New construction arms

[simsim314]

As we all know, universal constructors use arms to move a block and fire gliders. There are now few designs of arms (opposite collision, original Gemini 4 gliders recipes, and 9hd-10hd designs used in dvgrn UC).

I suggest to explore other universal construction recipes and options in this thread.

I'll start from 0hd recipe list (depth 7), that seems to cover all universal options (push, pull, and two colors gliders):

Code: Select all

x = 8274, y = 1595, rule = LifeHistory
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1572.2C896.C2499.C1800.C298.C99.C$1571.2C$1573.C4599.3C$3075.2C497.3C
2596.C$1676.2C98.2C1098.2C196.2C498.C1001.2C98.2C97.3C97.3C998.2C98.
2C97.3C96.C1401.2C97.3C97.3C$1675.2C98.2C1098.2C199.C498.C999.2C98.2C
98.C99.C999.2C98.2C98.C1499.2C98.C99.C$1677.C99.C1099.C1699.C99.C98.C
99.C1000.C99.C98.C1500.C98.C99.C232$2411.C199.C599.C99.C299.C99.C399.
C99.C399.C99.C99.C99.C299.C399.C499.C99.C1199.C$2310.3C97.2C98.3C97.
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97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.2C98.3C97.3C97.3C97.3C97.3C97.
3C$2310.C99.C.C97.C99.C.C97.C99.C99.C99.C99.C99.C.C97.C.C97.C99.C99.C
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99.C99.C99.C99.C99.C99.C99.C99.C99.C99.C.C97.C99.C99.C99.C99.C99.C$
2311.C199.C199.C99.C99.C99.C99.C299.C99.C299.C99.C99.C299.C99.C99.C
499.C99.C199.C99.C99.C199.C99.C99.C99.C299.C99.C99.C99.C99.C99.C99.C
99.C99.C99.C99.C199.C99.C99.C99.C99.C99.C2$4116.C99.C399.C99.C599.C
99.C299.C$3117.C797.3C97.3C97.2C98.2C99.2C97.3C97.3C97.2C98.2C598.2C
98.2C98.3C197.2C1398.3C97.3C$2417.2C99.C98.2C98.2C99.C297.2C99.2C299.
C98.2C98.2C196.C99.C99.C.C97.C.C97.2C98.C99.C99.C.C97.C.C99.2C98.2C
99.C99.C196.C.C97.C.C97.C199.C.C1099.2C296.C99.C$2416.2C99.2C98.C.C
97.C.C97.2C297.C.C97.2C299.2C98.C.C96.2C198.C99.C300.C98.C99.C300.C.C
97.C.C97.2C98.2C397.C1300.C.C99.C98.2C96.C99.C$2418.C98.C.C97.C99.C
99.C.C398.C298.C.C97.C100.C1098.C99.C99.C.C97.C.C1399.2C98.2C98.2C96.
C100.2C97.2C$3419.3C2499.C596.2C99.C.C97.C.C196.C.C98.C$3419.C2500.2C
598.C98.C99.C$3420.C2499.C.C1400.C99.C$7322.2C98.2C199.2C$5223.3C
2096.C.C97.C.C197.2C$2925.2C2296.C401.2C198.2C1797.C$2925.C.C2296.C
399.2C199.C.C$2925.C2700.C198.C$6127.3C97.3C1698.2C98.2C$6127.C99.C
1699.2C98.2C$6128.C99.C1700.C99.C2$2332.2C697.3C298.2C498.2C2197.3C
297.3C98.2C1098.2C197.3C98.2C$2331.2C698.C299.2C498.2C2198.C299.C99.
2C1098.2C198.C99.2C$2333.C698.C300.C499.C2198.C299.C100.C1099.C198.C
100.C232$4367.C99.C399.C99.C299.C99.C299.C299.C199.C299.C99.C399.C99.
C199.C199.C99.C699.C$4166.3C97.3C97.2C98.2C98.3C97.3C97.3C97.2C98.2C
98.3C97.3C97.2C98.2C98.3C97.3C97.2C98.3C97.3C97.2C98.3C97.2C98.3C97.
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97.3C97.3C97.3C97.3C97.3C97.2C$4166.C99.C99.C.C97.C.C97.C99.C99.C99.C
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97.C99.C99.C99.C99.C99.C99.C.C$4167.C99.C299.C99.C99.C299.C99.C299.C
99.C199.C99.C199.C199.C99.C299.C99.C99.C299.C199.C299.C99.C99.C99.C
99.C99.C2$5472.C1999.C$5471.2C899.2C198.2C97.3C97.3C197.3C97.3C297.3C
97.2C600.C197.3C$4174.C98.2C98.2C98.2C98.2C99.C98.2C98.2C98.2C99.C98.
2C98.2C98.2C96.C.C699.2C196.2C199.C.C96.C99.C199.C99.C101.2C196.C99.C
.C598.2C197.C$4173.2C98.C.C97.C.C96.2C99.C.C97.2C98.C.C97.C.C96.2C99.
2C98.C.C97.C.C96.2C798.2C199.C198.C99.C99.C199.C99.C100.C.C98.2C96.C
301.2C396.C.C197.C$4173.C.C97.C99.C100.C98.C99.C.C97.C99.C100.C98.C.C
97.C99.C100.C799.C998.C100.C.C297.3C96.2C$7274.C299.C100.C$7575.C301.
2C$7877.C.C$7877.C$5681.C$5580.3C97.2C$5580.C99.C.C$5581.C701.2C1698.
2C$6282.2C1698.2C$5986.C297.C1699.C$5985.2C$5985.C.C$5788.2C98.2C198.
2C398.2C398.2C898.2C398.2C$5787.2C98.2C198.2C398.2C398.2C898.2C398.2C
$5789.C99.C199.C399.C399.C899.C399.C!

As a reference here is a design of G+H setup, that those recipes built for:

Code: Select all

x = 70, y = 41, rule = B3/S23
bo$2bo$3o4$15b2o$16bo$16bobo$17b2o3$33b2o$22b3o8bo$22bo8bobo$21b3o7b2o
5$45bo$35b2o6b3o$35bo6bo$33bobo6b2o$33b2o3$20b2o$19bobo$19bo25b2o$18b
2o25b2o$68b2o$68b2o2$22b2o$21bobo$21bo4b2o$20b2o5bo$24b3o5bo$24bo6bobo
$32bo!

And here is a script that generated all those recipes:

Code: Select all

import golly as g 
from copy import copy

gld = g.parse("3o$o$bo!")
blockDelta = 5

blck = g.parse("2o$2o!", 0, -blockDelta)

evolved = []

for i in xrange(0, 500):
	evolved.append(g.evolve(gld, i))

def EvolveRecipe(recipe):
	g.new("")
	g.setstep(4)
	
	g.putcells(blck)
	
	for r in recipe:
		g.putcells(evolved[r[0]], 30, 30)
		g.putcells(evolved[r[1]], 80, 80)
		g.step()
		g.step()	

def ValidRecipes(cells, existing, finalResult):
	
	result = []
	
	for i in xrange(0, 2):
		for r in xrange(200-85, 200 - 18):
		
			g.new("")
			g.putcells(cells)
			
			g.setstep(2)
	
			g.putcells(evolved[i], 30, 30)
			g.putcells(evolved[r], 80, 80)
			
			explode = False
			
			for l in xrange(8 * 6):
				g.step()
				if int(g.getpop()) > 140 or int(g.getpop()) == 0:
					explode = True
					break
				
				rect = g.getrect()
				
				if rect[1] < -120 or rect[0] + rect[2] > 120:
					explode = True
					break
				
			if explode:
				continue
			
			
			if int(g.getpop()) < 40 and int(g.getpop()) > 0:
				
				rect = g.getrect()
				
				if rect[1] < -80 or rect[0] + rect[2] > 80:
					continue

				pop = g.getpop()
				g.run(1)
				
				cellsStr = str(g.getcells(g.getrect()))
				
				if pop == g.getpop() and not (cellsStr in existing):
					
					cl = g.getcells([-100, -100, 200, 200])
					
					if len(cl) == 0:
						continue 
						
					g.new("")
					g.putcells(cl)
					rect = g.getrect()
					
					if rect[2] > 15 or rect[3] > 15:
						continue
					
					isFinal = False
					
					if len(cl) == 4 * 2:
						x = cl[0]
						y = cl[1]
						cl = g.getcells([x, y, 2, 2])

						if len(cl) == 4 * 2 and x - y == blockDelta:
							finalResult.append((i, r))
							isFinal = True

				
					
					
					if not isFinal:
						result.append((i, r))
					
					existing.append(cellsStr)

	return result

	
def Iterate(recipes, existing, final):
	iterated = []
	idx = 0 
	
	for r in recipes:
		idx += 1
		
		g.show(str(idx) + "/" + str(len(recipes)))
		
		EvolveRecipe(r)
		cells = g.getcells(g.getrect())
		f = []
		result = ValidRecipes(cells, existing, f)
		
		for res in result:
			resCp = copy(r)
			resCp.append(res)
			iterated.append(resCp)
		
		for res in f:
			resCp = copy(r)
			resCp.append(res)
			final.append(resCp)
		
	return iterated

def PlaceResults(result):
	g.new("")
	d = 0 
	
	for r in result:
		idx = 0
		
		for s in r:
			g.putcells(blck, d, 0)
				
			g.putcells(evolved[s[0]], d + 30 + 256 * idx, 30 + 256 * idx)
			g.putcells(evolved[s[1]], d + 80 + 256 * idx, 80 + 256 * idx)
			idx += 1
			
		d += 100
		
recipes = [[]]
existing = []
final = []

for i in xrange(7):
	recipes = Iterate(recipes, existing, final)

PlaceResults(final)

EDIT @dvgrn you need to add g.setbase(8) everywhere g.new("") is called.

[simsim314]

Search with depth=8 brought some junk (probably some bug). I post it here because it has very nice INC operations, including INC10 with 8 pairs, which is the best ratio (INC is always slower than DEC):

Code: Select all

x = 6531, y = 1851, rule = LifeHistory
2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C
98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.
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98.2C98.2C98.2C98.2C98.2C98.2C98.2C$2C98.2C98.2C98.2C98.2C98.2C98.2C
98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.
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98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.2C98.
2C34$30.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.
3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C
97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.
3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C97.3C$30.C99.C99.C99.C99.C99.C
99.C99.C99.C99.C99.C99.C99.C99.C99.C99.C99.C99.C99.C99.C99.C99.C99.C
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99.C99.C99.C99.C99.C3$35.3C297.3C197.3C97.3C97.3C97.3C97.3C597.3C97.
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197.3C697.3C97.3C97.3C97.3C$139.C99.C199.C601.2C96.C99.C99.C99.C1001.
2C1298.2C$140.C99.C199.C600.C.C96.C99.C99.C99.C1000.C.C1297.C.C$1041.
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98.2C97.C.C598.2C98.2C98.2C98.2C98.2C$3692.C.C97.C.C97.C.C697.C.C97.C
.C97.C.C97.C.C97.C.C$995.2C98.2C98.2C1298.2C98.2C598.2C98.2C98.2C98.
2C98.2C898.2C$994.2C98.2C98.2C1199.3C96.2C98.2C598.2C98.2C98.2C98.2C
98.2C799.3C96.2C$297.2C697.C99.C99.C1198.C100.C99.C599.C99.C99.C99.C
99.C798.C100.C$297.C.C597.3C1197.3C97.3C97.3C96.C500.3C97.3C97.3C
1197.3C96.C$297.C599.C1199.C99.C99.C599.C99.C99.C1199.C$898.C1102.C
96.C99.C99.C599.C99.C99.C1199.C$2000.2C$2000.C.C3$604.3C197.3C997.3C
97.3C897.3C1297.3C97.3C$604.C199.C999.C99.C899.C1299.C99.C$605.C199.C
999.C99.C899.C1299.C99.C$408.2C98.2C198.2C698.2C98.2C98.2C97.3C$407.
2C98.2C198.2C698.2C98.2C98.2C98.C$409.C99.C199.C699.C99.C99.C98.C232$
843.C199.C899.C99.C99.C899.C1299.C99.C$642.3C97.3C97.2C98.3C97.2C98.
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97.3C$642.C99.C99.C.C97.C99.C.C97.C99.C99.C99.C99.C99.C99.C99.C99.C.C
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C99.C99.C99.C99.C99.C99.C99.C3$2149.C298.2C98.2C499.C198.2C98.2C1099.
C98.2C$849.2C198.2C998.2C97.2C298.C.C97.C.C497.2C99.2C97.C.C97.C.C
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297.C99.C100.3C396.C.C98.C.C96.C99.C1000.C.C96.C.C97.C100.3C$649.2C
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1158.3C197.3C97.3C897.3C1497.3C$1158.C102.C96.C99.C899.C502.C996.C
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99.C99.C99.C199.C99.C299.C99.C99.C199.C299.C99.C99.C99.C99.C399.C99.C
99.C99.C199.C3$1404.2C698.2C1298.2C$1305.2C96.2C698.2C100.2C1196.2C
800.2C98.2C98.2C698.2C98.2C98.2C98.2C98.2C$1304.2C99.C699.C98.2C101.C
1097.C798.2C98.2C98.2C698.2C98.2C98.2C98.2C98.2C$1007.2C297.C401.C
297.3C197.C99.2C698.3C197.3C497.3C97.3C97.3C97.3C197.C99.C99.C99.3C
197.3C397.C99.C99.C99.C99.C$1007.C.C597.3C97.2C199.2C96.C299.C.C400.C
296.C199.C499.C99.C99.C99.C499.C199.C102.C$1007.C599.C99.C.C197.2C98.
C601.2C97.2C297.C199.C499.C99.C99.C99.C101.2C396.C100.3C96.C100.2C99.
2C$1210.2C298.2C96.C300.C599.3C96.2C98.C.C1398.C.C496.C199.C.C98.C.C$
1110.3C97.C.C297.C.C996.C100.C500.2C198.2C796.C499.C299.C$1110.C99.C
299.C999.C401.2C197.C.C196.2C$913.2C196.C1800.C.C196.C200.C1701.C$
912.2C900.2C1096.C2100.2C$914.C898.2C3198.C.C$1815.C4$2420.2C398.2C
698.2C98.2C$2419.2C398.2C698.2C98.2C$2421.C399.C699.C99.C232$1455.C
99.C399.C499.C199.C99.C99.C399.C699.C99.C99.C99.C199.C99.C99.C299.C
299.C99.C99.C99.C99.C99.C$1454.2C98.2C98.3C97.3C97.3C97.2C98.3C97.3C
97.3C97.3C97.2C98.3C97.2C98.2C98.2C98.3C97.3C97.3C97.2C98.3C97.3C97.
3C97.3C97.3C97.3C97.2C98.2C98.2C98.2C98.3C97.2C98.2C98.2C98.3C97.3C
97.2C98.3C97.3C97.2C98.2C98.2C98.2C98.2C98.2C$1454.C.C97.C.C97.C99.C
99.C99.C.C97.C99.C99.C99.C99.C.C97.C99.C.C97.C.C97.C.C97.C99.C99.C99.
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97.C.C97.C99.C99.C.C97.C99.C99.C.C97.C.C97.C.C97.C.C97.C.C97.C.C$
1655.C99.C99.C199.C99.C99.C99.C199.C399.C99.C99.C199.C99.C99.C99.C99.
C99.C499.C399.C99.C199.C99.C3$2260.2C99.C198.2C197.3C599.C298.2C1198.
2C$1460.3C498.2C297.C.C97.2C197.2C198.C202.C198.2C197.2C98.3C196.2C
600.2C497.3C97.C.C199.C$1460.C500.C.C296.C99.C.C198.C198.C200.2C198.C
.C98.2C96.C.C97.C200.C499.3C96.2C498.C99.C200.2C98.3C$1461.C499.C999.
C.C197.C99.2C198.C699.C100.C498.C299.C.C97.C$3263.C700.2C98.2C96.C
999.C$3963.2C98.2C$2066.2C1897.C99.C$2065.2C3201.C$2067.C100.2C1698.
2C797.3C597.2C499.2C$1868.3C297.C.C498.2C1197.C.C796.C599.C.C497.2C$
1868.C299.C300.3C197.C.C897.3C296.C501.2C97.3C97.3C96.C700.3C97.3C97.
3C97.3C97.C$1869.C599.C199.C899.C799.2C98.C99.C799.C99.C99.C99.C$
1572.2C896.C1099.C800.C98.C99.C799.C99.C99.C99.C$1571.2C3401.C$1573.C
2199.3C1197.2C$3075.2C696.C1199.C.C$1676.2C98.2C1098.2C196.2C698.C$
1675.2C98.2C1098.2C199.C$1677.C99.C1099.C232$2411.C199.C599.C99.C299.
C199.C999.C499.C499.C99.C$2310.3C97.2C98.3C97.2C98.3C97.3C97.3C97.3C
97.3C97.2C98.2C98.3C97.3C97.2C98.3C97.2C98.3C97.3C97.3C97.3C97.3C97.
3C97.3C97.3C97.3C97.2C98.3C97.3C97.3C97.3C97.2C98.3C97.3C97.3C97.3C
97.2C98.2C98.3C$2310.C99.C.C97.C99.C.C97.C99.C99.C99.C99.C99.C.C97.C.
C97.C99.C99.C.C97.C99.C.C97.C99.C99.C99.C99.C99.C99.C99.C99.C99.C.C
97.C99.C99.C99.C99.C.C97.C99.C99.C99.C99.C.C97.C.C97.C$2311.C199.C
199.C99.C99.C99.C99.C299.C99.C199.C199.C99.C99.C99.C99.C99.C99.C99.C
99.C199.C99.C99.C99.C199.C99.C99.C99.C299.C2$5016.C$3117.C598.2C1297.
2C99.2C$2417.2C99.C98.2C98.2C99.C297.2C99.2C299.C98.2C96.2C700.2C596.
C.C97.2C$2416.2C99.2C98.C.C97.C.C97.2C297.C.C97.2C299.2C98.C.C97.C
699.C.C99.C98.2C497.C$2418.C98.C.C97.C99.C99.C.C398.C298.C.C97.C501.
2C98.2C98.2C96.C100.2C97.2C699.3C$3419.3C499.C196.2C99.C.C97.C.C196.C
.C98.C698.C201.2C$3419.C500.2C198.C98.C99.C999.C102.C97.C.C498.2C$
3420.C499.C.C800.C99.C597.2C97.C100.3C97.3C198.2C96.2C$4722.2C98.2C
597.C.C197.C99.C101.2C97.C.C97.C$3823.3C896.C.C97.C.C398.3C396.C99.C
100.C.C96.C$2925.2C896.C1399.C599.C$2925.C.C896.C1399.C$2925.C5$2332.
2C697.3C298.2C698.2C898.2C$2331.2C698.C299.2C698.2C898.2C$2333.C698.C
300.C699.C899.C232$4167.C399.C99.C199.C99.C399.C399.C99.C99.C299.C$
3966.3C97.3C97.2C98.3C97.3C97.3C97.2C98.2C98.3C97.2C98.2C98.3C97.3C
97.3C97.2C98.3C97.3C97.3C97.2C98.2C98.2C98.3C97.3C97.2C$3966.C99.C99.
C.C97.C99.C99.C99.C.C97.C.C97.C99.C.C97.C.C97.C99.C99.C99.C.C97.C99.C
99.C99.C.C97.C.C97.C.C97.C99.C99.C.C$3967.C99.C199.C99.C99.C299.C299.
C99.C99.C199.C99.C99.C399.C99.C2$4072.C$4071.2C198.3C97.3C197.3C97.3C
1597.3C$3973.2C96.C.C99.2C96.C99.C199.C99.C101.2C698.2C796.C$3973.C.C
196.2C98.C99.C199.C99.C100.C.C98.2C198.2C396.2C500.2C199.C96.C$3973.C
200.C598.C100.C.C97.3C96.2C399.C201.C98.2C196.2C199.2C$4874.C99.C100.
C599.2C97.2C199.C198.C.C$4975.C699.C.C98.C100.2C$5578.2C296.2C$5578.C
.C297.C$5281.C296.C$5280.2C799.2C$5280.C.C798.C.C$6081.C5$4488.2C698.
2C198.2C$4487.2C698.2C198.2C$4489.C699.C199.C232$5723.C199.C99.C199.C
299.C$5522.3C97.3C97.2C98.3C97.2C98.2C98.3C97.2C98.3C97.3C97.2C$5522.
C99.C99.C.C97.C99.C.C97.C.C97.C99.C.C97.C99.C99.C.C$5523.C99.C199.C
299.C199.C99.C3$6328.2C199.C$5530.C398.2C397.C.C197.2C$5529.2C199.2C
196.2C300.2C96.C199.C.C$5529.C.C197.2C199.C298.2C$5731.C499.C$6433.2C
$6134.2C297.C.C$6134.C.C296.C$6134.C6$5642.2C$5641.2C$5643.C200.2C
198.2C$5843.2C198.2C$5845.C199.C!

