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### 22da (Hexagonal Grid)

Posted: March 2nd, 2014, 8:44 pm
This is my first experiment with two-state hexagonal rules, and I made the following rule table:

Code: Select all

``````@RULE 22da

@TABLE

n_states:2
neighborhood:hexagonal
symmetries:rotate6reflect
var a={0,1}
var b={a}
var c={a}
0,1,1,0,0,0,0,1
0,1,0,1,0,0,0,1
0,1,0,0,1,0,0,1
1,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0
1,1,1,1,a,b,c,0
1,1,1,c,1,a,b,0
1,1,c,1,b,1,a,0
1,1,0,1,0,0,0,0``````
In Callahan's notation, this rule is B2/S2o2p, and I found it to be very interesting. The block in this rule is a failed replicator which lives for 31 generations and becomes two c/3 gliders, which also work in regular B2/S2H. (For some reason, the block nearly always acts like a failed replicator; if it wasn't for it, B2/S2H/C3 would be stable.) I also found a pattern that behaves much like the switch engine:

0 0 1
1 1 0
1 1 0

6-cell infinite growth:

Code: Select all

``````x = 4, y = 4, rule = 22da
2b2o\$2b2o\$bo\$o!``````
Sparky p16 eating glider:

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``````x = 26, y = 27, rule = 22da
25bo\$23b2o\$23b2o21\$bo\$2bo\$2obo\$bo!``````
The same p16 can eat a puffer (!):

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``````x = 38, y = 38, rule = 22da
36bo\$34bob2o\$35bo\$36bo31\$2b2o\$2b2o\$bo\$o!``````
and I believe this is the pattern less than 11 cells that has the highest growth rate:

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``````x = 9, y = 9, rule = 22da
2bo\$2o\$2o4\$8bo\$6b2o\$6b2o!``````
This is either a breeder with a period of at least 1000000 gens or an unlimited novelty generator:

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``````x = 195, y = 195, rule = 22da
2bo\$2o\$2o4\$8bo\$6b2o\$6b2o4\$14bo\$12b2o\$12b2o4\$20bo\$18b2o\$18b2o4\$26bo\$24b
2o\$24b2o4\$32bo\$30b2o\$30b2o4\$38bo\$36b2o\$36b2o4\$44bo\$42b2o\$42b2o4\$50bo\$
48b2o\$48b2o4\$56bo\$54b2o\$54b2o4\$62bo\$60b2o\$60b2o4\$68bo\$66b2o\$66b2o4\$74b
o\$72b2o\$72b2o4\$80bo\$78b2o\$78b2o4\$86bo\$84b2o\$84b2o4\$92bo\$90b2o\$90b2o4\$
98bo\$96b2o\$96b2o4\$104bo\$102b2o\$102b2o4\$110bo\$108b2o\$108b2o4\$116bo\$114b
2o\$114b2o4\$122bo\$120b2o\$120b2o4\$128bo\$126b2o\$126b2o4\$134bo\$132b2o\$132b
2o4\$140bo\$138b2o\$138b2o4\$146bo\$144b2o\$144b2o4\$152bo\$150b2o\$150b2o4\$
158bo\$156b2o\$156b2o4\$164bo\$162b2o\$162b2o4\$170bo\$168b2o\$168b2o4\$176bo\$
174b2o\$174b2o4\$182bo\$180b2o\$180b2o4\$188bo\$186b2o\$186b2o4\$194bo\$192b2o\$
192b2o!``````
It is probably much too bulky; I predict that someone will make a smaller breeder within a week.
There is also a 5-cell p126:
1 0 1
1 1 1
and a 5-cell 128-generation methuselah:

