86.E.E48.2D.D34.E$87.E48.D2.D$136.D.D$137.D5.2E25.2D$142.E2.E23.D2.D$
142.E.E24.D.D$140.2E.E23.2D.D$139.E2.E23.D2.D$139.E.E24.D.D$140.E26.D
5.2E$172.E2.E$172.E.E$153.2D15.2E.E$152.D2.D13.E2.E$152.D.D14.E.E$
150.2D.D16.E$149.D2.D$149.D.D$150.D5.2E$155.E2.E$155.E.E$118.2D33.2E.
E$117.D2.D31.E2.E$117.D.D32.E.E$115.2D.D34.E$114.D2.D$114.D.D$115.D5.
2E25.2D$120.E2.E23.D2.D$120.E.E24.D.D$118.2E.E23.2D.D$117.E2.E23.D2.D
$117.E.E24.D.D$118.E26.D5.2E$150.E2.E$150.E.E$131.2D15.2E.E$130.D2.D
13.E2.E$130.D.D14.E.E$128.2D.D16.E$127.D2.D$127.D.D$128.D5.2E$133.E2.
E$133.E.E$131.2E.E$130.E2.E$130.E.E$131.E56$127.2D$126.D2.D$126.D.D$
124.2D.D$123.D2.D$123.D.D$124.D5.2C$129.C2.C$129.C.C$127.2C.C$126.C2.
C9.2D$126.C.C9.D2.D$127.C10.D.D$136.2D.D$135.D2.D$135.D.D$136.D5.2C$
141.C2.C$141.C.C$122.2D15.2C.C$121.D2.D13.C2.C$121.D.D14.C.C$119.2D.D
16.C$118.D2.D$118.D.D$119.D5.2C22.2D$124.C2.C20.D2.D$124.C.C21.D.D$
122.2C.C20.2D.D$121.C2.C20.D2.D$121.C.C21.D.D$122.C23.D5.2C$151.C2.C$
133.2D16.C.C$132.D2.D13.2C.C$132.D.D13.C2.C$130.2D.D14.C.C$129.D2.D
16.C$129.D.D$130.D5.2C$135.C2.C$135.C.C$133.2C.C$132.C2.C$132.C.C$
133.C6$78.2D$77.D2.D$77.D.D$75.2D.D$74.D2.D$74.D.D$75.D5.2C$80.C2.C$
80.C.C$78.2C.C$77.C2.C9.2D$77.C.C9.D2.D$78.C10.D.D$87.2D.D$86.D2.D$
86.D.D$87.D5.2C$92.C2.C$92.C.C$73.2D15.2C.C$72.D2.D13.C2.C$72.D.D14.C
.C$70.2D.D16.C$69.D2.D$69.D.D29.2D$70.D5.2C22.D2.D$75.C2.C21.D.D$75.C
.C20.2D.D$73.2C.C20.D2.D$72.C2.C21.D.D$72.C.C23.D5.2C$73.C29.C2.C$
103.C.C$84.2D15.2C.C$83.D2.D13.C2.C$83.D.D14.C.C$81.2D.D16.C$80.D2.D$
80.D.D$81.D5.2C$86.C2.C$86.C.C$84.2C.C$83.C2.C$83.C.C$84.C6$29.2D$28.
D2.D$28.D.D$26.2D.D$25.D2.D$25.D.D$26.D5.2C$31.C2.C$31.C.C$29.2C.C$
28.C2.C$28.C.C9.2D$29.C9.D2.D$39.D.D$37.2D.D$36.D2.D$36.D.D$37.D5.2C$
42.C2.C$24.2D16.C.C$23.D2.D13.2C.C$23.D.D13.C2.C$21.2D.D14.C.C$8.2D
10.D2.D16.C$7.D2.D9.D.D$7.D.D11.D5.2C22.2D$5.2D.D17.C2.C20.D2.D$4.D2.
D18.C.C21.D.D$4.D.D17.2C.C20.2D.D$5.D5.2E10.C2.C20.D2.D$10.E2.E9.C.C
21.D.D$10.E.E11.C23.D5.2C$8.2E.E41.C2.C$7.E2.E24.2D16.C.C$7.E.E24.D2.
D13.2C.C$8.E25.D.D13.C2.C$32.2D.D14.C.C$31.D2.D16.C$15.2D14.D.D$14.D
2.D14.D5.2C$14.D.D20.C2.C$12.2D.D21.C.C$11.D2.D20.2C.C$11.D.D20.C2.C$
12.D5.2E14.C.C$17.E2.E14.C$17.E.E$15.2E.E$14.E2.E$14.E.E$15.E$4.2D$3.
D2.D$3.D.D$.2D.D$D2.D$D.D$.D5.2E$6.E2.E$6.E.E$4.2E.E$3.E2.E$3.E.E$4.E!