[dvgrn]

Search with depth=8 brought some junk (probably some bug). I post it here because it has very nice INC operations, including INC10 with 8 pairs, which is the best ratio (INC is always slower than DEC)...

If you're requiring that your G0 gliders always come in pairs, does that mean that you're thinking about encoding the recipes in a single glider stream -- prefix a Herschel period doubler to the input conduit you posted, maybe, and bounce the other glider in with a semi-Snark?

That makes the recovery time of the conduit a little worse, of course -- it will be interesting to see by how much -- but makes it a lot easier to move and copy the recipe glider stream, without the two parts getting out of synch with each other.

[simsim314]

your G0 gliders always come in pairs, does that mean that you're thinking about encoding the recipes in a single glider stream

That only means I was pretty lazy to add special case for single glider. I fixed it now (see below).

I'm actually thinking about alternative design. 2 glider streams instead of 4 (for two arms), that work together with glider gun to produce pairs. This obviously limits the pairs to have one of the gliders (the first or the second) with certain parity, and the pairs will have to always work, no matter what. This to me seems like probable alternative, with reasonable cost and nice compensation over the 4 signal streams.

But what I was mainly thinking about is G4 with 118 ticks recovery, and four streams (obviously the synchronization will be hell). Because we don't have fast enough H duplicator, the reasonable alternative is using non destructive H->G to produce "movement command" and converting the H back into G4, in the same cycle.

Here is the fixed script. I've added preference for closest glider, and added single gliders case. Waiting for results (doesn't seems to be so different):

Code: Select all

import golly as g 
from copy import copy

gld = g.parse("3o$o$bo!")
blockDelta = 5

blck = g.parse("2o$2o!", 0, -blockDelta)

evolved = []

for i in xrange(0, 500):
	evolved.append(g.evolve(gld, i))

def EvolveRecipe(recipe):
	g.new("")
	g.setstep(4)
	
	g.putcells(blck)
	
	for r in recipe:
		g.putcells(evolved[r[0]], 30, 30)
		
		if len(r) > 1:
			g.putcells(evolved[r[1]], 80, 80)
			
		g.step()
		g.step()	

def ValidRecipes(cells, existing, finalResult):
	
	result = []
	
	for r in xrange(200 - 18, 200 - 85, -1):
		for i in xrange(0, 2):
		
			g.new("")
			g.putcells(cells)
			
			g.setstep(2)
	
			g.putcells(evolved[i], 30, 30)
			
			if r != 200 - 18:
				g.putcells(evolved[r], 80, 80)
			
			explode = False
			
			for l in xrange(8 * 6):
				g.step()
				if int(g.getpop()) > 140 or int(g.getpop()) == 0:
					explode = True
					break
				
				rect = g.getrect()
				
				if rect[1] < -120 or rect[0] + rect[2] > 120:
					explode = True
					break
				
			if explode:
				continue
			
			
			if int(g.getpop()) < 40 and int(g.getpop()) > 0:
				
				rect = g.getrect()
				
				if rect[1] < -80 or rect[0] + rect[2] > 80:
					continue

				pop = g.getpop()
				g.run(1)
				
				#cellsStr = str(g.getcells([-100, -100, 200, 200]))
				cellsStr = str(g.getcells(g.getrect()))
				
				if pop == g.getpop() and not (cellsStr in existing):
					
					cl = g.getcells([-100, -100, 200, 200])
					
					if len(cl) == 0:
						continue 
						
					g.new("")
					g.putcells(cl)
					rect = g.getrect()
					
					if rect[2] > 15 or rect[3] > 15:
						continue
					
					isFinal = False
					
					if len(cl) == 4 * 2:
						x = cl[0]
						y = cl[1]
						cl = g.getcells([x, y, 2, 2])

						if len(cl) == 4 * 2 and x - y == blockDelta:
							if r != 200 - 18:
								finalResult.append((i, r))
							else:
								finalResult.append([i])
							isFinal = True

					if not isFinal:
					
						if r != 200 - 18:
							result.append((i, r))
						else:
							result.append([i])
					
					#existing.append(str(g.getcells([-100, -100, 200, 200])))
					existing.append(cellsStr)

	return result

	
def Iterate(recipes, existing, final):
	iterated = []
	idx = 0 
	
	for r in recipes:
		idx += 1
		
		g.show(str(idx) + "/" + str(len(recipes)))
		
		EvolveRecipe(r)
		cells = g.getcells(g.getrect())
		f = []
		result = ValidRecipes(cells, existing, f)
		
		for res in result:
			resCp = copy(r)
			resCp.append(res)
			iterated.append(resCp)
		
		for res in f:
			resCp = copy(r)
			resCp.append(res)
			final.append(resCp)
		
	return iterated

def PlaceResults(result):
	g.new("")
	d = 0 
	
	for r in result:
		idx = 0
		
		for s in r:
			g.putcells(blck, d, 0)
				
			g.putcells(evolved[s[0]], d + 30 + 256 * idx, 30 + 256 * idx)
			
			if len(s) > 1:
				g.putcells(evolved[s[1]], d + 80 + 256 * idx, 80 + 256 * idx)
				
			idx += 1
			
		d += 100
		
recipes = [[]]
existing = []
final = []

for i in xrange(7):
	recipes = Iterate(recipes, existing, final)

PlaceResults(final)

EDIT Attached is 7 signals search result, including single gliders. The most important novelty is INC 7 with 7, which is second best to the INC10 with 8. My guess is that the deeper we will look the better INC operation we will get.

[simsim314]

Here are recipes for the same basic structure, but the second glider is with same parity (because we have only blinkers in recipes, glider parity is the only limitation of gun usage).

The basic outline of the design: use H to generate the first glider, and use periodic gun for the second glider.

Halt operations exist for 5-7, and universality (with reasonable INC operation 7/7) was established. I'm hoping to find better INC in deeper searches. So far looks as very elegant design, the only problem in using gun is to synchronize between copy operations (the new gun should fit in the same period as the dying one).

Another open issue for universal constructors: is there a way to have two streams without intersecting? Some sort of snakish path, where one stream does the inner turn in the upper level, and the second stream does the inner turn in the lower level? How the arms will work without interacting with the streams? is it possible at all?

EDIT On the second thought the gun design can work in slow salvo mode and single stream. With two arms, the relative glider collision setup probably requires at least three streams (one arm can operate as slow salvo, but the second arm should be synchronized with the first, such requiring two streams for relative synchronization - or the recipes would need to be able to fit all 72 two glider collision potions, or at least most of them).

EDIT2 Thinking about dvgrn's replicator design (but which works X10 faster). Seems to fit perfect here. In addition of self destruct, we could get pretty fast Geminoid.

[simsim314]

Some good news from depth 9 search, where the second glider is of constant state.

First of all family where the first glider defines the output glider state. That means we could use this recipe in two arms mechanism, and use the first glider as we wish to calibrate the output glider in very rich range. In other words we could use glider gun + glider stream design in two arms as well. The only problem currently is that all the families with this property are of same parity. So I'm thinking to use other block lane (with pi), to check out if there would be some alternative there. The switcher of block lanes should be pretty simple.

Code: Select all

x = 2151, y = 2156, rule = LifeHistory
2C$2C95$91.3C$91.C$92.C7$100.3C$100.C$101.C249$352.2C$351.2C$353.C3$
356.3C$356.C$357.C249$608.2C$607.2C$609.C3$612.3C$612.C$613.C244$860.
C$859.2C$859.C.C8$868.3C$868.C$869.C240$1111.2C$1110.2C$1112.C12$
1124.3C$1124.C$1125.C246$1372.3C$1372.C$1373.C6$1380.3C$1380.C$1381.C
248$1630.3C$1630.C$1631.C4$1636.3C$1636.C$1637.C235$1875.C$1874.2C$
1874.C.C17$1892.3C$1892.C$1893.C254$2148.3C$2148.C$2149.C!

A little bit less important result is INC 18 operation with emitted glider using 9 commands.

Code: Select all

x = 2151, y = 2156, rule = LifeHistory
2C$2C99$95.3C$95.C$96.C3$100.3C$100.C$101.C243$345.3C$345.C$346.C9$
356.3C$356.C$357.C234$592.3C$592.C$593.C18$612.3C$612.C$613.C249$863.
3C$863.C$864.C3$868.3C$868.C$869.C243$1113.3C$1113.C$1114.C9$1124.3C$
1124.C$1125.C237$1363.3C$1363.C$1364.C15$1380.3C$1380.C$1381.C254$
1636.3C$1636.C$1637.C242$1881.2C$1880.2C$1882.C10$1892.3C$1892.C$
1893.C241$2136.2C$2136.C.C$2136.C11$2148.3C$2148.C$2149.C!

NOTE To clarify the design I'm talking about, here is very awful Herschel plumbing, that demonstrate the UC design (I hope some Herschel magician will help to reduce this one significantly):

The input and the output is the G4 glider stream, while it codes the glider pairs operations, into arm movements. The only limitation of such design is that the second glider is always with same parity, and therefor the attached recipes.

Code: Select all

x = 455, y = 590, rule = LifeHistory
452.C$452.C.C$452.2C13$434.C$432.2C$433.2C32$403.C$402.C$402.3C14$
383.C.C$383.2C$384.C88$297.C.C$297.2C$298.C13$278.C$278.C.C$278.2C36$
244.C$244.C.C$244.2C13$226.C$224.2C$225.2C90$138.C$136.2C$137.2C13$
118.C$117.C$117.3C32$88.C$87.C$87.3C14$68.C.C$68.2C$69.C35$35.C$35.C.
C$35.2C$65.2C$8.2C55.2C5.2C$9.C7.2C53.2C$9.C.C5.2C20.C9.2C$10.2C25.3C
10.C$36.C13.C.C17.2C$36.2C13.2C17.2C$76.2C$76.2C2$.2C$.2C$17.C21.2C$
12.2C.2C22.2C$12.2C2.2C2$9.C$7.3C$6.C$6.2C24.2C$18.2C12.C47.C$18.2C6.
C6.3C42.3C$25.C.C7.C11.2C28.C$26.C21.C28.2C$45.3C$45.C5$82.2C$82.C$
80.C.C$80.2C3$25.C18.C5.2C14.2C$25.C.C14.3C5.2C13.C.C$8.2C18.2C4.2C5.
C23.C$6.C3.C17.2C4.2C5.2C21.2C$5.C5.C16.2C$2C2.2C.C3.C8.C4.C.C22.3C$
2C3.C5.C9.C3.C24.3C29.2C$6.C3.C5.C2.3C16.3C8.C3.C28.C.C$8.2C38.C5.C
29.C$38.C.C8.C3.C21.2C7.2C$37.5C8.3C22.2C$36.2C3.2C$36.2C3.2C$28.C32.
2C$26.C.C33.C$27.2C10.C22.C.C$38.C.C22.2C$11.2C6.2C16.2C$10.C2.C4.C2.
C15.2C5.2C$10.C2.C4.C2.C15.3C4.C.C$10.C2.C4.C2.C25.C$11.2C6.2C18.C4.C
2.C$33.2C12.C$33.2C9.C.C$44.2C40.C$84.3C$83.C$83.2C7$88.2C$88.C$86.C.
C$86.2C3$72.2C$71.C.C$71.C$70.2C3$88.2C$88.C.C$90.C$81.2C7.2C$81.2C6$
70.2C$71.C$71.C.C$72.2C5$169.2C$91.2C76.2C5.2C$91.C84.2C$89.C.C51.C$
89.2C50.3C$128.C11.C14.2C17.2C$128.3C9.2C14.C17.2C$131.C24.C.C21.2C$
118.2C10.2C25.2C21.2C$103.C15.C$93.2C6.3C15.C.C$93.C6.C19.2C$91.C.C6.
2C41.2C$91.2C50.2C3$78.2C$77.C.C$77.C25.2C$76.2C25.2C2$134.2C16.2C29.
2C$134.C18.C29.C$80.2C53.3C12.3C28.C.C$79.C.C55.C12.C30.2C$79.C4.2C$
78.2C5.C$82.3C5.C21.2C$82.C6.C.C21.C$90.C19.3C$110.C6$163.2C15.2C$
162.C.C15.2C$162.C$161.2C7$168.2C$169.C$169.C.C$170.2C10$186.2C$186.
2C2$168.2C$167.C.C$167.C$166.2C$171.2C$172.C$169.3C$169.C!

[simsim314]

I was also thinking about something like this:

Code: Select all

x = 138, y = 229, rule = LifeHistory
A$.2A$2A38$40.A$41.2A$40.2A27$78.A$78.3A$81.A$80.A.A$80.A.A$81.A$76.A
$74.A.A$75.2A2$96.2A$96.2A4$76.2A$75.A.A$75.A33.2A9.2A$74.2A7.2A24.2A
8.2A$83.2A35.5A9.A$121.4A9.3A$91.2A4.2A.2A35.A$91.2A4.2A2.A.A17.4A9.
3A$96.A.A2.3A16.5A9.A$97.2A20.2A$97.A22.2A$99.2A$98.A2.A$71.2A25.3A$
72.A25.2A$72.A.A$73.2A7$96.3A5.3A$96.A2.2A.2A2.A$97.3A3.3A$98.A5.A2$
74.2A15.2A$74.2A15.A.A$93.A$93.2A4.2A.2A$100.A.A$100.A.A$101.A4$86.2A
$86.A$84.A.A$84.2A6$88.2A$88.A$86.A.A$86.2A3$73.2A$72.A.A$72.A$71.2A
5$82.2A$82.2A13$70.2A$70.2A3$67.2A$67.2A8.2A$77.A$70.2A6.A$70.2A5.2A
4$60.A$59.3A$59.3A2$59.4A$58.5A$58.2A.A6$59.2A$59.2A2$62.2A$62.2A3$
59.2A$59.2A18$41.2A5.2A11.A$41.2A5.2A9.A.2A$58.2A.A$45.2A13.A$45.2A4$
68.2A$68.2A2$65.2A5.2A$65.2A5.2A6$65.A.2A$65.2A.A!

It has nice window of (46 * k, 46 * k + 23) for construction. Although not sure that drying the p46 oscillator is better than slow salvo eater2 (now with Chris's slow salvo recipes for eater2 in all orientations).