Code: Select all

``````x = 5, y = 3, rule = 22da
o2\$ob3o!``````

### Re: 22da (Hexagonal Grid)

Posted: March 2nd, 2014, 10:18 pm
I assume that this rule is weighted? (I don't see anything weighted about it, and if it isn't then how is it different from a normal rule that can be run with QuickLife?)

(and in the future, any time you make a non-weighted rule, use the "permute" setting, which doesn't care what order the middle terms are in)

### Re: 22da (Hexagonal Grid)

Posted: March 2nd, 2014, 11:53 pm
c0b0p0 , I'm glad to see people experimenting with rules related to Callahan's hex rule, and sharing their results!

Awhile back, I was interested in extending Callahan's non-totalistic hexagonal rule notation so that it applies to more than just two neighbors. I tried out the following:
ExtendedCallahanHexagonal.gif (1.59 KiB) Viewed 21492 times
(Sorry for the gif -- I couldn't get the formatting right as text!)

Below I'm including a Golly script that will accept Callahan's notation (extended as shown above). The idea is to eliminate the need to create cumbersome rule tables for each new rule. You can simply enter "B2o4m6/S2o2p3o4" (or some such) and the script first converts your entry into Mcell's Weighted Life notation. You can stop there, or you can hit "OK", and the script will continue on, and create a Golly rule (in .rule format) for you to use in Golly. You can use the script to have fun exploring Callahan's notation!

Code: Select all

``````
import golly
from glife.RuleTree import *

dialog_box_message =  '''This script will convert Callhan's (extended) non-totalistic hexagonal notation into Weighted Life notation.'''

dummyvariable = '''

The following shows how this script extends Callahan's hexagaonl non-totalistic notation.   Unfortunately, it may be scrambled a bit when I post it to the ConwayLife.com forum.  Please refer to the ASCII art image I posted to the forum to help unscramble the following:

. .
0:   . x .
. .

O .
1:   . x .
. .

O O            O .            O .
2o:  . x .     2m:  . x O     2p:  . x .
. .            . .            . O

O O            O O            O .
3o:  O x .     3m:  . x .     3p:  . x O
. .            . O            O .

O O            O O            O O
4o:  O x O     4m:  . x O     4p:  . x .
. .            O .            O O

O O
5:    O x O
O .

O O
6:    O x O
O O

'''

CR = chr(13)
LF = chr(10)

rulestring = golly.getstring(dialog_box_message, "B2o/S2m34")

rulestring = rulestring.replace(" ", "")
rulestring = rulestring.lower()
rulestring = rulestring.replace("b", "B")
rulestring = rulestring.replace("s", "S")
rulestring = rulestring.replace("c", "C")

rulestring = rulestring.replace("hex_", "")
rulestring = rulestring.replace("_", "/")
rulestring_parts = rulestring.split("/")
rulestring_firstpart = rulestring_parts[0]
rulestring_secondpart = rulestring_parts[1]
if len(rulestring_parts) == 3:
rulestring_thirdpart = rulestring_parts[2]
rulestring_thirdpart = rulestring_thirdpart.replace("C", "")
decaystates = int(rulestring_thirdpart)

else:
decaystates = 0

rule_name = rulestring.replace("/", "_")

rulestring = rulestring_firstpart + "/" + rulestring_secondpart

if rulestring.startswith("B") or rulestring.startswith("S"):
rulestring = rulestring.replace("/", "")
else:
rulestring = rulestring.replace("/", "B")

rulestring = rulestring + "\n"

Callahandict = {
"0":   [0],
"1":   [1, 2, 4, 8, 16, 32],
"2o":  [3,   6,  12,  24, 48,  33],
"2m":  [5,   10,  20,  40,  17,  34],
"2p":  [9,  18,  36],
"3o":  [7,  14,  28,  56,  49,  35],
"3m":  [11,  22,  44,   25,  50,  37,  52, 26, 13, 38, 19, 41],
"3p":  [21,   42],
"4o":  [15,   30,   60,   57,  51,   39],
"4m":  [23,    46,   29,   58,    53,  43],
"4p":  [27,   54,   45],
"5":   [62, 61, 31, 59, 47, 55],
"6":   [63]
}

def create_rule_element(bs,totalistic_num, notation_letter, inverse_list):
result = ""
if notation_letter != "none":
for col in Callahandict[totalistic_num+notation_letter]:
result = result + bs + str(col) + ","
else:
for row in Callahandict:
if row.startswith(totalistic_num):
for col in Callahandict[row]:
result = result + bs + str(col) + ","
return result

bs = "RS"
totalistic_context = "none"
last_totalistic_context = "none"
notation_letter = "none"