Here three trails in the southeast happen to have a nice cleanup -- the yellow half-bakeries in the far south -- leaving one trail that needs guarding. Not too bad -- but what can we do with the northwest trails?

If we add a huge delay to the northwest gliders as shown above, we can add extra rakes in the southeast to shoot down some of those gliders -- well, one of them, that I've found so far. The others need more work; there certainly doesn't seem to be any guarantee that the timing will work out for all of them.

I also looked at having some of the NW trails generate internal NW or SE gliders to shoot down gliders on some of the other trails. That idea didn't work on its own, at least for this intermediate-pond recipe, but I haven't tried combining it with support from rakes in the far SE. And I haven't tried any of the dozens of other recipes. Way too many possibilities...!
dvgrn
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Posts: 3361
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Half-bakery reaction with glider

Postby dvgrn » June 19th, 2014, 8:04 pm

dvgrn wrote:Maybe it makes sense to try all the workable Herschel-based recipes, concentrating on finding an efficient absorber for the six northwest gliders -- on the theory that the four gliders in the southeast can probably be adjusted into a good absorber, one way or another.

Wait a minute! The minimum number of half-bakery trails is nine, not ten:

#C 9-glider rake #1 (i.e., 9 synchronized gliders needed)
#C One glider from the northwest and three gliders from the southeast
#C -- one trail cheaper, and the SEmost trails are very adjustable.
#C The trails are now labeled A, B, C, D to match the next post.
x = 219, y = 226, rule = B3/S23
88bo$87bo$87b3o16$106bo$106bobo$106b2o12$84bobo$84b2o$85bo6$199bo$197b
2o$198b2o12$176bo$176bobo$176b2o29$4b2o$3bo2bo$3bobo$b2obo$o2bo$obo$bo
32b2o$33bo2bo$33bobo$31b2obo$30bo2bo$30bobo$31bo156bo$188bobo$18b2o
168b2o$17bo2bo$17bobo$15b2obo$14bo2bo$14bobo$15bo5$6bo$5bobo158bobo$4b
o3bo157b2o$4bo3bo158bo$4bo3bo$4b5o$4bo3bo$4bo3bo8$218bo$216b2o$217b2o
12$195bo$195bobo$195b2o24$74b2o$73bo2bo$73bobo$71b2obo$70bo2bo$70bobo
43b2o$71bo43bo2bo$115bobo$58b2o53b2obo$57bo2bo51bo2bo$57bobo52bobo$55b
2obo54bo$54bo2bo$54bobo43b2o$55bo43bo2bo$99bobo$97b2obo$96bo2bo$96bobo
$97bo$46b3o$45bo3bo$45bo$45bo$45bo$45bo3bo$46b3o2$83b5o$84bo3bo$84bo3b
o$84b4o$84bo3bo$84bo3bo$83b5o$143b2o$142bo2bo$142bobo$140b2obo$139bo2b
o$139bobo$140bo2$127b2o$126bo2bo$126bobo$124b2obo$123bo2bo$123bobo$
124bo5$108b5o$109bo3bo$109bo3bo$109bo3bo$109bo3bo$109bo3bo$108b5o!

Unless there's some serious disadvantage that I'm not seeing, this looks like a good reaction to use as a standard HBK rake unit. EDIT: Here's the minimum spacing for the three "A" trails on the NW edge and the six "B", "C", and "D" trails on the SE edge -- the distance between is adjustable, of course, and the last two trails to the SE ("D") can be delayed as far as needed and can also move up by one or two lanes:

#C minimum spacing for 9-glider rake #1
x = 211, y = 213, rule = B3/S23
88bo$87bo$87b3o16$106bo$106bobo$106b2o12$84bobo$84b2o$85bo14$191bo$
189b2o$190b2o12$168bo$168bobo$168b2o21$4b2o$3bo2bo$3bobo204bo$b2obo
203b2o$o2bo176bo28b2o$obo177bobo$bo32b2o144b2o$33bo2bo$33bobo$31b2obo$
30bo2bo$30bobo$31bo2$18b2o$17bo2bo$17bobo167bo$15b2obo168bobo$14bo2bo
140bobo26b2o$14bobo141b2o$15bo143bo5$6bo$5bobo$4bo3bo$4bo3bo$4bo3bo$4b
5o$4bo3bo$4bo3bo45$108b2o$107bo2bo$107bobo$74b2o29b2obo$73bo2bo27bo2bo
$73bobo28bobo$71b2obo30bo$70bo2bo$70bobo19b2o$71bo19bo2bo$91bobo$58b2o
29b2obo$57bo2bo27bo2bo$57bobo28bobo$55b2obo30bo$54bo2bo62b2o$54bobo62b
o2bo$55bo63bobo$117b2obo$116bo2bo$116bobo$117bo2$46b3o26b5o24b2o$45bo
3bo26bo3bo22bo2bo$45bo30bo3bo22bobo$45bo30b4o21b2obo$45bo30bo3bo19bo2b
o$45bo3bo26bo3bo19bobo$46b3o26b5o21bo15$75b5o$76bo3bo$76bo3bo$76bo3bo$
76bo3bo$76bo3bo$75b5o!