I think it's certain that eater2 is better for two arms constructor. But two arms has some serious issues with the Gun+Stream design which is not entirely clear as beneficial. One issue is simple stream synchronization that could make the replicator much slower. Another issue is that recipes for two arms require pretty long operation for each emitted glider.

On the other hand having syringe makes things work much faster, and still it's not clear what's better:

1. Two arms with two guns, and two streams.
2. Two arms with two guns, and one stream using semi-snark.
3. Two arms and three streams + gun. Synchronization of arms is much simpler.
4. Four streams and two arms "Gemini style".
5. One streams and two arms using semi snarks "Replicator style".

[simsim314]

As expected even family of emitted gliders, using relative Pi instead of HF (see pair 7 - the first glider can move back and forth as it wishes to collide with boat and emit glider), and because Pi and HF are single cell apart, we covered all parities (see attached 9 operations for more recipes):

Code: Select all

x = 3769, y = 3073, rule = LifeHistory
215$714.2C$714.2C97$810.C$809.2C$809.C.C4$814.3C$814.C$815.C245$1063.
C$1062.2C$1062.C.C7$1070.3C$1070.C$1071.C248$1320.3C$1320.C$1321.C4$
1326.3C$1326.C$1327.C254$1582.3C$1582.C$1583.C245$1829.3C$1829.C$
1830.C7$1838.3C$1838.C$1839.C245$2087.C$2086.2C$2086.C.C7$2094.3C$
2094.C$2095.C241$2338.2C$2338.C.C$2338.C11$2350.3C$2350.C$2351.C249$
2602.2C$2601.2C$2603.C3$2606.3C$2606.C$2607.C248$2857.2C$2857.C.C$
2857.C4$2862.3C$2862.C$2863.C!

The only thing missing now is transition beween HF and Pi.

Here is Pi->HF (3 op):

Code: Select all

x = 815, y = 619, rule = LifeHistory
2C98.2C98.2C$2C98.2C98.2C96$295.C$196.C97.2C$96.2C97.2C97.C.C$95.2C
98.C.C$97.C3$100.3C97.3C97.3C$100.C99.C99.C$101.C99.C99.C239$343.C$
342.2C$342.C.C4$449.C98.2C$448.2C98.C.C$448.C.C97.C7$356.3C97.3C97.3C
$356.C99.C99.C$357.C99.C99.C247$606.2C98.2C$606.C.C97.C.C$606.C99.C5$
612.3C97.3C97.3C$612.C99.C99.C$613.C99.C99.C!

And HF->Pi (4 op):

Code: Select all

x = 1271, y = 876, rule = LifeHistory
2C98.2C98.2C98.2C98.2C$2C98.2C98.2C98.2C98.2C94$392.C98.2C$291.3C97.
2C97.2C$291.C99.C.C98.C$292.C2$95.3C97.3C$95.C99.C$96.C99.C3$100.3C
97.3C97.3C97.3C97.3C$100.C99.C99.C99.C99.C$101.C99.C99.C99.C99.C243$
445.3C$445.C$349.C96.C$348.2C$348.C.C2$552.2C$551.2C$553.C3$356.3C97.
3C97.3C97.3C97.3C$356.C99.C99.C99.C99.C$357.C99.C99.C99.C99.C238$898.
C99.C$897.2C98.2C$897.C.C97.C.C3$602.2C$601.2C$603.C$806.C$805.2C$
707.2C96.C.C$707.C.C$707.C4$612.3C97.3C97.3C97.3C97.3C$612.C99.C99.C
99.C99.C$613.C99.C99.C99.C99.C238$1154.C$1153.2C$1153.C.C4$1059.2C
198.2C$1059.C.C197.C.C$1059.C199.C2$963.2C$863.3C97.C.C$863.C99.C$
864.C3$868.3C97.3C97.3C97.3C97.3C$868.C99.C99.C99.C99.C$869.C99.C99.C
99.C99.C!

NOTE To clarify the meaning of this research once more: now it's possible to use setup of gun + command stream, for two arms. The synchronization of the arms can be done using the recipes of the families where the first glider decides the timing and state of the emitted glider, thus having full control over it, in very large range of movement (even and odd) and timing.

NOTE2 It seems that the setup although possible has some serious costs. It might be better to use cheap signal reflector, emit some glider, and than see how to make this glider compatible with some gun. This will require further recipe search. But I think this result is important as a milestone that shows the general setup of gun + signal, is very flexible formation, that can work even with two arms UCs.

EDIT In general case we could use 4 families of recipes of depth 9: HF->HF, Pi->Pi, Pi->HF, HF->Pi. Instead of using just HF->HF and Pi->Pi and fast transactions between them. But as mentioned I'm not searching to replace the setup, with simpler Signal->Signal and move the weight into the gun arena, and search recipes there.

[simsim314]

Here is much more optimized UC. It's based on p210 gun, and the recovery is 153 (if someone knows of spratan R or Rx with smaller recovery please tell me), it can work with 4hd and above, and has pretty large dead zone so the active 57 ticks (210-153) should be chosen very carefully, to avoid it.

Code: Select all

x = 280, y = 288, rule = LifeHistory
279.A$277.2A$278.2A13$259.A$258.A$258.3A35$226.A$225.A$225.3A14$206.A
.A$206.2A$207.A32$176.A.A$176.2A$177.A13$157.A$157.A.A$157.2A22$137.A
$137.A.A$137.2A3$65.2A$65.2A4$65.3A$65.3A$64.A3.A$63.A5.A$64.A3.A$65.
3A51.A$117.2A$118.2A3$66.A.A$65.A2.A$63.A.2A2$44.A21.A$43.A.A17.2A.A$
42.A3.A18.A$42.A3.A$42.A3.A$42.A3.A18.2A3.2A$42.A3.A19.5A$42.A3.A10.A
8.2A.2A$43.A.A11.A.A6.2A.2A$44.A12.2A8.3A5$50.A$49.A18.2A$49.3A16.2A
6$41.A$41.A$41.A$51.2A36.A$51.A.A33.2A$46.2A6.A7.2A24.2A$45.A2.A2.A2.
A7.2A$41.3A2.2A6.A$41.3A7.A.A$40.A3.A6.2A$39.A5.A$40.A3.A$41.3A4$10.A
$8.A.A$2A4.2A61.A$2A4.2A60.A$6.2A60.3A$8.A.A8.2A$10.A8.A.A19.2A$21.A
19.2A$21.2A7$93.2A$93.2A5.2A$45.2A53.2A$45.2A20.A9.2A$65.3A10.A$64.A
13.A.A17.2A$64.2A13.2A17.2A$104.2A$104.2A2$29.2A$29.2A33.3A2$40.2A25.
2A$40.2A21.A4.A$68.A$37.A26.A2.A$35.3A27.A$34.A$34.2A24.2A$46.2A12.A$
46.2A6.A6.3A43.2A$53.A.A7.A11.2A30.A$54.A21.A28.A.A$73.3A29.2A$73.A
11$87.2A15.2A$86.A.A15.2A$86.A$85.2A7$92.2A$93.A$93.A.A$94.2A10$110.
2A$110.2A2$92.2A$91.A.A$91.A$90.2A$95.2A$96.A$93.3A$93.A!

Considering some alternatives, using G5 in the same manner, might be a bit better: recovery 156, 18 SL instead of 22 (but including less common SL - which costs about the same). I would stick to spartan tradition, while it's possible:

Code: Select all

x = 169, y = 117, rule = B3/S23
168bo$166b2o$167b2o7$163bo$162bo$162b3o28$129bo$127b2o$128b2o7$124bo$
123bo$123b3o28$90bo$15b2o71b2o$8b2o5b2o62b2o8b2o$8b2o69b2o$42bo$42b3o$
10b2o33bo$10b2o32b2o$4b2o47b2o$4b2o46bobo30bo$53bo30bo$79b2o3b3o$78bo
2bo$41b2o36b2o$41b2o29b2o$72b2o5$2o$bo$bobo81b2o$2b2o81b2o$81b2o$81bob
o$83bo$83b2o$70b2o$70b2o3$13b2o3b2o48b2o$13bobobobo48b2o$15bobo$7b2o4b
obobobo$7bo5b2o3b2o$5bobo$5b2o!

EDIT G5 might be a little bit simpler to synchronize when using two streams, as the distance between the two gliders is pretty small.

This design obviously calls for further search for arm recipes.

EDIT Just noticed the arm is on the opposite side of signal reflection direction, in both cases. One solution is to add two 90 degree reflectors on the other side, the other is to redesign the reflector to emit glider to the right direction. Any suggestions?

[dvgrn]

EDIT Just noticed the arm is on the opposite side of signal reflection direction, in both cases. One solution is to add two 90 degree reflectors on the other side, the other is to redesign the reflector to emit glider to the right direction. Any suggestions?

I just did a quick review of new discoveries to see if there are any really nice ways to use tandem or triple gliders to get a U.C. design with a denser input stream. Seems as if that 153/156-tick speed limit is still very expensive to avoid -- if you're not allowed to use an R64 occasionally, you have to twist everything around the wrong way to make the transceivers line up.

About the best idea I could think of was to arrange a signal crossing in the safe zone just after the signal has gone by:

Code: Select all

x = 190, y = 110, rule = B3/S23
97b2o$97b2o3$95b2o$95b2o$82b2o$83bo$83bobo$84b2o$80b2o$80b2o49b2o$122b
2o7b2o$122b2o3$131bo$130bobo$93b2o35bobo$93b2o36bo$86b2o$85bo2bo$86b2o
$113bo$112bobo$112b2o3$116bo$114b3o$86b2o25bo$86b2o17b2o6b2o$105bobo$
106bo$135b2obo$111b2o22bob2o$66b3o42b2o5b2o$68bo49b2o8b2o$67bo60b2o2$
101b2o$101b2o2$116b2o$116bobo$118bo$118bobo$60b3o41b2o13b2o$62bo41b2o$
61bo4$138b2o$138bo$106b2o5b2o21bobo$106b2o5b2o21b2o2$109b2o74bo$109b2o
72b3o$166bo15bo$150bo15b3o13b2o4b2o$140b2o6b3o18bo18bo$86b2o52bo6bo20b
2o16bobo$86b2o12bo37bobo6b2o37b2o$100bobo35b2o$82b2o5b2o9b3o$82b2o5b2o
11bo$125b2o$124bobo$124bo25b2o$123b2o25b2o$93b2o$94bo$91b3o$91bo35b2o$
126bobo$126bo4b2o$125b2o5bo46b2o$129b3o5bo41b2o$129bo6bobo$137bo15$6b
3o$8bo$7bo9$3o$2bo$bo!

However, in this form the circuit takes a G2/G5/G6 as input and puts out a G4 as output, so the 180-degree turn at the other end will probably have to be fairly big and ugly.

The other idea here is -- why not use p240 instead of p210, if the gun is really supposed to be UC construction compatible? That p210 gun doesn't look at all pleasant to construct and get started up. Seems as if some circuitry might also be needed to shut it down again when there's no more recipe to go along with it... won't that also count toward the overall cost of this design?

[simsim314]

I think I have very nice design, that works at p120 rate, and uses only single gliders stream. The idea is to use stable technology to allow "continues gates of interaction". That means the second or the first glider can be in some range of (min, max) generations. In the other time we "close the gate" to reset and "reorganize". That time we use to generate SL for the next glider.

Code: Select all

x = 205, y = 278, rule = LifeHistory
111.C$111.3C$114.C$113.2C7$119.C.C$105.2C5.2C9.C.C$105.2C5.2C11.C$
119.C3.C.C$109.2C8.C.2C$109.2C4$132.2C$132.2C2$129.2C5.2C$129.2C5.2C
6$126.C.C$127.2C$127.C17$155.2C$154.3C$151.C.2C9.2C$151.C2.C4.C5.C$
151.C.2C5.C$145.2C7.3C3.C3.C$144.C.C8.2C5.C$144.C$143.2C9$119.2C$119.
2C$9.C$9.3C$12.C$11.2C$130.2C$130.C$128.C.C$128.2C3$115.2C$3.2C5.2C8.
2C92.C.C$3.2C5.2C7.2C93.C$21.C91.2C$7.2C16.C3.C$7.2C19.2C2$26.3C$24.
2C.C$25.2C90.2C$116.C.C$27.2C87.C$29.C4.2C79.2C$27.2C5.2C4$133.2C$
133.C.C$135.C$135.2C6$32.C$33.2C90.2C$32.2C82.2C7.2C$117.C$117.C.C$
118.2C$101.C32.2C$99.3C32.C$54.C20.C22.C33.C.C$53.C.C7.C11.3C20.2C32.
2C$54.C6.3C14.C$60.C16.2C38.C$60.2C55.3C$108.C11.C$108.3C8.2C14.C$
111.C22.C.C$110.2C23.C2$67.2C$52.C14.2C$51.C.C$51.C.C$52.C2$53.3C$53.
C10.2C32.2C$54.C9.C20.2C11.2C23.2C$65.3C18.C36.C$67.C15.3C38.3C$83.C
42.C2$102.2C$103.C$100.3C$100.C5$82.2C$29.2C51.2C$30.2C$29.C12$83.3C$
24.2C5.2C50.C$26.C4.2C51.C$24.2C2$22.2C$21.2C.C$23.3C2$4.2C19.2C$4.2C
16.C3.C$18.C$2C5.2C7.2C$2C5.2C8.2C6$103.2C$103.C.C$8.2C93.C$9.C$6.3C$
6.C28$136.2C$136.C.C$136.C31$169.2C$169.C.C$169.C31$202.2C$202.C.C$
202.C!

This design has 43 ticks of operations (from 78 to 120 both included). And requires always to use pairs. It also assumes all the recipes will work under 120 ticks (although there is an option to open single tick, to cancel the p30 reflector, thus allowing longer settle time - but this seems unnecessary). All these limitations (43 ticks + pairs) looks pretty reasonable to operate and to generate quite good recipes. Because the fast operation mode, it can use longer recipes without concerns.

From my experience thus far, "only pairs" recipes are a little bit more limited, but in all cases the recipes explode exponentially by depth search, and give a lot of options. 43 ticks is not much, but I think it's enough (I was looking for recipes with 57 ticks, and there were plenty of them).

EDIT The constructor is so long, because I couldn't find any spartan R->SE+NE gliders converter. The posted is the shortest I could find using spartan components. There is smaller H->SE + NE converter that uses eater2 in dvgrn collection.

Code: Select all

x = 69, y = 41, rule = LifeHistory
3$40.A$38.3A$37.A$26.A10.2A$25.A.A6.5B$25.A.A5.4B$23.3A.2A3.6B11.A$
22.A4.B4.6B9.3A9.B$16.A6.3AB2AB.7B8.A11.2B$16.3A6.A.2AB2.6B.2B5.2A9.
3B$19.A7.21B8.4B$18.2A3.B5.17B9.4B$18.8B2.15B2A2B7.4B$20.22BA2BA2B5.
4B$20.23B2A3B4.4B$19.19B3.9B.4B$17.21B4.12B$15.24B4.10B$15.2BC14B4.4B
3.9B$14.3BCBC4B.6B6.4B.9B$15.2B3C4B2.B.5B5.4B.7B$14.5BC4B7.2A6.10B$
13.10B8.A8.4B.2B$12.4B16.3A6.4B$12.3B19.A7.4B$10.4B29.4B$10.2A32.4B$
11.A33.4B$8.3A35.4B$8.A38.4B$48.4B$49.4B!

EDIT The results looks pretty good. INC7 with 4, in depth of 7 universality is achieved.