finalrulestring = ""
for x in rulestring:
if x == "S" or x == "B" or x.isdigit() or x == "\n":
last_totalistic_context = totalistic_context
totalistic_context = x
if last_totalistic_context != "none"  and notation_letter == "none":
finalrulestring = finalrulestring + create_rule_element(bs, last_totalistic_context, "none",[])
# Now lets get ready to move on to the next character.
notation_letter = "none"
if x == "S" or x == "B":
totalistic_context = "none"
if x == "S":
bs = "RS"
if x == "B":
bs = "RB"
elif x in ["o","m","p"] and totalistic_context != "none":
notation_letter = x
finalrulestring = finalrulestring + create_rule_element(bs, totalistic_context, notation_letter, [])

finalrulestring = "NW1,NN2,NE0,WW32,ME0,EE4,SW0,SS16,SE8," + "HI" + str(decaystates) + ", " + finalrulestring

golly.getstring('''
Here is the Weighted Life version - you can copy it below:                                                                                                                                    .''', finalrulestring)

#  Part 2:   This is WeightedLife->RuleTree

from glife.RuleTree import *

# Default values
RS = []
RB = []
ME_weight = 0
NW_weight = 1
NN_weight = 1
NE_weight = 1
WW_weight = 1
EE_weight = 1
SW_weight = 1
SS_weight = 1
SE_weight = 1

CR = chr(13)
LF = chr(10)

#name = "Temporary-rule-name"
name = "Hex_" + rule_name

#WeightedRulestring = golly.getstring(dialog_box_message, "Name=Temporary-rule-name NW4,NN1,NE0,WW1, ME0,EE4,SW0,SS4, SE1,HI0,RS1,RS6,RS8,RB5,RB6")

WeightedRulestring = finalrulestring

#WeightedRulestring = WeightedRulestring.replace("ame = ", "ame=")

WeightedRulestring = WeightedRulestring.replace(" ", ",")
WeightedRulestring = WeightedRulestring.replace(CR, ",")
WeightedRulestring = WeightedRulestring.replace(LF, ",")

for x in WeightedRulestring.split(","):
if x.startswith("Name=") or x.startswith("name="):
name = x.split("ame=")[1]
else:
x = x.upper()
if x.startswith("NW"):
NW_weight = int(x.split("NW")[1])
elif x.startswith("NN"):
NN_weight = int(x.split("NN")[1])
elif x.startswith("NE"):
NE_weight = int(x.split("NE")[1])
elif x.startswith("WW"):
WW_weight = int(x.split("WW")[1])
elif x.startswith("EE"):
EE_weight = int(x.split("EE")[1])
elif x.startswith("SW"):
SW_weight = int(x.split("SW")[1])
elif x.startswith("SS"):
SS_weight = int(x.split("SS")[1])
elif x.startswith("SE"):
SE_weight = int(x.split("SE")[1])
elif x.startswith("ME"):
ME_weight = int(x.split("ME")[1])
elif x.startswith("RS"):
RS.append(int(x.split("RS")[1]))
elif x.startswith("RB"):
RB.append(int(x.split("RB")[1]))
elif x.startswith("HI"):
n_states = (int(x.split("HI")[1]))

if n_states < 3:
n_states = 2
if n_states > 256:
n_states = 256
if n_states > 8:
golly.getstring('''Ruletrees with more than 8 or so states can take a long time to compute.

Save your work before continuing. Once this script starts computing your rule,
if you want to stop the calculation, you may have to abort Golly itelf.

Choose the cancel option now to stop this script.''', "Proceed")

n_neighbors = 8

def transition_function(a):
# order for 8 neighbors is NW, NE, SW, SE, N, W, E, S, C

n = NW_weight*(a[0] == 1) + NE_weight*(a[1] == 1) + SW_weight*(a[2] == 1) + SE_weight*(a[3] == 1) + NN_weight*(a[4] == 1) + WW_weight*(a[5] == 1) + EE_weight*(a[6] == 1) + SS_weight*(a[7] == 1) + ME_weight*(a[8] == 1)

if  a[8] == 1 and n in RS:
return 1

if a[8] == 0 and n in RB:
return 1

if a[8] > 0 and a[8] < (n_states - 1):
return a[8] + 1

return 0

golly.show("Please wait while a rule file is being created...")