There are a few faster timing adjustments that also work for the D glider, knocking out the block before the output glider comes along.

The next big challenge is to minimize the number of guard trails. I'm kind of betting on one guard trail on each side, but I'd be happy with less... I'm sure we haven't thought of all the possible tricks yet for stopping those nine gliders in a (-3,-6)-compatible way.

Let's find something good: once that's done we can start putting the splitters and turners together at the front end. After that, it will be fairly straightforward to put together slow-salvo recipes to rebuild those multi-glider seeds -- and then after a quick run of a compiler script, the Half-Baked Knightship will be complete!

I haven't done a gencols search yet to make sure that there's no clean three-glider solution along the above lines (shooting past a glider-generating half-bakery pair, instead of through the middle). I did find this alternate recipe with the Seeds of Destruction Game:

#C Seeds of Destruction
#C interesting but not HBK-compatible cleanup of B-heptomino
x = 132, y = 106, rule = B3/S23
o$b2o$2o47$78b3o$78bo$79bo3$61bo$60b2o$60bobo47$129b3o$129bo$130bo!

-- it isn't quite half-bakery-compatible, but it shows that something like this might just barely be possible.
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Re: Half-bakery reaction with glider

Postby codeholic » June 20th, 2014, 1:56 am

dvgrn wrote:Unless there's some serious disadvantage that I'm not seeing, this looks like a good reaction to use as a standard HBK rake unit.

A disadvantage I see is that the interim product is not periodic, therefore it reduces degrees of freedom for arranging half-bakery tracks, which is bad not only for absorbers, but also for shooting down gliders from parallel tracks.

In the meantime I realised, that I gave up absorbers too early, because I disregarded another degree of freedom, that is given, when one uses a glider emitter with a periodic interim product, because then you can move half-bakeries not only along NW-SE axis, but also along NE-SW, while shooting at a previously created interim product.
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Re: Half-bakery reaction with glider

Postby dvgrn » June 20th, 2014, 4:24 am

codeholic wrote:
dvgrn wrote:Unless there's some serious disadvantage that I'm not seeing, this looks like a good reaction to use as a standard HBK rake unit.

A disadvantage I see is that the interim product is not periodic, therefore it reduces degrees of freedom for arranging half-bakery tracks, which is bad not only for absorbers, but also for shooting down gliders from parallel tracks.

Is it an absolute loss in the total number of degrees of freedom, though? For any of these four-glider reactions, let's label the input gliders A, B, C, and D from NW to SE. If we use 10 synchronized input gliders to produce a recipe with a periodic intermediate target (either P1 or P2), then B collides with C and A collides with D. Taking A's spacetime location as a given, you have a degree of freedom with the timing of B. But then once you decide on the width of the shooting range, C and D are fixed.

For each trail individually, you also have the option of moving the half-bakeries along the NW/SE axis, and then adjusting the timing of that trail's input glider so that the actual spacetime locations of the A, B, C, and D gliders comes out the same. But that type of adjustment is equally available for any recipe.

I've gone back to the previous post and labeled the recipe gliders in the sample patterns. Here's another option with 9 synchronized input gliders:

#C HBK 9-glider rake #2, with labeled A, B, C, D gliders
x = 242, y = 192, rule = B3/S23
39bo$37b2o$38b2o7$239bobo$239b2o$240bo7$56bobo$56b2o$57bo2$218bo$217bo
$217b3o7$35bo$34bo$34b3o2$4b2o$3bo2bo$3bobo$b2obo$o2bo$obo$bo32b2o$33b
o2bo$33bobo$31b2obo$30bo2bo$30bobo$31bo2$18b2o$17bo2bo$17bobo$15b2obo$
14bo2bo$14bobo$15bo5$6bo$5bobo$4bo3bo$4bo3bo$4bo3bo$4b5o$4bo3bo$4bo3bo
15$192bobo$192b2o$193bo11$171bo$170bo$170b3o22$186bobo$186b2o$187bo10$
118b2o$117bo2bo44bo$117bobo44bo$115b2obo45b3o$114bo2bo$114bobo$115bo2$
102b2o$101bo2bo$101bobo$99b2obo$98bo2bo$98bobo$99bo8$80b5o$81bo3bo$81b
o3bo$81bo3bo$81bo3bo$81bo3bo$80b5o2$145b2o$144bo2bo$144bobo$142b2obo$
110b2o29bo2bo$109bo2bo28bobo$109bobo30bo$107b2obo$106bo2bo19b2o$106bob
o19bo2bo$107bo20bobo$126b2obo$94b2o29bo2bo$93bo2bo28bobo$93bobo30bo$
91b2obo$90bo2bo$90bobo$91bo6$82b3o31b5o$81bo3bo31bo3bo$81bo35bo3bo$81b
o35b4o$81bo35bo3bo$81bo3bo31bo3bo$82b3o31b5o!