Code: Select all

x = 9869, y = 280, rule = B3/S23
2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b
2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b
2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b
2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b
2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b
2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b
2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o$2o98b2o
98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o
98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o
98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o
98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o
98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o
98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o
98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o84$80b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o$80bo99bo99bo6b
o92bo6bo92bo99bo99bo99bo99bo99bo99bo99bo6bo92bo99bo99bo99bo99bo99bo99b
o99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo6bo92bo6bo92bo6bo92bo
6bo92bo6bo92bo6bo92bo6bo92bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
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99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo$81bo5b2o
92bo99bo4b2o93bo4b2o93bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o
92bo99bo4b2o93bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o
92bo5b2o92bo5b2o92bo5b2o92bo99bo99bo99bo99bo99bo99bo99bo99bo4b2o93bo4b
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5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o
92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b
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92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo99bo99bo99bo99bo99bo99bo99bo99bo
99bo99bo99bo99bo99bo99bo99bo99bo99bo$87bobo196bobo97bobo98bobo97bobo
97bobo97bobo97bobo97bobo196bobo98bobo97bobo97bobo97bobo97bobo97bobo97b
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97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bo
bo97bobo97bobo97bobo97bobo97bobo97bobo$87bo399bo99bo99bo99bo99bo99bo
101b2o196bo99bo99bo99bo99bo99bo99bo99bo99bo99bo101b2o98b2o1396bo99bo
99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
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99bo99bo99bo99bo99bo99bo101b2o99bo$1088b2o1198b2o98b2o5598b2o99b2o$
1090bo1199bo99bo5599bo98bobo99b2o98b2o98b2o$193bo2298b2o98b2o98b2o99bo
5396b2o98b2o98b2o99b3o98b2o98b2o99bo$192b2o2297b2o98b2o98b2o99b2o98b3o
99bo5197bo99bo99bo98bo99b2o98b2o99b2o98b3o99bo99bo99bo99bo99bo99bo99bo
99bo$192bobo2298bo99bo99bo98bobo97bo100b2o5497bo100bo99bo98bobo97bo
100b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o$2893bo99bobo5897bo99bobo97bo
bo97bobo97bobo97bobo97bobo97bobo97bobo20$110b3o97b3o97b3o97b3o97b3o97b
3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b
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3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o$110bo99bo99bo99bo99bo6bo92bo6bo
92bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
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99bo99bo99bo99bo6bo92bo99bo99bo99bo99bo99bo99bo$111bo99bo99bo99bo99bo
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99bo5b2o92bo4b2o93bo99bo99bo99bo99bo99bo99bo$117b3o396bobo97bobo98b3o
97b3o97b3o296b2o99b3o97b3o97b3o97b3o97b3o97b3o97b3o399bo99bo97bobo397b
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2o97bobo197b3o97bobo96bobo$117bo599bo99bo99bo202bo97bo98bo99bo99bo99bo
99bo99bo99bo400b2o98b2o97bo101b2o98b2o196bo200bo99bo101bo99bo796bo99bo
99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99b2o2501bo496b2o98bo101b
2o96bo99bo$118bo599bo99bo99bo200b2o197bo99bo99bo99bo99bo99bo99bo399bob
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98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o397b2o498bo199bobo
96bo$322bo99bo696bobo1497bo99bo599bobo97bobo97b2o101bo99bo1896b2o98b2o
98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o
98b2o98b2o98b2o98b2o98b2o398bobo697bo$321b2o98b2o3098bo99b2o98b2o1898b
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99bo99bo99bo$321bobo97bobo3197bobo97bobo5398b3o$1023b3o997b3o98b2o98b
2o5497b3o98b2o98b2o1196bo$1023bo999bo99b2o98b2o800b2o4696bo99b2o98b2o
1198bo101b2o98b2o98b2o98b2o98b2o98b2o$1024bo999bo100bo99bo798b2o4698bo
100bo99bo1298b2o98b2o98b2o98b2o98b2o98b2o$226b3o2597b3o197bo6199bo99bo
99bo99bo99bo99bo$226bo2599bo$227bo2599bo16$140b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
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97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o$140bo99bo99bo99bo99bo6bo92bo
6bo92bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo6bo92bo
99bo99bo99bo99bo99bo99bo99bo99bo5b2o92bo99bo99bo99bo99bo99bo99bo99bo5b
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5b2o92bo5b2o92bo5b2o92bo5b2o$141bo99bo99bo99bo99bo4b2o93bo4b2o93bo99bo
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92bo4b3o92bo99bo99bo99bo4bobo92bo4bobo92bo4b2o93bo4b2o93bo4bobo92bo4bo
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5b2o92bo5b2o92bo5b2o92bo99bo99bo4b3o92bo99bo99bo5b2o92bo4bobo92bo4bobo
92bo4bobo92bo4bobo92bo4bobo92bo4bobo92bo4bobo$148b2o198b2o98b2o96bobo
97bobo497bo199bo101b2o696bobo98b3o396bo102bo96b2o100b2o96bo99b2o98b2o
98bo99bo201b2o98b2o96bo99bo99bobo97bobo97bo99bo99bo99bobo97bo101b2o
796bobo97bobo97b2o99b2o99b2o99bo1696bo99bobo97bobo97bo100bobo97bobo97b
obo97bobo296bo201b2o96b2o98bo99bo99bo99bo99bo99bo99bo$147b2o198b2o98b
2o600b2o96bo199bo99b2o798bo399bo100b2o98bo98b2o199bo99bo98bo99bo199b2o
98b2o898bo99b2o999bo98bobo97b2o99b2o99b2o99bo1796bo99bo99bo99bo99bo
299bo199b2o99bo$149bo199bo99bo598b2o399bo798bo499bobo198bo699bo99bo
999bo1199bo98bobo97b2o99b2o99b2o99bo2497bo$251b2o797bo499b3o499bo498b
2o998b2o1297b3o97b3o1197bo98bobo97b2o99b2o99b2o99bo1998b2o$250b2o1298b
o102bo397b2o498bobo997bobo1296bo99bo102bo1297bo98bobo97b2o99b2o99b2o
99bo1698b2o97bobo$252bo499b3o97b3o696bo100b2o98b3o296bobo497bo999bo
1299bo99bo100b2o98b3o1397bo98bobo97b2o99b2o99b2o99bo1496b2o98bo200b3o$
752bo99bo799bobo97bo100b3o97b3o3096bobo97bo100b3o97b3o1397bo98bobo97b
2o99b2o99b2o99bo1297bo298bo$753bo99bo101b2o796bo99bo99bo401b2o98b2o
2696bo99bo99bo101b2o1497bo98bobo97b2o99b2o99b2o99bo1396bo$954b2o898bo
99bo399b2o98b2o2798bo99bo99b2o1699bo98bobo97b2o99b2o99b2o99bo$956bo
299b3o1097bo99bo2999bo1899bo98bobo97b2o99b2o$1256bo6300bo98bobo$1257bo
16$170b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
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97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
$170bo99bo99bo99bo99bo99bo99bo99bo99bo6bo92bo99bo99bo6bo92bo99bo99bo6b
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99bo99bo99bo$171bo99bo5b2o92bo99bo99bo99bo99bo99bo99bo4b2o93bo99bo99bo
4b2o93bo99bo99bo4b2o93bo99bo99bo99bo99bo5b2o92bo5b2o92bo4b2o93bo4b2o
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5b2o92bo5b2o92bo5b2o92bo99bo99bo4bobo92bo99bo99bo99bo5b2o92bo99bo99bo
99bo99bo99bo99bo99bo99bo99bo99bo$276b2o300b2o396bobo297bobo297bobo498b
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100b2o98b2o97bobo97b2o98b2o98bo99bobo497bobo197b2o98b2o98b2o98b2o98b2o
98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o
98b2o98b2o99bobo97bobo97bobo198b2o96bo399b2o601bo99bo$278bo299bobo198b
2o98b2o999bo99bo96bo99bo400bobo97b2o197bo200b2o97bo900bobo196bo99bobo
97bobo198bo99bo501bo397bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
99bo99bo99bo99bo99bo99bo99bo99bo99bo98bo99bo99bo200bobo198b2o198b2o97b
o99b3o497b2o98b2o$578bo200bobo97bobo198b2o797b2o98b2o597bo99bobo197bo
199bobo799b2o196bo1100b3o97b2o2897bo200bobo99bo96b2o198bo499bobo97bobo
99b2o98b2o$381b2o98b2o296bo99bo199b2o100b2o598b2o96bobo97bobo1300bo
398b2o98b2o96b2o1201bo96bo99bobo2799b2o296bo100b2o98bo198bo101b2o596b
2o99bobo97b3o97b3o$183bo197bobo97bobo597bo98b2o201bo97b3o197b3o97bobo
999bo497b2o398bobo97bobo97bo101bo1097b2o97bo400b3o2497bobo396bobo398bo
bo597bo98bo99bo99bo$182b2o197bo99bo700bo199b2o97bo199bo99bo1000b2o497b
obo99b2o98b2o196bo99bo200b2o1097bobo497bo2499bo799bo300b3o496bo99bo$
182bobo498b3o696bobo97bo199bo1099bobo598bobo97bobo496bobo198b3o1198b2o
196bo3599bo$683bo2301b2o396bo99bo699bo1199b2o3600b2o97b3o96bo$684bo
2300bobo1196bo1200bo3599bobo96bo$2985bo5999bo99bo18$400b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
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97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
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97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o$400bo99bo99bo99bo99bo99bo99bo
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99bo99bo5b2o92bo99bo99bo99bo99bo99bo99bo99bo99bo$401bo99bo99bo99bo99bo
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4bobo92bo99bo4b3o92bo99bo6bo92bo6bo92bo99bo99bo5b2o92bo$608b2o98b2o
397b3o196bo199bo199bo99bo100b3o98b2o297bobo96bobo297bo199bo501b2o98b2o
96bo399bobo97b2o98b2o198b2o199bobo96bobo100bo99bo297bobo198b2o297bobo
97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bo
bo97bobo97bobo97bobo97bobo97bobo97bobo97bobo97bobo199bo99bo96bo400b3o
96bo299bo199bo200b2o98b2o100bo197bobo$409b2o196b2o98b2o100b2o296bo199b
o300b3o296bo100bobo296bo901b2o98b2o96b2o98b2o400b2o197bo99bo199bo198bo
200b2o98b2o98b3o196bo200bobo296bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo200b2o98b2o97bo201b2o196bo
599bo199bobo97bobo98b2o197bo$408b2o199bo99bo98b2o298bo301b2o196bo299bo
99bo201b2o399bo198b2o299bo97bobo97bobo97bo99bo398b2o399b3o197b3o296bob
o97bobo97bo301b2o96bo2400b3o96bobo97bobo298bobo196bo202bo796bobo$410bo
100b2o297bo100b2o497bobo196bo599b2o399b2o198bobo297b2o97bo99bo600bo
398bo199bo499bo101b2o197bobo2496bo499bo400b2o$510b2o398b2o101bo198b2o
196bo701b2o97bo398bobo197bo299bobo1197bo199bo600bobo196bo200b3o2296bo
402bo199bo296bobo900bo197b3o$512bo399bo99b2o197b2o899bobo397b3o1198b2o
98b2o1296bo399bo2700b2o198b2o399b2o797b2o197bo$1012bobo198bo898bo399bo
1199b2o98b2o1698bo2699bobo197bobo397b2o798bobo197bo$2513bo1200bo99bo
4999bo$3015b3o5997b3o199bo$3015bo2600b3o3396bo200b2o$3016bo2599bo3399b
o199bobo$5617bo16$1330b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o$1330bo99bo99bo99bo99bo99bo99bo99bo99bo
99bo99bo99bo99bo99bo99bo99bo99bo99bo6bo92bo99bo99bo99bo99bo99bo5b2o92b
o99bo99bo99bo99bo99bo99bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo99bo99bo99bo
99bo6bo92bo5b2o92bo99bo99bo5b2o92bo99bo5b2o92bo5b2o92bo5b2o92bo5b2o92b
o5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o
92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo5b2o92bo
99bo99bo99bo99bo99bo6bo92bo99bo99bo6bo92bo99bo5b2o92bo99bo99bo5b2o92bo
99bo99bo99bo5b2o92bo99bo99bo5b2o$1331bo99bo99bo99bo99bo5b2o92bo5b2o92b
o99bo99bo99bo99bo99bo99bo99bo99bo5b2o92bo99bo99bo4b2o93bo99bo99bo99bo
99bo99bo4bobo92bo99bo99bo99bo4b3o92bo99bo99bo4bobo92bo4bobo92bo4bobo
92bo4bobo92bo99bo99bo99bo99bo4b2o93bo4bobo92bo99bo5b2o92bo4bobo92bo99b
o4bobo92bo4bobo92bo4bobo92bo4bobo92bo4bobo92bo4bobo92bo4bobo92bo4bobo
92bo4bobo92bo4bobo92bo4bobo92bo4bobo92bo4bobo92bo4bobo92bo4bobo92bo4bo
bo92bo4bobo92bo4bobo92bo4bobo92bo4bobo92bo4bobo92bo99bo5b2o92bo99bo99b
o99bo4b2o93bo99bo5b2o92bo4b2o93bo99bo4bobo92bo5b2o92bo99bo4bobo92bo4b
3o92bo99bo99bo4bobo92bo99bo99bo4bobo$1736b2o98b2o499b3o396b2o200b2o96b
obo99b2o98b2o98b2o296bo101b2o296bo202bo96bo99bo99bo99bo499bobo97bo101b
2o97bobo96bo199bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
99bo99bo99bo99bo99bo99bo99bo102bo96b2o398bobo198bobo96bobo197bo100bobo
196bo99bo299bo299bo$1338b3o397bo99bo100b2o396bo400bo198b2o198b2o99bobo
97bobo396b2o99b3o196bo102bo97b2o800bo296b2o98bo200b3o2197b2o98bo598bo
399bo100b3o196bo101b2o99bo$1338bo599b2o101bo98b2o196bo600bo199bo98bo
99bo400bo98bo101b2o197b2o97bobo500bo99bo99bo97b2o298bo298bo2199bobo
399b2o198b2o596bo299b2o99b2o199b2o$1339bo302bo297bo99b2o97b2o1300b2o
98b2o296bo99b2o198bobo598b2o98b2o98b2o97bobo597bo2501b2o97bobo197bobo
297b3o296bo300bo98bobo198bobo98b2o$1443bo197b2o397bobo98bo300b2o399bo
597bobo97bobo397bo798bobo97bobo97bobo3197b2o98bo199bo299bo899bo100bobo
$1442b2o197bobo599b2o197bobo199bo197b2o597bo99bo4501b2o97bo598bo999bo$
1442bobo797b2o198bo200b2o197bobo5197b2o$2244bo301bo96bobo5398bo$1546b
2o997b2o$1545b2o998bobo$1547bo17$3260b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o97b3o
97b3o97b3o97b3o97b3o$3260bo99bo99bo99bo99bo5b2o92bo99bo99bo99bo99bo99b
o99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
99bo99bo99bo99bo99bo$3261bo99bo99bo99bo99bo4bobo92bo4b3o92bo5b2o92bo
99bo99bo99bo99bo4b3o92bo99bo4b3o92bo99bo99bo99bo99bo4b3o92bo99bo99bo4b
3o92bo5b2o92bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo5b2o92bo99bo5b
2o92bo99bo5b2o92bo5b2o92bo99bo5b2o92bo99bo99bo99bo99bo5b2o92bo99bo99bo
5b2o$3268b2o98b2o296bo99bo99b2o99b3o396bo199bo201b2o98b2o98b2o96bo299b
o99b2o2400b2o497bobo196b2o198b2o98b2o198b2o300b2o98b2o96b2o298b2o$
3267b2o98b2o100b2o296bo100bo98bo100b3o296bo199bo101b2o96b2o98b2o98b2o
98bo201b2o96bo100bo300b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o
98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o96b2o498bo200bo
199bo99bo100b2o97bo100b2o196b2o98b2o99bo199b3o97bo$3269bo99bo98b2o498b
o99bo401b2o196b2o99bo99bo99bo298b2o498b2o98b2o98b2o98b2o98b2o98b2o98b
2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b2o98b
2o99bo800b2o296b2o199bobo197bo99bo298bo$3470bo100b2o496bo399b2o199bo
599bo401bo97bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo99bo
99bo99bo99bo99bo99bo99bo898b2o299bo198bo599bo$3570b2o601bo99bo197bo
1199b2o2499b2o99bo199bo197bo599b3o399bo$3572bo599b2o98b2o1397bobo2299b
2o98b2o96b2o99b2o198b2o797bo400b2o$4172bobo97bobo3697b2o98b2o99bo98bob
o197bobo797bo399bobo$7974bo99bo$5576b2o$5176b3o396b2o$5176bo400bo$
5177bo!

EDIT: I think using etaer2 should be more efficient (and interesting). Obviously this design is currently targeting slow salvo, I hope deeper search will find family of emitters with free second glider. Maybe there will be no escape from using line switching recipes (for two arms constructors).

Another point is that this design is making synchronization easy, as there is only 43/120 active options, the other 77 ticks are free of interaction, and the intersection could be done there as well.

EDIT2 Here is eater2 variant recipe. It looks like eater2 is about the cost of 5-6 SLs with slow salvo as well. This is the only orientation eater2 is needed, so I post here chric_c recipe (I don't think the block behind the eater2 needs cleaning at all - in the future, with destruction seeds it can influence the recipes a bit):

Code: Select all

x = 338, y = 340, rule = LifeHistory
6.2A$5.A2.A23.D$6.A.A21.3D$7.A21.D$19.2D8.2D$19.D$17.D.D7.2A$15.3D.2D
5.A2.A11.D$14.D12.2A10.3D$8.D6.3D.2D17.D$8.3D6.D.2D17.2D$11.D6.A$10.
2D6.A$18.A16.2D$9.3A22.D2.D$20.3A12.2D$7.A5.A$7.A5.A$7.A5.A2$9.3A2$
23.2D$23.D$24.3D$26.D2$2.2D$3.D$3D$D26$44.2A$43.2A$45.A13$69.2A$69.A.
A$69.A21$87.2A$87.A.A$87.A36$149.3A$149.A$150.A19$169.2A$168.2A$170.A
18$188.3A$188.A$189.A26$222.3A$222.A$223.A33$269.3A$269.A$270.A9$288.
3A$288.A$289.A75$315.2A$315.A.A$315.A11$335.2A$335.A.A$335.A!

[dvgrn]

EDIT The constructor is so long, because I couldn't find any spartan R->SE+NE gliders converter. The posted is the shortest I could find using spartan components. There is smaller H->SE + NE converter that uses eater2 in dvgrn collection.

There's a SE glider output that you had blocked off. So you can make this a little bit smaller, but not too much -- it really hurts to not be able to use the 153-tick recovery version of the R64:

Code: Select all

x = 205, y = 211, rule = LifeHistory
9.C$9.3C$12.C$11.2C3$114.2C$114.2C4$3.2C5.2C8.2C$3.2C5.2C7.2C104.2C$
21.C103.C$7.2C16.C3.C93.C.C$7.2C19.2C93.2C2$26.3C$24.2C.C82.2C$25.2C
82.C.C$109.C$27.2C79.2C$29.C4.2C$27.2C5.2C4$112.2C$111.C.C$111.C$110.
2C6$32.C$33.2C$32.2C5$101.2C$54.C20.C25.C$53.C.C7.C11.3C21.C.C18.2C$
54.C6.3C14.C20.2C10.2C7.2C$60.C16.2C33.C$60.2C50.C.C$107.2C4.2C$108.C
20.2C$108.C.C18.C$109.2C16.C.C$127.2C$67.2C$52.C14.2C$51.C.C$51.C.C$
52.C2$53.3C$53.C10.2C32.2C$54.C9.C20.2C11.2C$65.3C18.C$67.C15.3C35.2C
$83.C37.2C2.2C$125.C.C$102.2C23.C$103.C23.2C$100.3C$100.C5$82.2C$29.
2C51.2C$30.2C$29.C12$83.3C$24.2C5.2C50.C$26.C4.2C51.C$24.2C2$22.2C$
21.2C.C$23.3C2$4.2C19.2C$4.2C16.C3.C$18.C$2C5.2C7.2C$2C5.2C8.2C6$103.
2C$103.C.C$8.2C93.C$9.C$6.3C$6.C28$136.2C$136.C.C$136.C31$169.2C$169.
C.C$169.C31$202.2C$202.C.C$202.C!