# The code below this line is copied from make-ruletree.py

try:

MakeRuleTreeFromTransitionFunction( n_states, n_neighbors, transition_function,
golly.getdir("rules")+name+".tree" )

# use name.tree to create name.rule (with no icons);
# note that if name.rule already exists then we only replace the info in
# the @TREE section to avoid clobbering any other info added by the user
ConvertTreeToRule(name, n_states, [])

golly.setrule(name)
golly.show("Created "+golly.getdir("rules")+name+".rule and switched to that rule.")

except:
import sys
import traceback
exception, msg, tb = sys.exc_info()
golly.warn(\
'''A problem was encountered with the supplied rule:'''+ '\n'.join(traceback.format_exception(exception, msg, tb)))
golly.exit()

``````
Edited Mar 3, 2014 to fix naming convention for rules with extra decay states.

### Re: 22da (Hexagonal Grid)

Posted: March 2nd, 2014, 11:54 pm
Paul Callahan's original essay which explains his non-totalistic notation can be found here:
http://www.mirekw.com/ca/files/hexrule.txt

### Re: 22da (Hexagonal Grid)

Posted: March 3rd, 2014, 6:46 pm
@EricG: Does the script make a rule table or rule tree, and how does it name the rule?

@Sphenocorona: This rule table was made by hand, and it was not intended to be weighted. The rule table that it uses cannot be expressed using the permute symmetry.

Some other observations from this rule:
The p16 is so sparky it can eat an exact copy of itself:

Code: Select all

``````x = 12, y = 12, rule = 22da
10bo\$8bob2o\$9bo\$10bo\$2bobo\$bobob2o\$2bob3o\$o4bobo\$3bo2bo\$b2o2bobo\$2bo3b
o\$4bo!``````
Another puffer eater:

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``````x = 24, y = 25, rule = 22da
22bo\$23bo2\$20b2o\$20b2o17\$2bo\$ob2o\$bo\$2bo!``````
The longest-lived pattern I can find which has less than 10 cells and fits in a 20x20 bounding box (368 gens):

Code: Select all

``````x = 15, y = 17, rule = 22da
4bo\$4bo4\$o\$bo8\$10bo2\$10bob3o!``````
A 2-glider synthesis of the smallest p4 I could find:

Code: Select all

``````x = 22, y = 18, rule = 22da
b2o\$b2o\$o11\$19bo\$19b2o\$20bo2\$21bo!``````
The closest I could get to a double-barreled rake in this rule:

Code: Select all

``````x = 16, y = 16, rule = 22da
bo\$3bo\$3b2o\$2bo\$2o3bo\$2o5\$11bo\$13bo\$13b2o\$12bo\$10b2o3bo\$10b2o!``````
If someone could make a synthesis for the 6-cell infinite growth I posted above, and find a way to clean up my near-rake, then a smaller breeder would be almost built. (That is, unless someone finds a kickback reaction in this rule, in which case we could build a breeder from sideways rakes alone.)

My rule was based on the rule in LifeLine volume 2, page 15. In Callahan's notation, it would be B2o2m/S2.

### Re: 22da (Hexagonal Grid)

Posted: March 8th, 2014, 1:43 pm
An 82-generation 4-cell methuselah:

Code: Select all

``````x = 5, y = 3, rule = 22da
3o2\$4bo!``````
A factory:

Code: Select all

``````x = 11, y = 17, rule = 22da
3o2\$2bo\$2b2o10\$7b2o\$8bo2\$8b3o!``````
The closest thing I could get to a glider duplicator, based on the almost-transparent junk reaction:

Code: Select all

``````x = 17, y = 25, rule = 22da
obobo2\$3bo\$3b2o\$4bo14\$15bo\$16bo2\$5bo\$5b2obo\$8bo\$8bo!``````
Unfortunately, one of the gliders crashes into the sparky p16 and deletes it (although not cleanly).