Like the previous 9-trail pattern, A collides with B, and then C collides with the product. No degrees of freedom there, once you decide on a shooting-range width. But D now has two degrees of freedom -- temporal and spatial: it can be delayed arbitrarily, and the D half-bakeries and input gliders can also be moved up either one or two cells.

On the temporal side, the D glider can also be advanced by up to 101 ticks, so it could actually hit its target block before the C glider hits. Let's still call it the D glider in that case!

codeholic wrote:In the meantime I realised, that I gave up absorbers too early, because I disregarded another degree of freedom, that is given, when one uses a glider emitter with a periodic interim product, because then you can move half-bakeries not only along NW-SE axis, but also along NE-SW, while shooting at a previously created interim product.

It's certainly possible that the two degrees of freedom for the D trails in these 9-glider options won't make up for some 10-glider option's lucky advantage in timing. All other things being equal, though, 9 is better than 10. Let's add a few guard trails to any promising recipe and look for a clean configuration. At this point, the winner will be the option with the smallest total number of synchronized input gliders, including guards.

EDIT: Rake #1 seems promising so far. At least, there are ways to shoot down all three A gliders cleanly, without even trying to hit a half-bakery reaction in mid-shift:

x = 453, y = 480, rule = LifeHistory
330.C$329.C$329.3C16$348.C$348.C.C$348.2C12$326.C.C$326.2C$327.C14$
433.C$431.2C$432.2C12$410.C$410.C.C$410.2C18$263.C$262.C.C$261.C3.C$
246.2C13.C3.C$245.C2.C12.C3.C$245.C.C13.5C186.C$243.2C.C14.C3.C184.2C
$242.C2.C15.C3.C156.C28.2C$242.C.C177.C.C$243.C32.2C144.2C$275.C2.C$
275.C.C$273.2C.C$272.C2.C$272.C.C$273.C2$260.2C$259.C2.C$259.C.C167.C
$257.2C.C168.C.C$256.C2.C140.C.C26.2C$256.C.C141.2C$257.C143.C3$225.
2E$224.E2.E$224.E.E$222.2E.E$221.E2.E$221.E.E$222.E32.2E$254.E2.E$
254.E.E$252.2E.E$251.E2.E$251.E.E$252.E3$238.2E$237.E2.E$237.E.E$235.
2E.E$234.E2.E$234.E.E$235.E3$203.2E$202.E2.E$202.E.E$200.2E.E$199.E2.
E$199.E.E$200.E32.2E$232.E2.E$232.E.E$230.2E.E$229.E2.E$229.E.E$230.E
3$216.2E$215.E2.E$215.E.E$213.2E.E$212.E2.E$212.E.E$213.E3$181.2E$
180.E2.E$180.E.E$178.2E.E$177.E2.E$177.E.E$178.E32.2E137.2C$210.E2.E
135.C2.C$210.E.E136.C.C$208.2E.E104.2C29.2C.C$207.E2.E104.C2.C27.C2.C
$207.E.E105.C.C28.C.C$208.E104.2C.C30.C$312.C2.C$312.C.C19.2C$194.2E
117.C19.C2.C$193.E2.E136.C.C$193.E.E104.2C29.2C.C$191.2E.E104.C2.C27.
C2.C$190.E2.E105.C.C28.C.C$190.E.E104.2C.C30.C$191.E104.C2.C62.2C$
296.C.C62.C2.C$297.C63.C.C$159.2E198.2C.C$158.E2.E196.C2.C$158.E.E
197.C.C$156.2E.E199.C$155.E2.E$155.E.E130.3C26.5C24.2C$156.E32.2E96.C
3.C26.C3.C22.C2.C$188.E2.E95.C30.C3.C22.C.C$188.E.E96.C30.4C21.2C.C$
186.2E.E97.C30.C3.C19.C2.C$185.E2.E98.C3.C26.C3.C19.C.C$185.E.E100.3C
26.5C21.C$186.E3$172.2E$171.E2.E$171.E.E$169.2E.E$168.E2.E$168.E.E$
169.E3$137.2E$136.E2.E$136.E.E178.5C$134.2E.E180.C3.C$133.E2.E181.C3.
C$133.E.E182.C3.C$134.E32.2E149.C3.C$166.E2.E148.C3.C$166.E.E148.5C$
164.2E.E$163.E2.E$163.E.E$164.E3$150.2E$149.E2.E$149.E.E$147.2E.E$
146.E2.E$146.E.E$147.E3$115.2E$114.E2.E$114.E.E$112.2E.E$111.E2.E$
111.E.E$112.E32.2E$144.E2.E$144.E.E$142.2E.E$141.E2.E$141.E.E$142.E3$
128.2E$127.E2.E$127.E.E$125.2E.E$124.E2.E$124.E.E$125.E3$93.2E$92.E2.
E$92.E.E$90.2E.E$89.E2.E$89.E.E$90.E32.2E$122.E2.E$122.E.E$120.2E.E$
119.E2.E$119.E.E$120.E3$106.2E$105.E2.E$105.E.E$103.2E.E$102.E2.E$
102.E.E$103.E3$71.2E$70.E2.E$70.E.E$68.2E.E$67.E2.E$67.E.E$68.E32.2E$
100.E2.E$100.E.E$98.2E.E$97.E2.E$97.E.E$98.E3$84.2E$83.E2.E$83.E.E$
81.2E.E$80.E2.E$80.E.E$81.E9$79.2E$78.E2.E$78.E.E$76.2E.E$75.E2.E$75.
E.E$76.E3$62.2E$61.E2.E$61.E.E$59.2E.E$58.E2.E$58.E.E$59.E8$50.2E$49.
E2.E$49.E.E$47.2E.E$46.E2.E$46.E.E$47.E11$35.2E$34.E2.E$34.E.E$32.2E.
E$31.E2.E$31.E.E$32.E6$25.2E$24.E2.E$24.E.E$22.2E.E$21.E2.E$21.E.E$
22.E23$127.2E$126.E2.E$126.E.E$124.2E.E$123.E2.E$123.E.E$124.E2$111.
2E$110.E2.E$110.E.E$108.2E.E$107.E2.E$107.E.E$108.E12$128.2E$127.E2.E
$127.E.E$125.2E.E$124.E2.E$124.E.E$125.E2$112.2E$111.E2.E$111.E.E$
109.2E.E$108.E2.E$108.E.E$109.E5$51.2A$50.A2.A$50.A.A$48.2A.A$47.A2.A
$47.A.A$48.A2$103.2E$102.E2.E$33.2A67.E.E$32.A2.A64.2E.E$32.A.A64.E2.
E$30.2A.A65.E.E$29.A2.A67.E$29.A.A$30.A56.2E$86.E2.E$86.E.E$65.2A17.
2E.E$64.A2.A15.E2.E$64.A.A16.E.E$62.2A.A18.E$61.A2.A$61.A.A$62.A3$48.
2A$47.A2.A$47.A.A$45.2A.A$21.2A21.A2.A$20.A2.A20.A.A$20.A.A22.A$18.2A
.A$17.A2.A$17.A.A$18.A3$4.2A$3.A2.A$3.A.A$.2A.A$A2.A$A.A$.A!