What does the cost analysis look like, if you add a semi-Snark to each p120 gun, move the base period up to 240 and allow R64s and all sorts of other efficient slightly-slower conduits? All you have to do is zoom out one step in Golly, and the gliders will be moving just as fast...!

[simsim314]

So you can make this a little bit smaller, but not too much

Thx, looks much better to me.

What does the cost analysis look like, if you add a semi-Snark to each p120 gun, move the base period up to 240 and allow R64s and all sorts of other efficient slightly-slower conduits?

Well very approximately 60 SL - 30 SL per side (3 guns - each gun is about 6 SL, 18 SL for the reflector). Each SL about 10 gliders. Each glider is about 10 commands. We get 120 * 60 * 10 * 10 = 720K ticks. Sounds good to me.

P240 is another 6 SL per semi snark per gun - so the construction is twice bigger and twice slower.

[simsim314]

Few updates:

1. I was thinking about the other side of the constructor. It can use the symmetry properties of beehive to push the signal in the right direction:

Code: Select all

x = 368, y = 269, rule = LifeHistory
9.C$9.3C$12.C$11.2C3$114.2C$114.2C4$3.2C5.2C8.2C$3.2C5.2C7.2C104.2C$
21.C103.C$7.2C16.C3.C93.C.C$7.2C19.2C93.2C2$26.3C$24.2C.C82.2C$25.2C
82.C.C$109.C$27.2C79.2C$29.C4.2C$27.2C5.2C4$112.2C$111.C.C$111.C$110.
2C6$32.C$33.2C$32.2C5$101.2C$54.C20.C25.C$53.C.C7.C11.3C21.C.C18.2C$
54.C6.3C14.C20.2C10.2C7.2C$60.C16.2C33.C$60.2C50.C.C$107.2C4.2C$108.C
20.2C$108.C.C18.C$109.2C16.C.C$127.2C$67.2C$52.C14.2C$51.C.C$51.C.C$
52.C2$53.3C$53.C10.2C32.2C$54.C9.C20.2C11.2C$65.3C18.C$67.C15.3C35.2C
$83.C37.2C2.2C$125.C.C$102.2C23.C$103.C23.2C$100.3C$100.C5$82.2C$29.
2C51.2C$30.2C$29.C12$83.3C$24.2C5.2C50.C$26.C4.2C51.C$24.2C2$22.2C$
21.2C.C$23.3C2$4.2C19.2C$4.2C16.C3.C$18.C$2C5.2C7.2C$2C5.2C8.2C6$103.
2C$103.C.C$8.2C93.C$9.C$6.3C$6.C23$310.2C$310.2C4$136.2C$136.C.C$136.
C5$296.2C$295.C.C$295.C34.2C$294.2C34.C$331.3C$333.C4$315.2C$315.C$
316.3C$318.C4$299.2C$298.C.C23.C$298.C23.3C$297.2C22.C$305.2C14.2C$
305.2C5$169.2C$169.C.C$169.C5$304.2C$303.C.C$303.C$291.2C9.2C$291.2C
4$320.2C$320.C.C$322.C$322.2C7$312.2C$303.2C7.2C$304.C$304.C.C$305.2C
$321.2C$321.C$319.C.C$202.2C115.2C$202.C.C$202.C3$322.C$321.C.C$322.C
17$327.2C$327.C.C14.2C$327.C16.2C$292.2C$275.2C14.C.C$275.2C16.C52.C$
344.C.C$343.C.C$274.C67.C2.C6.C$274.C.C69.C5.C$275.C.C65.C2.C$268.C6.
C2.C65.3C$268.C5.C$274.C2.C$274.3C3$358.C$356.C.C$357.2C$262.C$262.C.
C$262.2C2$364.2C$355.2C7.C.C$355.2C9.C$255.2C109.2C$254.C.C7.2C86.2C$
254.C9.2C86.2C$253.2C$267.2C$267.2C86.2C$355.2C2$264.2C$264.2C!

2. Attached is the depth 9 search for 43 ticks gate, pairs only, p120 compatible (there is some junk in the search).

I add here the script as it is for future reference:

Code: Select all

import golly as g 
from copy import copy

gld = g.parse("3o$o$bo!")
blockDelta = 5
dy = -4 
valids = [5, 4, 3, -2, -3, -4]
blck = g.parse("2o$2o!", 0, -blockDelta)

evolved = []

for i in xrange(0, 500):
	evolved.append(g.evolve(gld, i))

def EvolveRecipe(recipe):
	g.new("")
	g.setstep(2)
	
	g.putcells(blck)
	
	for r in recipe:
		g.putcells(evolved[r[0]], 80, 80)
		
		if len(r) > 1:
			g.putcells(evolved[r[1]], 100, 100 + dy)
		
		for i in xrange(12):
			g.step()
		
	
def Explode(max):
	g.setstep(2)
	
	for l in xrange(max):
		g.step()
		if int(g.getpop()) > 140 or int(g.getpop()) == 0:
			return True
		
		rect = g.getrect()
		
		if rect[1] < -120 or rect[0] + rect[2] > 120:
			return True

	return False


def PlaceRecipe(d, r, id):
	idx = id
	g.putcells(blck, d, 0)
		
	for s in r:
			
		g.putcells(evolved[s[0]], d + 80 + 30 * idx, 80 + 30 * idx)
		
		if len(s) > 1:
			g.putcells(evolved[s[1]], d + 100 + 30 * idx, 100 + 30 * idx + dy)
			
		idx += 1
				
def ValidRecipes(cells, existing, finalExisting, finalResult, initRecipe):
	
	result = []
	idx = len(initRecipe)
					
	for r in xrange(0, 43, 1):
		for i in xrange(0, 1):
		
			g.new("")
			g.putcells(cells)
	
			g.putcells(evolved[i], 80, 80)
			
			if r != -1:
				g.putcells(evolved[((100 - 80) * 4 - 22) - r ], 100, 100 + dy)
			
			if Explode(20):
				continue
			
			if int(g.getpop()) < 40 and int(g.getpop()) > 0:
				
				rect = g.getrect()

				pop = g.getpop()
				g.run(2)
				
				#cellsStr = str(g.getcells([-100, -100, 200, 200]))
				cellsStr = str(g.getcells(g.getrect()))
				
				
				if pop == g.getpop() and not (cellsStr in finalExisting[len(cellsStr) % 1000]):
					
					cl = g.getcells([-150, -150, 300, 300])
					
					if len(cl) == 0:
						continue 

					g.new("")	
					g.setstep(2)
					
					PlaceRecipe(0, initRecipe, 0)
					
					g.putcells(evolved[i], 80 + 30 * idx, 80 + 30 * idx)
					
					if r != -1:
						g.putcells(evolved[((100 - 80) * 4 - 22) - r], 100 + 30 * idx, 100 + 30 * idx + dy)
						
					for gen in xrange(idx + 2):
						g.step()
						g.step()
					
					if Explode(20):
						continue
			
					g.new("")
					g.putcells(cl)
					rect = g.getrect()
					
					if rect[2] > 17 or rect[3] > 17:
						continue
					
					isFinal = False
					
					if len(cl) == 4 * 2:
						x = cl[0]
						y = cl[1]
						cl = g.getcells([x, y, 2, 2])

						
						#if len(cl) == 4 * 2 and x - y in valids:
						#if len(cl) == 4 * 2 and x - y == 4:
						if len(cl) == 4 * 2 and x - y == blockDelta:

							g.new("")	
							g.setstep(2)
							
							PlaceRecipe(0, initRecipe, 0)
							PlaceRecipe(0, initRecipe, idx + 1)
							
							g.putcells(evolved[i], 80 + 30 * idx, 80 + 30 * idx)
							g.putcells(evolved[i], 80 + 30 * (2 * idx + 1), 80 + 30 * (2 * idx + 1))

							if r != -1:
								g.putcells(evolved[((100 - 80) * 4 - 22) - r], 100 + 30 * idx, 100 + 30 * idx + dy)
								g.putcells(evolved[((100 - 80) * 4 - 22) - r], 100 + 30 * (2 * idx + 1), 100 + 30 * (2 * idx + 1) + dy)
							
							for gen in xrange(2 * idx + 4):
								g.step()
								g.step()
							
							if Explode(20):
								continue
					
							if r != -1:
								finalResult.append((i, ((100 - 80) * 4 - 22) - r))
							else:
								finalResult.append([i])
							isFinal = True

					clstr = str(cl)
					
					if not isFinal:# and not (clstr in existing[len(clstr) % 1000]):
						
						#existing[len(clstr) % 1000].append(clstr)
						
						if r != -1:
							result.append((i, ((100 - 80) * 4 - 22) - r ))
						else:
							result.append([i])
					
					#existing.append(str(g.getcells([-100, -100, 200, 200])))
					finalExisting[len(cellsStr) % 1000].append(cellsStr)

	return result


def Iterate(recipes, existing, finalExisting, final):
	iterated = []
	idx = 0 
	
	for r in recipes:
		idx += 1
		
		g.show(str(idx) + "/" + str(len(recipes)))
		
		EvolveRecipe(r)
		cells = g.getcells(g.getrect())
		f = []
		result = ValidRecipes(cells, existing, finalExisting, f, r)
		
		for res in result:
			resCp = copy(r)
			resCp.append(res)
			iterated.append(resCp)
		
		for res in f:
			resCp = copy(r)
			resCp.append(res)
			final.append(resCp)
		
	return iterated

def PlaceResults(result):
	g.new("")
	d = 0 
	
	for r in result:
		PlaceRecipe(d, r, 0)
			
		d += 100
		
recipes = [[]]
existing = []
finalExisting = []
final = []

for id in xrange(15):
	existing = []
	finalExisting = []
	for i in xrange(1000):
		existing.append([])
		finalExisting.append([])
		
	recipes = Iterate(recipes, existing, finalExisting, final)
	
	PlaceResults(final)
	g.save("C:\\Users\\SimSim314\\Downloads\\Arm\\" + str(id) + ".rle", "rle", False)

3. An idea came to me to search for all valid block placements in both directions - as there are 6 valid block placements, there are 36 (6 * 6) possible combinations. This can allow much better and shorter recipes, but will make it harder to compile glider sequence into them. On the other hand I need at least another direction recipes, as the UC work in both directions, and because I have 4 lanes distance, there is no symmetry out of the box.

EDIT

4. Timing will be an issue as both sides should be exactly matched, and work well with the glider sequence. I'm hoping the first ignition glider degree of freedom, will be enough to allow last moment timing adjustments. But this might mean the top and the bottom sides of the UC should have exactly the same design.

EDIT2

Good news from depth 10 results. Now we have at least one family that can be adjusted by the second glider (that proves the concept can work with two arms - if we will find other parity family as well). See 8th pair second glider (and depth 10 attachement).

Code: Select all

x = 443, y = 389, rule = LifeHistory
F$.2F$2.F$3.2F$4.F$5.2F$6.F$7.2F$8.F$9.2F$10.F$11.2F$12.F$13.2F$14.F$
15.2F$16.F$17.2F$18.F$19.2F$20.F$21.2F$22.F$23.2F$24.F$25.2F$26.F$27.
2F$28.F54.2C$29.2F52.2C$30.F$31.2F$32.F$33.2F$34.F$35.2F$36.F$37.2F$
38.F$39.2F$40.F$41.2F$42.F$43.2F$44.F$45.2F$46.F$47.2F$48.F$49.2F$50.
F$51.2F$52.F$53.2F$54.F$55.2F$56.F$57.2F$58.F$59.2F$60.F$61.2F$62.F$
63.2F$64.F$65.2F$66.F$67.2F$68.F$69.2F$70.F$71.2F$72.F$73.2F$74.F$75.
2F$76.F$77.2F$78.F$79.2F$80.F$81.2F$82.F$83.2F$84.F$85.2F$86.F$87.2F$
88.F$89.2F$90.F$91.2F$92.F$93.2F$94.F$95.2F$96.F$97.2F$98.F$99.2F$
100.F$101.2F$102.F$103.2F$104.F$105.2F$106.F$107.2F$108.F$109.2F$110.
F$111.2F$112.F$113.2F48.3C$114.F48.C$115.2F47.C5.2C$116.F53.C.C$117.
2F51.C$118.F$119.2F$120.F$121.2F$122.F$123.2F$124.F$125.2F$126.F$127.
2F$128.F$129.2F$130.F$131.2F$132.F$133.2F$134.F$135.2F$136.F$137.2F$
138.F$139.2F$140.F$141.2F$142.F$143.2F48.3C$144.F48.C6.C$145.2F47.C4.
2C$146.F52.C.C$147.2F$148.F$149.2F$150.F$151.2F$152.F$153.2F$154.F$
155.2F$156.F$157.2F$158.F$159.2F$160.F$161.2F$162.F$163.2F$164.F$165.
2F$166.F$167.2F$168.F$169.2F$170.F$171.2F$172.F$173.2F48.3C$174.F48.C
5.2C$175.2F47.C4.C.C$176.F52.C$177.2F$178.F$179.2F$180.F$181.2F$182.F
$183.2F$184.F$185.2F$186.F$187.2F$188.F$189.2F$190.F$191.2F$192.F$
193.2F$194.F$195.2F$196.F$197.2F$198.F$199.2F$200.F$201.2F$202.F$203.
2F48.3C$204.F48.C$205.2F47.C$206.F55.C$207.2F52.2C$208.F52.C.C$209.2F
$210.F$211.2F$212.F$213.2F$214.F$215.2F$216.F$217.2F$218.F$219.2F$
220.F$221.2F$222.F$223.2F$224.F$225.2F$226.F$227.2F$228.F$229.2F$230.
F$231.2F$232.F$283.3C$283.C$284.C3$294.C$293.2C$293.C.C23$313.3C$313.
C$314.C$321.2C$320.2C$322.C25$343.3C$343.C5.2C$344.C4.C.C$349.C27$
373.3C$373.C$374.C4$385.C$384.2C$384.C.C22$403.3C$403.C5.2C$404.C4.C.
C$409.C27$433.3C$433.C$434.C$441.2C$440.2C$442.C!

EDIT3

Another second glider control family with 8 glider and same parity turned up in a search with beehive (see pair 7):

Code: Select all

x = 333, y = 325, rule = LifeHistory
2C$2C75$80.3C$80.C$81.C5.2C$87.C.C$87.C26$110.3C$110.C$111.C4$121.2C$
121.C.C$121.C22$140.3C$140.C$141.C2$149.2C$148.2C$150.C24$170.3C$170.
C$171.C5.2C$176.2C$178.C26$200.3C$200.C$201.C5.2C$207.C.C$207.C26$
230.3C$230.C$231.C3$239.3C$239.C$240.C23$260.3C$260.C$261.C4$271.2C$
270.2C$272.C22$290.3C$290.C5.2C$291.C4.C.C$296.C27$320.3C$320.C$321.C
4$330.3C$330.C$331.C!

And another one with opposite parity and length 9 (see second glider of pair 4):

Code: Select all

x = 333, y = 325, rule = LifeHistory
2C$2C75$80.3C$80.C$81.C5$91.3C$91.C$92.C21$110.3C$110.C6.C$111.C4.2C$
116.C.C27$140.3C$140.C$141.C5.2C$147.C.C$147.C26$170.3C$170.C$171.C4$
181.2C$181.C.C$181.C22$200.3C$200.C$201.C5.2C$206.2C$208.C26$230.3C$
230.C$231.C$238.2C$238.C.C$238.C25$260.3C$260.C5.2C$261.C4.C.C$266.C
27$290.3C$290.C$291.C5.2C$296.2C$298.C26$320.3C$320.C$321.C4$330.3C$
330.C$331.C!

Makes me consider to make two arms.

Fast approximation shows that instead of 10x10 operations per SL, we will get 20 operations for SL (10 for placing and another 10 for glider), three times bigger to compensate for two streams complexity - gives us 60 per relative SL, assuming each SL is single glider pair (looks reasonable as the SL placed pretty sparsely).

EDIT Thinking once more, many of the SLs can't be generated by single pair (many eater in the stable circuitry, which built mainly from eaters require at least two pairs). So even if 50% of them is of price of 2 pairs we are back to 90 vs 100. And it's also not so simple to make circuitry on the bottom side to work the same as the upper side, so even X3 might be optimistic. On the other hand if we make top+bottom in the same unit, it will shorten the recipes (the bottom side is now built with the same stream), but will require special design. In total it seems like X2 or X2.5, this allows the avg recipe per SL to be raised to 2.

I still think it's pretty unclear.

[simsim314]

Using the classic G->H with beehive, I've managed to reduce to total 3 guns instead of 5. And SL count has also dropped as H is oriented more favorably.