### Re: 22da (Hexagonal Grid)

Posted: March 9th, 2014, 9:29 pm
p16 pulls a p4:

Code: Select all

``````x = 7, y = 7, rule = 22da
4b2o\$6bo\$6bo\$2bo\$ob2o\$2o\$3o!``````
Probably the longest-lived methuselah that is less than 7 cells and fits in a 10x10 box:

Code: Select all

``````x = 5, y = 9, rule = 22da
3bo\$2bo5\$o2\$2b3o!``````
It stabilizes at time 232.

### Re: 22da (Hexagonal Grid)

Posted: March 12th, 2014, 1:59 pm
I set a new record for the smallest puffer to puff the p126 (previously 20 cells):

Code: Select all

``````x = 31, y = 26, rule = 22da
3bo\$3bo\$2bo\$2o3bo\$2o13\$24bo\$22b2o\$22b2o4\$30bo\$28b2o\$28b2o!``````

### Re: 22da (Hexagonal Grid)

Posted: March 13th, 2014, 5:55 pm
What happens when two p16s pull a p4? They duplicate it:

Code: Select all

``````x = 12, y = 12, rule = 22da
9b3o\$10b2o\$8b2obo\$9bo2\$4b2o\$6bo\$6bo\$2bo\$ob2o\$2o\$3o!``````
In fact, the p4 gets duplicated twice.

This is definitely a breeder:

Code: Select all

``````x = 123, y = 123, rule = 22da
2bo\$2o\$2o4\$8bo\$6b2o\$6b2o4\$14bo\$12b2o\$12b2o4\$20bo\$18b2o\$18b2o4\$26bo\$24b
2o\$24b2o4\$32bo\$30b2o\$30b2o4\$38bo\$36b2o\$36b2o4\$44bo\$42b2o\$42b2o4\$50bo\$
48b2o\$48b2o4\$56bo\$54b2o\$54b2o4\$62bo\$60b2o\$60b2o4\$68bo\$66b2o\$66b2o4\$74b
o\$72b2o\$72b2o4\$80bo\$78b2o\$78b2o4\$86bo\$84b2o\$84b2o4\$92bo\$90b2o\$90b2o4\$
98bo\$96b2o\$96b2o4\$104bo\$102b2o\$102b2o4\$110bo\$108b2o\$108b2o4\$116bo\$114b
2o\$114b2o4\$122bo\$120b2o\$120b2o!``````
p16 converts a p2 to a p4, which surprisingly does not destroy the p16:

Code: Select all

``````x = 7, y = 7, rule = 22da
5bo\$6bo2\$2bo\$ob2o\$2o\$3o!``````

### Re: 22da (Hexagonal Grid)

Posted: March 15th, 2014, 9:23 pm
Because of the c/3 glider's sparkiness, I made a G -> G + duoplet reaction involving only one p16 with no problem:

Code: Select all

``````x = 32, y = 16, rule = 22da
27bo2\$29bo\$27b2o\$27b2o2bo8\$3o2\$2bo\$2b2o!``````

### Re: 22da (Hexagonal Grid)

Posted: March 16th, 2014, 5:25 pm
More reactions of the same type as in my previous post are below.

This glider ends up becoming a glider and a p4, which is promptly turned into a duoplet, which is at once deleted.

Code: Select all

``````x = 32, y = 37, rule = 22da
27bo2\$29bo\$27b2o\$27b2o2bo8\$3o2\$2bo\$2b2o18\$12b2o\$13bo2\$13b3o!``````
This glider apparently refuses to accept the inevitability of its becoming a glider and a duoplet, and because of this behavior I have dubbed it "the procrastinator".

Code: Select all

``````x = 32, y = 36, rule = 22da
27bo2\$29bo\$27b2o\$27b2o2bo8\$3o2\$2bo\$2b2o17\$12b3o2\$14bo\$14b2o!``````
This one leaves a rotated duoplet:

Code: Select all

``````x = 32, y = 51, rule = 22da
27bo2\$29bo\$27b2o\$27b2o2bo8\$3o2\$2bo\$2b2o17\$12b3o2\$14bo\$14b2o12\$7b3o2\$9b
o\$9b2o!``````

### Re: 22da (Hexagonal Grid)

Posted: March 17th, 2014, 10:02 pm
[This breeder] is probably much too bulky; I predict that someone will find a smaller breeder quite soon.
Two weeks later, I accidentally found 16-cell quadratic growth, fitting in a 13x15 bounding box! Talk about a smaller breeder!