Really I should probably have looked at the BCD side first, though. D's timing or spacing can be adjusted to make pretty much any single annihilation reaction work -- but it will be important to choose D so that it solves the largest number of problems simultaneously.

That very likely means we should clean up everything on the A side using only B and C, if possible. Then adjust D to allow it to clean up B and C and any leftover A gliders... and finally put a guard on D, and we're done! Theoretically.
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Re: Half-bakery reaction with glider

Postby dvgrn » June 20th, 2014, 7:31 am

dvgrn wrote:That very likely means we should clean up everything on the A side using only B and C, if possible. Then adjust D to allow it to clean up B and C and any leftover A gliders... and finally put a guard on D, and we're done! Theoretically.

I tried out my theory on Rake #2, and it worked okay, more or less. The problem with Rake #2 is that the D glider is NW of the B and C gliders. You can adjust D so that B or C can clean it up, but I don't see how adjustments to D can help clean up B and C. Haven't looked at changing D's color yet, though -- and that would allow kickbacks...!

Meanwhile, here's a cleanup of Rake #2 that seems to allow an 11-glider synchronized salvo:

x = 637, y = 635, rule = LifeHistory
440.A$438.2A$439.2A12$635.A$634.A$634.3A2$457.A.A$457.2A$458.A8$614.A
$612.2A$613.2A$436.A$422.C12.A$421.C.C11.3A$420.C3.C$405.2C13.C3.C$
404.C2.C12.C3.C$404.C.C13.5C$402.2C.C14.C3.C$401.C2.C15.C3.C$401.C.C$
402.C32.2C$434.C2.C$434.C.C$432.2C.C$431.C2.C$431.C.C$432.C2$419.2C$
418.C2.C$418.C.C$416.2C.C$415.C2.C$415.C.C$416.C3$384.2E$383.E2.E$
383.E.E$381.2E.E$380.E2.E$380.E.E$381.E32.2E$413.E2.E$413.E.E$411.2E.
E$410.E2.E$410.E.E$411.E3$397.2E$396.E2.E$396.E.E$394.2E.E$393.E2.E$
393.E.E$394.E3$362.2E229.A.A$361.E2.E228.2A$361.E.E230.A$359.2E.E$
358.E2.E$358.E.E$359.E32.2E$391.E2.E$391.E.E$389.2E.E$388.E2.E$388.E.
E$389.E$572.A$571.A$375.2E194.3A$374.E2.E$374.E.E$372.2E.E$371.E2.E$
371.E.E$372.E3$340.2E$339.E2.E$339.E.E$337.2E.E$336.E2.E$336.E.E$337.
E32.2E$369.E2.E$369.E.E$367.2E.E$366.E2.E$366.E.E$367.E$587.A.A$587.
2A$353.2E233.A$352.E2.E$352.E.E$350.2E.E$349.E2.E$349.E.E$350.E3$318.
2E$317.E2.E198.2C$317.E.E198.C2.C44.A$315.2E.E199.C.C44.A$314.E2.E
198.2C.C45.3A$314.E.E198.C2.C$315.E32.2E165.C.C$347.E2.E165.C$347.E.E
$345.2E.E154.2C$344.E2.E154.C2.C$344.E.E155.C.C$345.E154.2C.C$499.C2.
C$499.C.C$331.2E167.C$330.E2.E$330.E.E$328.2E.E$327.E2.E$327.E.E$328.
E2$481.5C$296.2E184.C3.C$295.E2.E183.C3.C$295.E.E184.C3.C$293.2E.E
185.C3.C$292.E2.E186.C3.C$292.E.E186.5C$293.E32.2E$325.E2.E217.2C$
325.E.E217.C2.C$323.2E.E218.C.C$322.E2.E217.2C.C$322.E.E186.2C29.C2.C
$323.E186.C2.C28.C.C$510.C.C30.C$508.2C.C$309.2E196.C2.C19.2C$308.E2.
E195.C.C19.C2.C$308.E.E197.C20.C.C$306.2E.E217.2C.C$305.E2.E186.2C29.