The only nuance there is to mention, is that the width of the constructor is 125 lanes and the "move" of the reflected gliders is by 55 lanes, that means the other side will need to use another 6 SL to extend the move (the width of the reflector should be less than the sum of two reflection moves - otherwise the coming back gliders will collide with the parent constructor):

Code: Select all

x = 463, y = 412, rule = LifeHistory
.A$2.A$3A28$31.A$32.A$30.3A28$61.A$62.A$60.3A28$91.A$92.A$90.3A28$
121.A$122.A$120.3A25$148.A$149.A$147.3A31$181.A$182.A$180.3A28$211.A$
212.A$210.3A28$241.A$242.A$240.3A28$271.A$272.A$270.3A28$301.A$302.A$
300.3A10$405.2A$405.2A3$408.2A$408.2A$394.2A15.3A$395.A9.2A3.A2.A$
395.A.A7.2A3.A3.A$396.2A11.A2.3A$410.4A3$414.A.A$415.2A$328.A86.A$
329.A$327.3A7$416.2A$416.2A2$413.2A$413.2A3$416.2A$416.2A7$446.2A$
445.A.A$447.A5.2A$428.A23.A3.A$428.3A20.A5.A3.2A$431.A19.A3.A.2A2.2A$
430.2A19.A5.A$442.2A8.A3.A$441.A.A9.2A$361.A79.A$362.A77.2A$360.3A32.
A$369.A9.A15.3A$369.3A5.3A18.A$372.A3.A20.2A11.2A$371.2A3.2A32.2A4$
442.2A$442.2A3$385.2A$385.2A34.2A$373.2A45.A.A$372.A2.A44.A$367.2A4.
2A44.2A$366.A.A30.2A$366.A32.2A$365.2A$375.2A33.2A$375.A25.A8.A$376.
3A20.A.A9.3A$378.A19.A.A12.A$383.2A12.A2.A6.A$384.A16.A5.A$381.3A14.A
2.A$381.A17.3A3$426.2A$425.A.A$425.A$413.A10.2A$411.A.A$412.2A2$416.
2A$416.A.A$418.A$418.2A$410.2A$410.2A2$407.2A$407.2A3$410.2A$410.2A!

EDIT Now I've checked the timing gate and it's only 29 ticks. Sounds a bit tight.

Just for reference, here is the starting point of 29 ticks gate, and valid width fix for this setup:

Code: Select all

x = 699, y = 627, rule = B3/S23
o$b2o$2o28$30bo$31b2o$30b2o28$60bo$61b2o$60b2o28$90bo$91b2o$90b2o28$
120bo$121b2o$120b2o28$150bo$151b2o$150b2o28$180bo$181b2o$180b2o28$210b
o$211b2o$210b2o28$240bo$241b2o$240b2o28$270bo$271b2o$270b2o28$300bo$
301b2o$300b2o28$330bo$331b2o$330b2o28$360bo$361b2o$360b2o28$390bo$391b
2o$390b2o28$420bo$421b2o$420b2o28$450bo$451b2o$450b2o28$480bo$481b2o$
480b2o28$510bo$511b2o$510b2o28$540bo$541b2o$540b2o21$683bo$683b3o$686b
o$685b2o4$570bo$571b2o77bo$570b2o62bo15b3o$632b3o18bo$619bo11bo20b2o
11b2o$619b3o9b2o32b2o$622bo$609b2o10b2o$584bo9bo15bo$584b3o5b3o15bobo
84b2o$587bo3bo19b2o84b2o$586b2o3b2o41b2o$634b2o2$676b2o$675bobo$675bo$
674b2o2$600b2o$600b2o23b2o$588b2o35bo39b2o$587bo2bo35b3o12b2o22bo$582b
2o4b2o38bo13bo23b3o$581bobo30b2o23b3o26bo$581bo32b2o23bo$580b2o$590b2o
$590bo25bo$591b3o20bobo$593bo19bobo$598b2o12bo2bo6bo58b2o$599bo16bo5bo
57bobo$596b3o14bo2bo63bo$596bo17b3o62b2o6$628bo$626bobo$627b2o2$631b2o
$631bobo$633bo$633b2o$625b2o$625b2o2$622b2o$622b2o3$625b2o$625b2o!

[codeholic]

Another nuance is that this design doesn't allow singleton gliders anymore. (Not such a deal perhaps.)

[simsim314]

Another nuance is that this design doesn't allow singleton gliders anymore.

Definitely, but this was true for the previous gun based design as well.

I'm working with "pairs only" arms now, and many recipes posted above are working well with pairs only and 120 ticks. I've found a recipe of length 8, that emits glider using the state of the second glider, that means a lot of control on the emitted glider - so this design can work even for two arms that need constant "micro" synchronization.

Unfortunately the operation gate of this design is different, and the previous design was devised for 43 ticks.

[simsim314]

Another design which is a bit cheaper, it has total 3 guns and 3 reflectors instead of 5 guns and 2 reflectors (reflectors do seem to be cheaper but need synchronization), and has 26 instead of 20 SLs. It's gate operation is also a bit smaller 35 instead of 42.

Code: Select all

x = 642, y = 695, rule = B3/S23
641bo$639b2o$640b2o37$601bo$601bobo$601b2o19$581bo$579b2o$580b2o28$
551bo$549b2o$550b2o37$511bo$511bobo$511b2o19$491bo$489b2o$490b2o28$
461bo$459b2o$460b2o37$421bo$421bobo$421b2o19$401bo$399b2o$400b2o37$
361bo$361bobo$361b2o19$341bo$339b2o$340b2o28$311bo$309b2o$310b2o37$
271bo$271bobo$271b2o19$251bo$249b2o$250b2o28$221bo$219b2o$220b2o37$
181bo$181bobo$181b2o19$161bo$159b2o$160b2o28$131bo$129b2o$130b2o2$120b
2o$120bo$108bobo7bobo$103bo4bo2bo6b2o$104b2o5b2o$99b2o8bo3b2o$99b2o10b
2o$108bo2bo$108bobo9$106bo$104b2o$105b2o6$136b2o$101bo34bobo$99b2o35bo
$100b2o5$127b2o5b2o$127b2o5b2o2$131b2o$131b2o4$154b2o$142bobo9b2o$140b
obobo$138b2o11b2o5b2o$140bo10b2o5b2o2$76bo$74b2o$75b2o4$150b2o$150bo$
151b3o$71bo81bo$69b2o$70b2o$82b2o$82b2o17$46bo$44b2o$45b2o13$71bo$71b
3o$74bo23b2o$31bo41b2o23bo$7b2o22bobo62bobo$8bo7b2o13b2o21bo37b2o2b2o$
8bobo5b2o20bo15b3o35b2o$9b2o25b3o18bo$35bo20b2o11b2o$35b2o32b2o4$2o$2o
$16bo21b2o$11b2ob2o22b2o$11b2o2b2o81b2o$80b2o16bobo$8bo70bobo18bo$6b3o
70bo20b2o$5bo72b2o4b2o$5b2o24b2o50bobo$17b2o12bo16b2o33bo$17b2o6bo6b3o
14bo20b2o10b2o7b2o$24bobo7bo11b3o21bobo18b2o$25bo20bo25bo$72b2o$133b2o
$133b2o3$130b2o$130b2o$144b2o$133b2o9bo$133b2o7bobo$142b2o3$81b2o$82bo
$82bobo$83b2o2$132b3o$134bo$133bo$128bo$79b2o46bo2bo$80bo45bo4bo$80bob
o43bo5bo$81b2o39b2o3b3o$122b3o6bo$131bo$94b2o30bo3bo$94bobo11bo$96bo
10bo$96b2o9b3o$122b2o$122b2o3$85b2o$85b2o2$89bo$89b3o$92bo$91b2o5$94bo
$93b3o$93b3o2$91b2o3b2o$91b2o3b2o3$94bo$93bobo$92b2o$92b2o$92b3o$93bob
o$94b2o!

Now I need to chose between:

a. 3 guns + 1 reflectors + 20 SL and gate of 29.
b. 3 guns + 3 reflectors + 26 SL and gate of 36.
c. 5 guns + 2 reflectors + 20 SL and gate of 43.

Looks very balanced. Any thoughts?

EDIT Some speculative calculations. Assuming gun for ignition etc. costs 8 SL reflector 5 SL (each oscillating mechanism comes with 2 SL for reflection). Average recipe length is inversely proportional to gate length.

a. (3 * 8 + 5 + 20) / 29 = 1.69
b. (3 * 8 + 3 * 5 + 26) / 36 = 1.81
c. (5 * 8 + 2 * 5 + 20) / 43 = 1.63

[simsim314]

I have compiled results from gate of 29 ticks, and they look pretty much the same as 43 ticks. Turns out that only the first ticks matter most for recipes.

There are 6 files, each file starts with 9 means it uses recipes of length 10 max, then the block placement dy. In the result there are block from all 6 valid lanes as well. The result include some mess, two directions, and *WSS.

Here is a small script I run to add borders (convert to LifeHistory first)

Code: Select all

import golly as g 

rect = g.getrect()

cells = g.getcells([rect[0], rect[1], rect[2], 10])

for i in xrange(2, len(cells), 3):
	maxx = 100 + cells[i - 2]

for x in xrange(50, maxx, 100):
	for t in xrange(-100, 200):
		g.setcell(x + t, t, 6)
		
		g.setcell(x + t + 1 - 2 * (t % 2), t, 6)

EDIT

The next steps would be

1. Compile all the results into movement + glider emission table.
The table consist of the following input->output:

<Initial block lane>, <output glider lane>, <output glider parity>, <result block lane>, <result block movement>, <best recipe>.

2. Convert from slow salvo recipe format, into arm movements commands.

[dvgrn]

I have compiled results from gate of 29 ticks, and they look pretty much the same as 43 ticks. Turns out that only the first ticks matter most for recipes.

I'm curious now about what the cost analysis would look like without the "dead zone" caused by the recipe stream crossing the carrier stream. At 10hd or 9hd or 8hd, there wouldn't be any possible conflicts between the gliders in each pair, if the recipe stream ended in an NW31 edge shooter:

Code: Select all

x = 246, y = 294, rule = LifeHistory
185.B$175.2A7.2B$175.2A6.3B$182.4B$181.4B$171.2A7.4B$169.B.A7.4B$168.
BA.A6.4B$167.2B2A6.4B$166.4B6.4B$165.4B6.4B$164.4B6.4B$163.4B6.4B$
162.4B6.4B$161.4B6.4B.2A$160.4B6.4B2.2A$159.4B6.4B$158.4B6.4B$157.4B
6.4B$156.4B6.4B$155.4B6.4B$154.4B6.4B$153.4B6.4B$152.4B6.4B$151.4B6.
4B$150.4B6.4B$149.4B6.4B$148.4B6.5B$147.4B6.6B17.2A$146.4B5.9B17.A25.
A$145.4B6.9B17.A.AB20.3A11.A$144.4B6.10B18.2AB.B17.A14.3A$143.4B6.12B
19.4B16.2A16.A14.A$142.4B6.14B18.4B14.4B15.2A12.3A$151.15B8.2A8.5B12.
3B5.B.7B3.3B.2B7.A$150.15B9.A8.6B11.4B.13B5.5B6.2A$149.4B2.12B4.BA.A
8.8B2.36B2.5B$148.4B3.15B.B2A8.14BD37B$147.4B4.17B11.13B3D34B2A$146.
4B5.17B12.7B.4BDBD15B2A17B2A$145.4B3.B.17B12.15BD15B2A16B.B$144.4B3.
2A19B11.19B2.2B3.23B$143.4B4.2AB.19B8.17B11.10B2.9B$142.4B6.B4.20B2.
2B.15B16.6B3.8B$141.4B12.16BD22B19.3B4.7B$140.4B13.9B.4BDBD13B.8B21.B
3.11B$139.4B15.7B2.4B3D9B2A2B3.8B19.2A2.12B$138.4B16.7B2.4BD11B2A2B5.
B3.2A20.A2.12B$137.4B17.6B4.18B10.A18.3A4.11B$136.4B18.7B10.4B.3B.B
12.3A15.A4.4B.4B3DB$135.4B19.6B12.3B20.A20.2A4.4BD2B$134.4B19.7B13.4B
40.A4.2B3D2B$133.4B21.6B15.2A37.3A6.6B$132.4B23.5B15.A38.A8.7B$131.4B
24.6B15.3A44.8B$130.4B27.4B17.A45.8B$129.4B27.B2A2B63.9B$128.4B29.2A
64.6B.4B$127.4B96.7B.4B$126.4B98.6B2.4B$125.4B99.6B3.4B$124.4B100.6B
4.4B$123.4B100.8B4.4B$122.4B100.8B6.4B$121.4B101.9B6.4B$120.4B102.9B
7.4B$119.4B102.10B8.3B$118.4B103.3B2A5B9.2B$117.4B98.2A3.4B2A5B10.B$
116.4B100.A3.11B$115.4B60.A40.A.A12B$114.4B61.3A33.2A4.2A2.8B$113.4B
49.2A3.2A9.A17.A15.A9.7B4.2A$112.4B49.B2AB.B2AB7.2A15.3A15.A.AB7.6B4.
A$111.4B51.2B2.3B3.B4.4B12.A19.2AB.3B3.6B.BA.A$110.4B53.3B.3B.4B4.3B
11.2A20.14B.B2A$109.4B46.2A5.7B.13B11.B20.16B$108.4B48.A5.23B9.3B19.
14B$107.4B49.A.AB.19B.8B4.6B16.16B$106.4B51.2AB.29B2.10B11.18B$105.4B
54.44B3.2B2.20B$104.4B55.37B2A15BD15B$103.4B56.37B2A15BDBD4B.7B$102.
4B58.53B3D4B2.6B$101.4B61.53BD4B3.6B$100.4B60.59B6.4B$99.4B61.2A3.25B
4.13B.4B12.B2A2B$98.4B63.A3.20B4.B4.7B.B5.3B14.2A.B2A$97.4B61.3A6.15B
7.2A17.2B18.BA.A$96.4B62.A8.11B12.A40.A$95.4B71.13B8.3A41.2A$94.4B71.
15B7.A$93.4B72.16B$92.4B73.17B$91.4B74.16B$90.4B77.13B$89.4B78.3B.2B
2A5B$88.4B77.4B2.2B2A3B$87.4B78.2A3.8B$86.4B80.A4.2B3D3B$85.4B78.3A5.
3BD4B$84.4B79.A8.2B3D2B$83.4B89.7B$82.4B82.A7.6B$81.4B82.A.A6.6B$80.
4B83.A.A6.5B$79.4B82.3A.2A4.6B$78.4B82.A4.B6.6B$77.4B84.3AB2AB3.7B$
76.4B87.A.2AB.8B$75.4B92.10B$74.4B93.6B2A3B5.2A$73.4B94.6B2A2B5.A.A$
72.4B95.10B5.A$71.4B95.11B2.BA.A$70.4B96.12B.B2A$69.4B96.15B$59.2A7.
4B96.16B$59.2A6.4B94.2B.16B$66.4B94.2A18B$65.4B95.2AB.17B$55.2A7.4B
97.B.4B.8B2.4B$53.B.A7.4B105.7B4.4B$52.BA.A6.4B107.6B5.4B$51.2B2A6.4B
110.4B6.4B$50.4B6.4B113.3BA5.2B2D$49.4B6.4B115.BA.A5.BDBD$48.4B6.4B
117.A.A6.DB$47.4B6.4B119.A$46.4B6.4B121.3A$45.4B6.4B.2A121.A$44.4B6.
4B2.2A$43.4B6.4B$42.4B6.4B$41.4B6.4B$40.4B6.4B$39.4B6.4B$38.4B6.4B$
37.4B6.4B$36.4B6.4B$35.4B6.4B$34.4B6.4B$33.4B6.4B$32.4B7.4B$31.4B7.5B
17.2A$30.4B5.9B17.A25.A$29.4B6.9B17.A.AB20.3A11.A$28.4B7.9B18.2AB.B
17.A14.3A$27.4B8.10B19.4B16.2A16.A14.A$26.4B8.12B18.4B14.4B15.2A12.3A
$25.4B8.13B8.2A8.5B12.3B5.B.7B3.3B.2B7.A$24.4B10.11B9.A8.6B11.4B.13B
5.5B6.2A$23.4B12.12B4.BA.A8.8B2.36B2.5B$22.3AB13.15B.B2A8.14BD37B$21.
3BA14.17B11.13B3D34B2A$20.3BA15.17B12.7B.4BDBD15B2A17B2A$19.4B13.B.
17B12.15BD15B2A16B.B$18.4B13.2A19B11.19B2.2B3.23B$17.4B14.2AB.19B8.
17B11.10B2.9B$16.4B16.B4.20B2.2B.15B16.6B3.8B$15.4B22.16BD22B19.3B4.
7B$14.4B6.2A5.2A8.9B.4BDBD13B.8B21.B3.11B$13.4B7.2A5.2A9.7B2.4B3D9B2A
2B3.8B19.2A2.12B$12.4B26.7B2.4BD11B2A2B5.B3.2A20.A2.12B$27.2A13.6B4.
18B10.A18.3A4.11B$27.2A13.7B10.4B.3B.B12.3A15.A4.4B.4B3DB$42.6B12.3B
20.A20.2A4.4BD2B$41.7B13.4B40.A4.2B3D2B$42.6B15.2A37.3A6.6B$4.2A37.5B
15.A38.A8.7B$4.2A13.A23.6B15.3A44.8B$17.2A.A24.4B17.A45.8B$2A5.2A9.A.
2A22.B2A2B63.9B$2A5.2A11.A24.2A64.6B.4B$111.7B.4B$112.6B2.4B$112.6B3.
4B$112.6B4.4B$111.8B4.4B$110.8B6.4B$110.9B6.4B$8.2A100.9B7.4B$9.A99.
10B8.3B$6.3A100.3B2A5B9.2B$6.A96.2A3.4B2A5B10.B$104.A3.11B$63.A40.A.A
12B$63.3A33.2A4.2A2.8B$50.2A3.2A9.A17.A15.A9.7B4.2A$49.B2AB.B2AB7.2A
15.3A15.A.AB7.6B4.A$50.2B2.3B3.B4.4B12.A19.2AB.3B3.6B.BA.A$51.3B.3B.
4B4.3B11.2A20.14B.B2A$43.2A5.7B.13B11.B20.16B$44.A5.23B9.3B19.14B$44.
A.AB.19B.8B4.6B16.16B$45.2AB.29B2.10B11.18B$47.44B3.2B2.20B$47.37B2A
15BD15B$47.37B2A15BDBD4B.7B$48.53B3D4B2.6B$50.53BD4B3.6B$48.59B6.4B$
48.2A3.25B4.13B.4B12.B2A2B$49.A3.20B4.B4.7B.B5.3B14.2A.B2A$46.3A6.15B
7.2A17.2B18.BA.A$46.A8.11B12.A40.A$54.13B8.3A41.2A$53.15B7.A$53.16B$
53.17B$53.16B$55.13B$55.3B.2B2A5B$53.4B2.2B2A3B$53.2A3.8B$54.A4.2B3D
3B$51.3A5.3BD4B$51.A8.2B3D2B$60.7B$52.A7.6B$51.A.A6.6B$51.A.A6.5B$49.
3A.2A4.6B$48.A4.B6.6B$49.3AB2AB3.7B$51.A.2AB.8B$55.10B$55.6B2A3B5.2A$
55.6B2A2B5.A.A$55.10B5.A$54.11B2.BA.A$54.12B.B2A$53.15B$52.16B$49.2B.
16B$48.2A18B$48.2AB.17B$49.B.4B.8B2.4B$56.7B4.4B$57.6B5.4B$59.4B6.4B$
61.3BA5.2B2C$62.BA.A5.BCBC$63.A.A6.CB$64.A$65.3A$67.A20$97.2C$97.C.C$
97.C23$122.2C$122.C.C$122.C!