C2.C$305.E.E186.C2.C28.C.C$306.E187.C.C30.C$492.2C.C$491.C2.C$274.2E
215.C.C$273.E2.E215.C$273.E.E$271.2E.E$270.E2.E$270.E.E$271.E32.2E$
303.E2.E176.3C31.5C$303.E.E176.C3.C31.C3.C$301.2E.E177.C35.C3.C$300.E
2.E178.C35.4C$300.E.E179.C35.C3.C$301.E180.C3.C31.C3.C$483.3C31.5C2$
287.2E$286.E2.E$286.E.E$284.2E.E$283.E2.E$283.E.E$284.E3$252.2E$251.E
2.E$251.E.E$249.2E.E$248.E2.E$248.E.E$249.E32.2E$281.E2.E$281.E.E$
279.2E.E$278.E2.E$278.E.E$279.E3$265.2E$264.E2.E$264.E.E$262.2E.E$
261.E2.E$261.E.E$262.E3$230.2E$229.E2.E$229.E.E$227.2E.E$226.E2.E$
226.E.E$227.E32.2E$259.E2.E$259.E.E$257.2E.E$256.E2.E$256.E.E$257.E3$
243.2E$242.E2.E$242.E.E$240.2E.E$239.E2.E$239.E.E$240.E3$208.2E$207.E
2.E$207.E.E$205.2E.E$204.E2.E$204.E.E$205.E32.2E$237.E2.E$237.E.E$
235.2E.E$234.E2.E$234.E.E$235.E3$221.2E$220.E2.E$220.E.E$218.2E.E$
217.E2.E$217.E.E$218.E3$186.2E$185.E2.E$185.E.E$183.2E.E$182.E2.E$
182.E.E$183.E32.2E$215.E2.E$215.E.E$213.2E.E$212.E2.E$212.E.E$213.E3$
199.2E$198.E2.E$198.E.E$196.2E.E$195.E2.E$195.E.E$196.E3$164.2E$163.E
2.E$163.E.E$161.2E.E$160.E2.E$160.E.E$161.E32.2E$193.E2.E$193.E.E$
191.2E.E$190.E2.E$190.E.E$191.E3$177.2E$176.E2.E$176.E.E$174.2E.E$
173.E2.E$173.E.E$174.E3$142.2E$141.E2.E$141.E.E$139.2E.E$138.E2.E$
138.E.E$139.E32.2E$171.E2.E$171.E.E$169.2E.E$168.E2.E$168.E.E$169.E2$
130.2E$129.E2.E22.2E$129.E.E22.E2.E$127.2E.E23.E.E$126.E2.E22.2E.E$
126.E.E22.E2.E$127.E23.E.E$152.E17$108.2E$107.E2.E22.2E$107.E.E22.E2.
E$105.2E.E23.E.E$104.E2.E22.2E.E$104.E.E22.E2.E$105.E23.E.E$130.E17$
86.2E$85.E2.E$85.E.E$83.2E.E$82.E2.E$82.E.E$83.E18$64.2E$63.E2.E$63.E
.E$61.2E.E$60.E2.E$60.E.E$61.E26$238.2E$237.E2.E$237.E.E$235.2E.E$
234.E2.E$234.E.E$235.E2$222.2E$221.E2.E$221.E.E$219.2E.E$218.E2.E$
218.E.E$219.E14$241.2E$240.E2.E$4.2E234.E.E$3.E2.E231.2E.E$3.E.E231.E
2.E$.2E.E232.E.E$E2.E234.E$E.E202.2E$.E202.E2.E17.2E$204.E.E17.E2.E$
202.2E.E18.E.E$201.E2.E17.2E.E$201.E.E17.E2.E$202.E18.E.E$222.E2$188.
2E$187.E2.E$187.E.E$185.2E.E$184.E2.E$184.E.E$185.E6$215.2E$214.E2.E$
214.E.E$212.2E.E$211.E2.E$211.E.E$212.E2$178.2E$177.E2.E17.2E$177.E.E
17.E2.E$175.2E.E18.E.E$174.E2.E17.2E.E$174.E.E17.E2.E$175.E18.E.E$
195.E2$161.2E$160.E2.E$160.E.E$158.2E.E$157.E2.E$157.E.E$158.E8$186.
2E$185.E2.E$185.E.E$183.2E.E$182.E2.E$182.E.E$183.E$150.2E$149.E2.E$
149.E.E17.2E$115.2E30.2E.E17.E2.E$114.E2.E28.E2.E18.E.E$114.E.E29.E.E
17.2E.E$112.2E.E31.E17.E2.E$111.E2.E50.E.E$111.E.E52.E$112.E20.2E$
132.E2.E$132.E.E$98.2E30.2E.E$97.E2.E28.E2.E$97.E.E29.E.E$95.2E.E31.E
$94.E2.E$94.E.E$95.E8$155.2E$154.E2.E$154.E.E$152.2E.E$151.E2.E$151.E
.E$152.E$119.2E$118.E2.E$118.E.E17.2E$116.2E.E17.E2.E$115.E2.E18.E.E$
115.E.E17.2E.E$73.2E41.E17.E2.E$72.E2.E58.E.E$72.E.E28.2E30.E$70.2E.E
28.E2.E$69.E2.E29.E.E$69.E.E28.2E.E$70.E28.E2.E$99.E.E$100.E39$97.2E$
96.E2.E$96.E.E$94.2E.E$93.E2.E$93.E.E$94.E2$81.2E$80.E2.E$80.E.E$78.
2E.E$77.E2.E$77.E.E$78.E!