Add another p120 glider gun to replace the syringe, if that seems better. The important thing is to find the best/simplest/most efficient geometry that allows an edge-shooter to deliver the recipe gliders, using only circuitry that recovers within about 90 ticks. That would allow a significantly wider range of glider pairs, with the recipe glider either leading or following the p120 glider.

The above pattern shows that starting up this kind of carrier-signal construction arm wouldn't be difficult at all -- lots of possible solutions. With the new period-independent self-destruct method from the 10hd and 0hd Demonoids, getting a correctly-timed shutdown signal wouldn't be a problem either: the self-destruct trigger glider can be adjusted to the exact timing where it's needed, and if the self-destruct circuitry is calibrated correctly, it will automatically produce an output trigger glider with the right timing to trigger the next self-destruct sequence.

That just leaves the problem of self-destruct-seeding the reflector circuit, whatever form that ends up taking. Self-destruct circuitry seems like an unavoidably painful puzzle, since it has to be started again from scratch whenever the circuitry changes. But it's not really all that difficult or time-consuming to come up with a workable solution.

EDIT: One way to create a reasonably easy standard self-destruct system is to write a script to create a "meteor shower seed". This would be chain of cheap glider splitters that build a slow salvo that shoots down the target circuit. Most commonly the slow salvo would be found automatically by a greedy search algorithm, as in the Gemini, but it could be combined with a scattering of bait still lifes if that turned out to be more efficient (which it probably would).

[simsim314]

I was also thinking how the 0-hd design could be used. Considering the most costly part is G->H converter, one can use p120 to clear the extra beehive from the usual known G->H + beehive.

One should convert this design to edge shooter to make it work:

Code: Select all

x = 444, y = 412, rule = LifeHistory
.A$2.A$3A28$31.A$32.A$30.3A28$61.A$62.A$60.3A28$91.A$92.A$90.3A28$
121.A$122.A$120.3A25$148.A$149.A$147.3A31$181.A$182.A$180.3A28$211.A$
212.A$210.3A28$241.A$242.A$240.3A28$271.A$272.A$270.3A28$301.A$302.A$
300.3A25$328.A$329.A$327.3A25$428.A$428.3A$431.A$430.2A3$361.A$362.A$
360.3A32.A$369.A9.A15.3A$369.3A5.3A18.A$372.A3.A20.2A11.2A$371.2A3.2A
32.2A4$442.2A$442.2A3$385.2A$385.2A34.2A$373.2A45.A.A$372.A2.A44.A$
367.2A4.2A44.2A$366.A.A30.2A$366.A32.2A$365.2A$375.2A33.2A$375.A25.A
8.A$376.3A20.A.A9.3A$378.A19.A.A12.A$383.2A12.A2.A6.A$384.A16.A5.A$
381.3A14.A2.A$381.A17.3A3$426.2A$425.A.A$425.A$413.A10.2A$411.A.A$
412.2A2$416.2A$416.A.A$418.A$418.2A$410.2A$410.2A2$407.2A$407.2A3$
410.2A$410.2A!

As for self destruct, this pattern is naturally "unstable" so the self destruct could be based upon this inherent instability.

[simeks]

I was trying to prove that "fast singleton" gliders with a minimum spacing of 90 ticks is enough to make a universal elbow.

This would make a Demonoid spaceship possible using just half of dvgrn's design here.

Here are four recipes to prove it is possible, although they are pretty awkward.

I used a small modification to chris_c's elbow0.py script published here to find these. Thanks!

Code: Select all

x = 1875, y = 1878, rule = LifeHistory
1297.2E190.2E190.2E190.2E$1297.2E190.2E190.2E190.2E26$1273.2A190.2A
190.2A190.2A$1274.2A190.2A190.2A190.2A$1273.A191.A191.A191.A25$1246.
2A190.2A190.2A190.2A$1245.A.A189.A.A189.A.A189.A.A$1247.A191.A191.A
191.A51$1193.2A190.3A189.2A190.3A$1194.2A191.A190.2A191.A$1193.A192.A
190.A192.A21$1170.A191.2A190.A191.2A$1170.2A191.2A189.2A191.2A$1169.A
.A190.A190.A.A190.A55$1113.3A189.3A189.3A189.3A$1115.A191.A191.A191.A
$1114.A191.A191.A191.A78$1033.2A190.3A189.2A190.2A$1034.2A191.A190.2A
190.2A$1033.A192.A190.A191.A21$1010.2A$1011.2A572.2A$1010.A189.3A383.
2A$1202.A382.A$1201.A4$1386.2A$1387.2A$1386.A47$953.2A190.2A190.3A
189.2A$954.2A190.2A191.A190.2A$953.A191.A192.A190.A21$1506.3A$1508.A$
1120.2A385.A$1119.A.A189.2A$1121.A190.2A$1311.A2$923.3A$925.A$924.A
48$873.3A189.3A189.2A190.2A$875.A191.A190.2A190.2A$874.A191.A190.A
191.A24$1231.A$1231.2A$1037.2A191.A.A$1038.2A$1037.A50$1177.2A190.2A$
1178.2A190.2A$1177.A191.A21$1346.2A$1347.2A$1346.A2$1150.2A$1151.2A$
1150.A51$1289.2A$1290.2A$1289.A21$1266.3A$1268.A$1267.A55$1209.2A$
1210.2A$1209.A22$1185.2A$1184.A.A$1186.A54$1129.A$1129.2A$1128.A.A78$
1049.2A$1048.A.A$1050.A23$1024.2A$1023.A.A$1025.A53$969.2A$968.A.A$
970.A21$946.2A$947.2A$946.A55$889.A$889.2A$888.A.A21$866.2A$865.A.A$
867.A55$809.2A$808.A.A$810.A21$786.2A$785.A.A$787.A55$729.2A$728.A.A$
730.A25$702.A$702.2A$701.A.A51$649.2A$648.A.A$650.A21$626.2A$625.A.A$
627.A63$561.A$561.2A$560.A.A26$533.3A$535.A$534.A50$481.2A$480.A.A$
482.A21$458.A$458.2A$457.A.A55$401.2A$400.A.A$402.A78$321.A$321.2A$
320.A.A22$297.A$297.2A$296.A.A54$241.A$241.2A$240.A.A21$218.2A$217.A.
A$219.A55$161.2A$160.A.A$162.A21$138.2A$139.2A$138.A55$81.A$81.2A$80.
A.A27$52.A$52.2A$51.A.A49$.A$.2A$A.A!

[Kazyan]

I was trying to prove that "fast singleton" gliders with a minimum spacing of 90 ticks is enough to make a universal elbow.

This would make a Demonoid spaceship possible using just half of dvgrn's design here.

Here are four recipes to prove it is possible, although they are pretty awkward.

I used a small modification to chris_c's elbow0.py script published here to find these. Thanks!

Code: Select all

x = 1875, y = 1878, rule = LifeHistory
1297.2E190.2E190.2E190.2E$1297.2E190.2E190.2E190.2E26$1273.2A190.2A
190.2A190.2A$1274.2A190.2A190.2A190.2A$1273.A191.A191.A191.A25$1246.
2A190.2A190.2A190.2A$1245.A.A189.A.A189.A.A189.A.A$1247.A191.A191.A
191.A51$1193.2A190.3A189.2A190.3A$1194.2A191.A190.2A191.A$1193.A192.A
190.A192.A21$1170.A191.2A190.A191.2A$1170.2A191.2A189.2A191.2A$1169.A
.A190.A190.A.A190.A55$1113.3A189.3A189.3A189.3A$1115.A191.A191.A191.A
$1114.A191.A191.A191.A78$1033.2A190.3A189.2A190.2A$1034.2A191.A190.2A
190.2A$1033.A192.A190.A191.A21$1010.2A$1011.2A572.2A$1010.A189.3A383.
2A$1202.A382.A$1201.A4$1386.2A$1387.2A$1386.A47$953.2A190.2A190.3A
189.2A$954.2A190.2A191.A190.2A$953.A191.A192.A190.A21$1506.3A$1508.A$
1120.2A385.A$1119.A.A189.2A$1121.A190.2A$1311.A2$923.3A$925.A$924.A
48$873.3A189.3A189.2A190.2A$875.A191.A190.2A190.2A$874.A191.A190.A
191.A24$1231.A$1231.2A$1037.2A191.A.A$1038.2A$1037.A50$1177.2A190.2A$
1178.2A190.2A$1177.A191.A21$1346.2A$1347.2A$1346.A2$1150.2A$1151.2A$
1150.A51$1289.2A$1290.2A$1289.A21$1266.3A$1268.A$1267.A55$1209.2A$
1210.2A$1209.A22$1185.2A$1184.A.A$1186.A54$1129.A$1129.2A$1128.A.A78$
1049.2A$1048.A.A$1050.A23$1024.2A$1023.A.A$1025.A53$969.2A$968.A.A$
970.A21$946.2A$947.2A$946.A55$889.A$889.2A$888.A.A21$866.2A$865.A.A$
867.A55$809.2A$808.A.A$810.A21$786.2A$785.A.A$787.A55$729.2A$728.A.A$
730.A25$702.A$702.2A$701.A.A51$649.2A$648.A.A$650.A21$626.2A$625.A.A$
627.A63$561.A$561.2A$560.A.A26$533.3A$535.A$534.A50$481.2A$480.A.A$
482.A21$458.A$458.2A$457.A.A55$401.2A$400.A.A$402.A78$321.A$321.2A$
320.A.A22$297.A$297.2A$296.A.A54$241.A$241.2A$240.A.A21$218.2A$217.A.
A$219.A55$161.2A$160.A.A$162.A21$138.2A$139.2A$138.A55$81.A$81.2A$80.
A.A27$52.A$52.2A$51.A.A49$.A$.2A$A.A!

Nice! I'd had an inkling about something like this here; nice to see it works. A possible advantage is not having to use edge-shooters anymore, though I'm not sure about that, since I don't fully understand the Demonoid geometry.

Weird thought: Consider the use of a periodic circuit that rephases a glider, in order to "artificially" turn two singleton gliders into a doubleton. Perhaps a p120 gun that fires across the singleton glider stream. The singleton stream may need two gliders at 50 (arbitrary number) ticks apart, but the arm can't do that. Instead, the arm fires them 230 (arbitrary number) ticks apart, so that the leading glider will be caught by the gun's stream. This collision produces a signal, which is fed into some circuitry that edge-shoots a glider back into the singleton glider stream, but 180 ticks late, so that it has effectively transformed the 230-tick-spacing into 50-tick spacing. Would a throttle of that sort be useful?

[dvgrn]

I was trying to prove that "fast singleton" gliders with a minimum spacing of 90 ticks is enough to make a universal elbow... Here are four recipes to prove it is possible, although they are pretty awkward.

Good Golly. That's really impressive -- another radical simplification in Life universal constructors. It didn't really occur to me to hope that a pi explosion could be reduced back to a clean set of elbow ops, with following gliders at 90+ ticks distance. Kazyan's guess was better than mine.

A block isn't the only possible elbow object that might work in this context, though it's probably far and away the most likely one. Other elbow candidates might be honeyfarms, blinkers, traffic lights, possibly beehives, and possibly possibly a few other small constellations. Did you try searches starting from anything other than a block?

It might be worth trying to find a multi-elbow toolkit similar to the one chris_c came up with for the 0hd Demonoid. Obviously the other elbows will be a lot harder to find, though, and the nice simple block-only toolkit is good enough.

These four operations are actually more than is strictly needed for universality. We could get by with just the cheaper of the two glider outputs; monochromatic P1 is still universal. It's quite a lot less efficient, though, so it's definitely nice to have the other glider color available for emergencies!

The next two things I would wish for would be a recipe that can turn one elbow into two, and a recipe that could flip the block to the other side of the construction lane -- allowing gliders to be sent in the opposite direction using the same two recipes.

Then if someone can just come up with halfway-decent slow salvo recipes for different orientations of Snarks, then self-constructing circuitry would get a really big boost. It's okay if it's fairly expensive, but it would be nice if the construction reaction didn't have a really huge bounding box. -- But maybe I might as well just wish for a new Spartan Snark, while I'm at it.

Weird thought: Consider the use of a periodic circuit that rephases a glider, in order to "artificially" turn two singleton gliders into a doubleton. Perhaps a p120 gun that fires across the singleton glider stream. The singleton stream may need two gliders at 50 (arbitrary number) ticks apart, but the arm can't do that. Instead, the arm fires them 230 (arbitrary number) ticks apart, so that the leading glider will be caught by the gun's stream. This collision produces a signal, which is fed into some circuitry that edge-shoots a glider back into the singleton glider stream, but 180 ticks late, so that it has effectively transformed the 230-tick-spacing into 50-tick spacing. Would a throttle of that sort be useful?

Given recent experience, I'm reluctant to say that it definitely wouldn't be useful. However, I spent quite a bit of time as far back as 2010 trying to figure out how to send two gliders right after one another in an input stream, and send a copy of them into a construction arm while either delaying the lead one or advancing the trailing one -- to produce usable glider pairs.

Your idea of using a p120 gun in the design has the possible advantage of allowing singleton gliders on either stream. My original delaying circuitry used period doublers, so both gliders had to be there. (It also used 9hd, and syringes were still far in the future at that point, but those are just implementation details.)

The key difficulty I'm having is imagining "some circuitry that edge-shoots a glider" that could possibly end up being small enough to be worth building. My mental picture just ends up looking unnecessarily big and complicated and awkward, especially compared to simeks' new design. But I've been wrong before -- very recently, in fact...!

[dvgrn]

A possible advantage is not having to use edge-shooters anymore, though I'm not sure about that, since I don't fully understand the Demonoid geometry.

Yes, that's exactly why it't such a radical improvement. Any spare glider output from any signal track carrying one of these simeks-recipes can be turned into another construction arm, just by aiming the gliders at a block.

(If there's anything that anyone doesn't understand about Demonoid geometry, by the way, please go ahead and ask questions, here or on the Demonoid thread. The 0hd Demonoid is actually fairly clean and simple, at least compared to the 10hd version and earlier designs.)

There have been quite a number of Geminoid designs that managed to pack a complete construction recipe into one glider stream. That was at least better than the twelve streams in the original Gemini. But up until now, that single glider stream always had to be decoded somehow -- and decoding circuitry tends to be big and expensive, especially when you have to have a recipe for every single little piece of it.

Now suddenly there's no decoder needed at all -- just send the glider stream out and let it do its work. The total complexity goes way down, no matter how inefficient the actual recipes are -- and Golly's simulation speed goes way up.

New Demonoid Possibilities

This would make a Demonoid spaceship possible using just half of dvgrn's design here.