A guard glider for each of the B and C glider pairs would make 11, right? But I bet somebody can improve on this. Rake #1 has the D trail to the southeast of B and C, so it seems likely that there's a cleanup of Rake #1 that needs only a single guard glider on D -- 10 trails total. Possibly even just 9, if someone can come up with a new trick or two.
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Re: Half-bakery reaction with glider

Postby simsim314 » June 20th, 2014, 8:42 am

I've a small modification to the plan:

1. Use a thin universal constructor, that requires 3-4 different lanes for all operations.
2. Use unique A-B-C-D construction for each lane.
3. Using universal constructor, we can make dry salvo of the 9-glider combinations for the next step. This only requires about 40 dried gliders, which will be build with universal slow salvo thin constructor.

I was trying to optimize universal construction lanes. The best I really came up with is (although I vaguely remember dvgrn had posted some improvement over it):

x = 128, y = 106, rule = LifeHistory
4$58.2A3.3A$58.2A3.A$64.A$61.2D$61.2D8$65.3A$65.A$66.A6$38.2A$38.2A3$
42.2D2.3A$42.2D2.A$47.A13$17.2D10.2F$17.D2A10.F23.3A6.3A$18.2A34.A8.A
$55.A8.A$18.A$17.2A$17.A.A10$27.2A51.3A$27.A.A50.A$27.A13.2A38.A$40.
2A$42.A4$44.2A$43.2A$35.3A7.A$35.A$36.A13.A$49.2A$49.A.A4$93.3A$93.A$
94.A3$98.3A$98.A$99.A5$106.3A$106.A$107.A3$112.3A$112.A$113.A!


But we know that push-pull can be done with only two lanes, so it looks promising direction:

x = 522, y = 291, rule = LifeHistory
44$65.3A297.3A2$63.A5.A293.A5.A$63.A5.A293.A5.A$63.A5.A293.A5.A2$65.
3A297.3A53$128.A299.A$127.2A298.2A$127.A.A297.A.A59$187.3A296.3A$187.
A298.A$188.A298.A57$246.A$245.2A$245.A.A!
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Re: Half-bakery reaction with glider

Postby dvgrn » June 20th, 2014, 12:33 pm

simsim314 wrote:I've a small modification to the plan:

1. Use a thin universal constructor, that requires 3-4 different lanes for all operations.
2. Use unique A-B-C-D construction for each lane.
3. Using universal constructor, we can make dry salvo of the 9-glider combinations for the next step. This only requires about 40 dried gliders, which will be build with universal slow salvo thin constructor.