A Demonoid could be made a good bit smaller than that, actually. The minimal circuitry might be something along these lines, not including the self-destruct mechanism:

Code: Select all

x = 167, y = 163, rule = LifeHistory
79.2E$79.2E10$152.D$152.3D$155.D$154.2D10$142.2D$93.2D3.2D27.D15.D$
93.2D3.2D25.3D15.D.D$124.D19.2D$124.2D$86.2D$87.D$87.D.D75.2D$88.2D
75.2D2$127.2D$127.2D4$91.2D$92.D$89.3D28.2D$89.D31.D$118.3D$118.D$
153.2D$154.D$151.3D$151.D$104.2D$104.2D$96.2D$97.D$94.3D$94.D2$95.D$
94.D.D$94.D.D$92.3D.2D$91.D$92.3D.2D$94.D.2D2$104.2D8.2D$104.2D7.D.D$
113.D$111.D.D$111.2D4$91.2D$91.2D5$107.D$2E104.D.D$2E104.D.D$107.D$
108.3D$110.D6$70.4B$71.2BAB$72.B3A$18.B54.3BA$18.2B54.B2AB$18.3B54.4B
$18.4B54.4B$19.4B53.4B$20.4B52.5B$21.4B50.9B$22.4B49.9B$23.4B48.9B$
24.4B46.10B$25.4B44.12B$26.4B33.2A8.13B$14.2A3.2A6.4B17.A15.A9.11B$
13.B2AB.B2AB6.4B14.3A15.A.AB4.12B$14.2B2.3B3.B4.4B12.A19.2AB.15B$15.
3B.3B.4B3.4B11.2A20.17B$7.2A5.7B.13B11.B20.17B$8.A5.23B9.3B19.17B.B$
8.A.AB.19B.8B4.6B16.19B2A$9.2AB.29B2.10B11.19B.B2A$11.44B3.2B2.20B4.B
$11.37B2A15BD16B$11.37B2A15BDBD4B.9B$12.53B3D4B2.7B$14.53BD4B2.7B$12.
59B4.6B$12.2A3.25B4.13B.4B10.7B$13.A3.20B4.B4.7B.B5.3B12.6B$10.3A6.
15B7.2A32.7B$10.A8.11B12.A33.5B$18.13B8.3A34.6B$17.15B7.A34.9B$17.16B
41.2A.7B$17.17B41.A5.4B$17.16B39.3A7.4B$19.13B40.A10.4B$19.3B.2B2A5B
52.4B$17.4B2.2B2A3B55.4B$17.2A3.8B56.4B$18.A4.2B3D3B56.4B$15.3A5.3BD
4B57.4B$15.A8.2B3D2B58.4B$24.7B59.4B$16.A7.6B61.4B$15.A.A6.6B62.3BD$
15.A.A6.5B64.3BD$13.3A.2A4.6B65.3D$12.A4.B6.6B$13.3AB2AB3.7B$15.A.2AB
.8B$19.10B$19.6B2A3B5.2A$19.6B2A2B5.A.A$19.10B5.A$18.11B2.BA.A$18.12B
.B2A$17.15B$16.16B$13.2B.16B$12.2A18B$12.2AB.17B$13.B.4B.8B2.4B$20.7B
4.4B$21.6B5.4B$23.4B6.4B$25.3BA5.2B2D$26.BA.A5.BDBD$27.A.A6.DB$28.A$
29.3A$31.A!

This one is kind of silly, because a second slow elbow would be needed to hit the next construction site with slow gliders. Exponential loss of efficiency is usually bad. So probably something like this would be better:

Code: Select all

x = 92, y = 128, rule = LifeHistory
86.4B$85.4B$84.4B$83.4B$82.4B$81.4B$80.4B$79.4B$78.4B$77.4B$76.4B$75.
4B$74.4B$73.4B$72.4B$71.4B$70.4B$69.4B$68.4B$67.4B6.2A3.2A$66.4B6.B2A
B.B2AB$65.4B4.B3.3B2.2B$64.4B3.4B.3B.3B$63.13B.7B5.2A$61.23B5.A$57.8B
.19B.BA.A$56.29B.B2A$54.33B$53.34B$52.35B$51.35B$51.33B$52.34B$51.30B
3.2A$50.B2A2B6.20B3.A$51.2A11.15B6.3A$68.11B8.A$67.13B$66.15B$65.16B$
64.17B$65.16B$66.13B$66.5B2A2B.4B$66.5B2A2B2.4B$66.10B2.4B$66.4B3D2B
4.4B$67.4BD3B5.4B$67.2B3D2B7.4B$67.7B8.4B$68.5B10.4B$68.5B11.4B$69.4B
12.4B$69.4B13.4B$68.5B14.4B$68.5B15.4B$69.6B14.3B$69.6B15.2B$69.6B16.
B$68.8B$67.8B$67.9B$67.9B$66.10B$66.3B2A5B$60.2A3.4B2A5B$61.A3.11B$
20.A40.A.A12B$20.3A33.2A4.2A2.8B$7.2A3.2A9.A17.A15.A9.7B4.2A$6.B2AB.B
2AB7.2A15.3A15.A.AB7.6B4.A$7.2B2.3B3.B4.4B12.A19.2AB.3B3.6B.BA.A$8.3B
.3B.4B4.3B11.2A20.14B.B2A$2A5.7B.13B11.B20.16B$.A5.23B9.3B19.14B$.A.A
B.19B.8B4.6B16.16B$2.2AB.29B2.10B11.18B$4.44B3.2B2.20B$4.37B2A15BD15B
$4.37B2A15BDBD4B.7B$5.53B3D4B2.6B$7.53BD4B3.6B$5.59B6.4B$5.2A3.25B4.
13B.4B12.B2A2B$6.A3.20B4.B4.7B.B5.3B14.2A.B2A$3.3A6.15B7.2A17.2B18.BA
.A$3.A8.11B12.A40.A$11.13B8.3A41.2A$10.15B7.A$10.16B$10.17B$10.16B$
12.13B$12.3B.2B2A5B$10.4B2.2B2A3B$10.2A3.8B$11.A4.2B3D3B$8.3A5.3BD4B$
8.A8.2B3D2B$17.7B$9.A7.6B$8.A.A6.6B$8.A.A6.5B$6.3A.2A4.6B$5.A4.B6.6B$
6.3AB2AB3.7B$8.A.2AB.8B$12.10B$12.6B2A3B5.2A$12.6B2A2B5.A.A$12.10B5.A
$11.11B2.BA.A$11.12B.B2A$10.15B$9.16B$6.2B.16B$5.2A18B$5.2AB.17B$6.B.
4B.8B2.4B$13.7B4.4B$14.6B5.4B$16.4B6.4B$18.3BA5.2B2C$19.BA.A5.BCBC$
20.A.A6.CB$21.A$22.3A$24.A!

It just occurred to me that an L112+SE31T160 is much better than the L112+L112+Fx77+NW31T120 from the link, because the output lane is an exact power of two away from the input lane (128hd). Unfortunately the temporal offset is odd, which is as bad as it could possibly be -- but Golly might still manage to run away with a Demonoid that uses this circuitry. Can't really tell for sure without building it...

Nowadays there are quite a few Spartan H-to-Gs that recover in less than 90 ticks. These are just the SE ones:

Code: Select all

x = 412, y = 101, rule = LifeHistory
366.3D2.5D.5D.5D.5D3.D5.D3.5D$365.D3.D.D5.D9.D3.D4.2D4.2D3.D$365.D5.D
5.D8.D4.D5.D5.D3.D$366.3D2.3D4.3D4.D5.D5.D5.D4.3D$369.D.D9.D2.D6.D5.D
5.D7.D$365.D3.D.D5.D3.D.D7.D5.D5.D3.D3.D$366.3D2.5D2.3D2.D7.D4.3D3.3D
3.3D4$366.3D2.5D2.3D3.3D2.5D8.3D$365.D3.D.D5.D3.D.D3.D3.D9.D3.D$365.D
5.D9.D5.D3.D9.D3.D$366.3D2.3D6.D5.D4.D3.5D2.3D$369.D.D7.D5.D5.D9.D3.D
$365.D3.D.D6.D5.D6.D9.D3.D$366.3D2.5D.5D.5D3.D10.3D3$316.3D2.5D4.D5.D
2.5D2.3D4.D$315.D3.D.D7.2D4.2D4.D3.D3.D2.2D$315.D5.D6.D.D3.D.D4.D3.D
3.D3.D$316.3D2.3D3.D2.D2.D2.D4.D4.4D3.D$319.D.D5.5D.5D3.D7.D3.D33.2AB
$315.D3.D.D8.D5.D4.D7.D3.D31.BA2BA2B$316.3D2.5D4.D5.D4.D4.3D3.3D29.3B
2A3B$382.12B$381.14B$381.13B$380.14B$155.D3.D.D3.D2.3D4.D3.5D3.D4.3D
3.3D179.15B$155.2D2.D.D3.D.D3.D2.2D5.D4.2D3.D3.D.D3.D130.2AB46.14B$
155.D.D.D.D3.D5.D3.D5.D5.D7.D.D2.2D128.BA2BA2B45.13B$155.D2.2D.D.D.D
3.2D4.D5.D5.D6.D2.D.D.D127.3B2A3B46.3B.8B$155.D3.D.D.D.D5.D3.D5.D5.D
5.D3.2D2.D125.12B49.7B$155.D3.D.2D.2D.D3.D3.D5.D5.D4.D4.D3.D124.14B
48.7B$155.D3.DBD3.D2.3D3.3D4.D4.3D2.5D2.3D125.13B50.6B$325.14B50.7B$
325.15B49.8B$326.14B50.8B$65.3D2.5D8.3D2.5D2.3D3.3D52.3D2.5D.5D.5D3.D
6.D78.3D2.5D2.3D4.D3.5D2.3D3.3D21.13B50.9B$64.D3.D.D11.D3.D3.D3.D3.D.
D3.D50.D3.D.D9.D3.D4.2D5.2D77.D3.D.D5.D3.D2.2D5.D3.D5.D3.D21.3B.8B49.
6B.4B$64.D5.D15.D3.D3.D3.D.D2.2D50.D5.D8.D4.D5.D4.D.D77.D5.D9.D3.D5.D
3.D5.D2.2D26.7B49.7B.4B$65.3D2.3D3.5D4.D4.D4.3D2.D.D.D51.3D2.3D5.D5.D
5.D3.D2.D78.3D2.3D5.2D4.D5.D3.4D2.D.D.D26.7B50.6B2.4B$68.D.D13.D5.D3.
D3.D.2D2.D54.D.D6.D6.D5.D3.5D80.D.D9.D3.D5.D3.D3.D.2D2.D27.6B50.6B3.
4B$64.D3.D.D12.D6.D3.D3.D.D3.D50.D3.D.D5.D7.D5.D6.D77.D3.D.D5.D3.D3.D
5.D3.D3.D.D3.D27.7B49.6B4.4B$65.3D2.5D7.5D3.D4.3D3.3D52.3D2.5D.D7.D4.
3D5.D78.3D2.5D2.3D3.3D4.D4.3D3.3D28.8B47.8B4.4B$.3D2.5D9.D3.5D.5D3.D
4.3D3.3D163.3D2.5D2.3D3.3D2.5D8.3D81.8B45.8B6.4B$D3.D.D12.2D7.D3.D4.
2D3.D3.D.D165.D3.D.D5.D3.D.D3.D3.D9.D84.9B44.9B6.4B$D5.D13.D6.D4.D5.D
3.D2.2D.D120.4B41.D5.D9.D5.D3.D9.D83.6B.4B43.9B7.4B$.3D2.3D3.5D3.D5.D
5.D5.D3.D.D.D.4D32.2B29.3D2.5D.5D.5D2.3D3.3D22.4B41.3D2.3D6.D4.2D4.D
3.5D.4D80.7B.4B41.10B8.4B$4.D.D13.D4.D6.D5.D3.2D2.D.D3.D31.BA2B26.D3.
D.D5.D7.D3.D3.D.D3.D22.4B43.D.D7.D7.D3.D9.D3.D80.6B2.4B40.3B2A5B9.4B$
D3.D.D13.D3.D7.D5.D3.D3.D.D3.D30.BABA2B25.D5.D5.D7.D7.D5.D23.4B38.D3.
D.D6.D4.D3.D3.D9.D3.D80.6B3.4B38.4B2A5B10.3B$.3D2.5D8.3D2.D7.D4.3D3.
3D3.3D30.2BABA2B26.3D2.3D4.3D4.D6.D4.2D25.4B38.3D2.5D.5D2.3D4.D10.3D
81.6B4.4B37.11B11.2B$82.3BA2B30.D.D9.D3.D5.D7.D25.4B110.B45.8B4.4B31.
2A.A12B12.B$81.6B27.D3.D.D5.D3.D3.D4.D4.D3.D26.4B108.2AB.2B40.8B6.4B
30.A.2A2.8B$82.7B26.3D2.5D2.3D4.D3.5D2.3D27.4B108.2A5B39.9B6.4B36.7B
4.2A$83.7B2.B82.5B108.7B38.9B7.4B36.6B4.A$83.7B.B2A80.9B105.8B36.10B
8.4B35.6B.BA.A$84.8B2A80.9B59.A46.7B36.3B2A5B9.3B34.7B.B2A$84.6B.2B
81.9B57.3A46.8B34.4B2A5B10.2B35.8B$83.7B83.10B56.A49.9B28.2A3.11B11.B
28.A6.7B$82.8B46.2A34.12B55.2A48.9B28.A2.A12B40.3A4.7B$72.2A8.8B32.2A
10.2B2AB23.2A8.13B37.2A12.5B48.9B24.2A4.2A2.8B33.A11.A2.7B4.B$73.A9.
8B32.A10.4B25.A9.11B39.A11.4B50.9B25.A9.7B4.2A27.3A8.2A3.6B.B.2BA$73.
A.AB4.10B32.A.AB6.7B23.A.AB4.12B40.A.AB7.6B48.11B24.A.AB7.6B4.A31.A7.
15BA.A$27.A46.2AB.14B32.2AB.3B.8B24.2AB.15B41.2AB.3B3.7B47.11B25.2AB.
3B3.6B.BA.A30.2A3.B5.12B.BA$25.3A48.17B33.14B26.17B43.16B46.12B26.14B
.B2A31.8B2.13B$24.A51.17B33.14B26.17B43.17B39.B4.14B25.16B35.21B$24.
2A51.17B.B31.13B27.17B.B41.17B33.B3.3B3.10B.4B25.14B36.20B$19.7B6.2A
42.19B2A29.14B.2B23.19B2A39.19B31.2B.6B2.16B23.16B34.19B$18.8B6.A41.
19B.B2A27.18B2A20.19B.B2A37.17B.4B27.5B.7B.17B20.18B32.21B$17.10B2.BA
.A39.21B2.B26.18B.B2A18.19B4.B36.19B2.4B24.A28B.4B17.19B31.24B$17.7BC
3B.B2A40.2BC17B30.2BC15B2.B19.2BC16B41.2BC15B4.4B21.3B2AD25B2.4B16.2B
C15B32.2BC14B4.4B$18.6BCBC3B41.3BCBC4B.9B30.3BCBC4B.7B22.3BCBC4B.9B
40.3BCBC4B.7B6.4B20.4BACBD23B3.4B14.3BCBC4B.7B32.3BCBC4B.6B6.4B$17.7B
3C3B42.2B3C4B.8B32.2B3C4B.8B22.2B3C4B2.7B42.2B3C4B2.6B7.4B19.5BDCDB2A
21B3.3B15.2B3C4B2.6B33.2B3C4B2.B.5B5.4B$14.12BC3B41.5BC4B.8B31.5BC4B
2.7B21.5BC4B2.7B41.5BC4B2.6B8.4B18.B5ABDB2A21B4.2B14.5BC4B3.6B31.5BC
4B7.2A6.4B$13.17B40.10B.9B30.10B3.7B20.10B4.6B40.10B3.5B10.3B18.4BA
28B18.10B6.4B30.10B8.A8.4B$13.16B40.4B6.10B.2B27.4B11.6B.BA16.4B10.7B
39.4B8.9B9.2B18.4B2.26B18.4B12.B2A2B29.4B16.3A6.4B$14.15B40.3B5.14B2A
26.3B12.7BA.A15.3B12.6B39.3B9.2AB4.2A10.B26.B2.20B19.3B14.2A.B2A27.3B
19.A7.4B$18.10B39.4B5.15B2A24.4B13.8BA14.4B13.7B36.4B11.A5.A40.20B.B.
B14.4B18.BA.A24.4B29.4B$17.13B37.2A6.17B25.2A15.6B.B15.2A16.5B37.2A
10.3A7.3A36.24B2A13.2A23.A24.2A32.4B$18.12B38.A7.13B29.A15.5B19.A16.
6B37.A10.A11.A36.24B2A14.A23.2A24.A33.4B$17.13B35.3A11.10B26.3A16.6B
15.3A15.9B33.3A58.2AB2.5B2.12B.2B12.3A47.3A35.4B$17.13B2.A32.A13.11B
25.A16.2AB.5B14.A17.2A.7B32.A59.A.AB2.4B3.13B14.A49.A38.4B$16.14B.A.A
45.10B42.A.AB3.4B32.A5.4B91.A14.11B.B102.4B$14.16B2.A47.8B43.A7.4B28.
3A7.4B89.2A14.12B2A102.4B$14.13B2AB53.4B43.2A8.4B27.A10.4B24.B79.10B.
B2A103.3B$14.9B3.A2BA54.4B53.3B39.4B101.2AB.6B4.B105.2B$12.2AB.8B3.2A
56.4B53.2B40.4B99.A.AB.4B113.B$11.A.AB.9B61.4B95.4B98.A5.5B$11.A8.B.
4B61.4B95.4B96.2A8.2A$10.2A11.4B61.4B95.4B105.A$24.4B61.3B96.4B105.3A
$25.4B160.4B106.A$26.4B$27.4B$28.4B$29.4B$30.4B$31.4B!

I still haven't gotten around to wrestling with Hersrch, to find the smallest Demonoid circuit that can be adjusted to allow exact power-of-two offsets in both space and time. No doubt one of these H-to-Gs would complete a pure power-of-two circuit that isn't too horribly large.

But Never Mind Those Silly Demonoids, Anyway!
I think it's probably worth avoiding any further Gemini-style boustrophedonic designs from now on. Golly just unavoidably has a lot of trouble with nearby recipe streams traveling in opposite directions.

The place where simeks-recipe construction arms will really come in handy is in a quadratic-growth replicator. I think they'll simplify a diamond-shaped replicator design by about an order of magnitude...!