The current plan involves reducing the number of half-bakery trails to the bare minimum needed to build universal slow salvos (currently 11, including two "guard trails"). These NEward gliders will use adjustable elbows to fire gliders SE and NW to rebuild and trigger a freeze-dried 11-glider seed at the NE end of the ship.

Let's see if I understand this new proposal correctly. The idea is to increase the number of half-bakery trails until we can build synchronized triplets or quadruplets of northeast-traveling gliders -- is that right?

The advantage of using synchronized gliders would be that you get exactly the combinations of gliders you want, as fast as you can build them; theoretically you could pack the rakes as tightly together as the half-bakery reaction allows.

Here are some notes on why I don't think this will work very well for a knightship using half-bakeries:

- Three synchronized gliders would need about 30 trails, and four would need 40 trails. (Please correct me if I go wrong here.) It might be hard to find a universal set of elbow operations with just three gliders, especially because the available ABCD recipes will restrict where we can build multiple gliders close to each other.

- Synchronized salvos will only work if the elbow is drifting 2hd south and east with every operation, because that's how these strange half-bakery rakes work! I don't know if even four synchronized gliders can manage to make an elbow do this 2hd drifting trick. The alternative would be to do a reset after every glider, same as in the 9-trail design, but that would almost certainly make up for any efficiency gains from the synchronized method.

- Another disadvantage of synchronized gliders is that elbow movement wouldn't be very efficient, due to the limited number of operations. The elbow would have to be constrained to stay on a particular line, diagonal or oblique, and each operation would have to restore the elbow to the same state to accept the next synchronized salvo. In practice an N-glider synchronized salvo would allow a lot less than 2^N-N working ops, I think -- you might just find INC1, DEC1, BLACK and WHITE... and for this knightship to work we'll really need separate operations to shoot each color of glider left and right from the elbow.

- By contrast, the "slow elbow" method can convert any random piece of junk into an elbow target, and the target can drift around anywhere inside the wide 79hd shooting range without causing any particular problems, and we can shoot gliders to the left and the right equally well. If we're hitting multiple slow targets simultaneously, each elbow might be constrained to drift around inside about a 30hd diagonal stripe.

- A major disadvantage of doubling or tripling the number of trails is that each ABCD set will need a different custom way of suppressing the synchronized gliders coming out at the SW end. There might end up being standard ways to clean up any SW-traveling gliders using a small set of dedicated rakes on the SE side... but for the moment it's looking a lot easier to solve one specific suppression problem that's as simple as we can make it, for one particular minimal set of nine trails.

- The more half-bakery trails we have, the bigger the freeze-dried salvos will be that we'll need to build and rebuild at the NE end. The increase in recipe size will be something-or-other bigger than O(N), where N is the number of trails, because all the glider seeds have to be triggered in precise synchrony with each other. This will tend to require more and more "one-time wiring" as N increases. Also seeds with a larger area take proportionally more work to construct.

----------------------------------

Currently known recipes seem to indicate we can get a 90-degree glider out for about every 6 slow gliders that we shoot at a target -- three or four gliders to move the target to a good spot, and two or three more to extract a 90-degree glider. With the 9-trail system we can use only about one out of every 20 gliders that we could theoretically shoot, so that works out to about 100-150 half-bakeries in each trail for every 90-degree glider that we get from the elbows in the NE to do actual construction

(It would be more like 1:13 instead of 1:20 if we assume we're working with three elbows simultaneously and using P1 slow salvos -- but every now and then we'll have to skip taking a shot at one elbow or another, and reset to get the other phase of a glider on a particular lane.)

We might have to rebuild about a 50-still life seed to get our 9 synchronized gliders. Let's say 10 slow gliders are needed to build each still life, with 150 half-bakeries per still life. That give us 75,000 half-bakeries in each trail, more or less, and a bounding box of maybe 40x75K=3 million cells on a side.

That's going to be pretty big! So... have we missed anything? Or are my calculations badly off somehow? Is there another design that will allow for a significantly smaller knightship?

simsim314 wrote:I was trying to optimize universal construction lanes. The best I really came up with is (although I vaguely remember dvgrn had posted some improvement over it)...

The key improvement is the one I described above. With slow-elbow constructions, it's generally kind of a waste of gliders to move an elbow back to its exact original location -- or even to convert it back to the same type of object again. For the next sideways glider the elbow will have to move somewhere else anyway, and will go through all kinds of other object stages along the way. Might as well work directly from whatever junk is left over from the last sideways glider construction.

Each new output glider is buildable anywhere along its lane, so it will be a matter of hunting through lots of possible elbow moves to find the cheapest one. As we've discussed elsewhere, it will probably take some significant new search software to come up with longer slow-elbow salvos that are really optimal.
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