Code: Select all

``````#C p120 MMS breeder
x = 13, y = 15, rule = 22da
bo2\$3b2o\$2bo\$2o\$2o5\$11bo\$11b2o\$10bo\$8b2o\$8b2o!``````
G -> G + 2 duoplets reaction:

Code: Select all

``````x = 32, y = 53, rule = 22da
27bo2\$29bo\$27b2o\$27b2o2bo8\$3o2\$2bo\$2b2o17\$12b3o2\$14bo\$14b2o14\$8b2o\$9bo
2\$9b3o!``````
Below is the rule table for 22da with white holes, which probably requires a different thread.

Code: Select all

``````@RULE W22da

@TABLE
n_states:3
neighborhood:hexagonal
symmetries:rotate6reflect
var a={0,1,2}
var b={a}
var c={a}
var d={0,2}
var e={d}
var f={d}
var g={d}
var h={d}
var i={d}
var j={a}
var k={a}
0,1,1,0,0,0,0,1
0,1,0,1,0,0,0,1
0,1,0,0,1,0,0,1
1,d,e,f,g,h,i,0
1,1,d,e,f,g,h,0
1,1,1,1,a,b,c,0
1,1,1,c,1,a,b,0
1,1,c,1,b,1,a,0
1,1,d,1,e,f,g,0
0,2,a,b,c,j,k,1

@COLORS
1    0    0 255
2    0 255    0
3 255    0    0
4 255 255   0
5 255    0 255
6    0 255 255``````

### Re: 22da (Hexagonal Grid)

Posted: March 19th, 2014, 2:06 pm
Finally, the gun has been built. (Well, it has not quite been built, but it has been proven to exist.) Below is a glider duplicator with only three p16s.

Code: Select all

``````x = 36, y = 50, rule = 22da
31bo2\$33bo\$31b2o\$31b2o2bo8\$4b3o2\$6bo\$6b2o17\$16b3o2\$18bo\$18b2o11\$2bo\$ob
2o\$bo\$2bo!``````
Now that I have hexrot.py, it should be no more than a day before the actual gun is built.

### Re: 22da (Hexagonal Grid)

Posted: March 20th, 2014, 9:34 pm
Original 12-barreled p690 (switchable?) gun:

Code: Select all

``````x = 192, y = 190, rule = 22da
44bob2o\$46b2o2\$47bo10\$28bo2bo\$30bo\$30b2o\$31bo17\$40bo2bo\$42bo71bo\$42b2o
71bo\$43bo69b2obo\$2o112bo\$bo\$18bo2b2o\$b3o17b2o\$2b2o16bo\$3bo\$22bo3\$106bo
\$107bo\$105b2obo\$106bo\$141bo\$141bo\$141bob2o\$144bo15\$13b3o\$14b2o\$15bob2o
\$18bo5\$33b3o\$34b2o\$35bob2o\$38bo31\$153bo\$153b2obo\$156b2o\$156b3o5\$173bo\$
173b2obo\$176b2o\$176b3o15\$47bo\$47b2obo\$50bo\$50bo\$85bo\$83bob2o\$84bo\$85bo
4\$188bo\$188b2o\$188b3o2\$190bo\$77bo112b2o\$75bob2o69bo\$76bo71b2o\$77bo71bo
\$148bo2bo17\$160bo\$160b2o\$161bo\$160bo2bo10\$144bo2\$144b2o\$144b2obo!``````
6-barreled glider gun:

Code: Select all

``````x = 429, y = 593, rule = 22da
203b2o\$204bo2\$204b3o132\$161bo\$161bo\$161bob2o\$164bo15\$215bob2o\$217b2o2\$
218bo10\$199bo2bo\$201bo\$201b2o\$202bo17\$211bo2bo\$213bo71bo\$213b2o71bo\$
214bo69b2obo\$171b2o112bo\$172bo\$189bo2b2o\$172b3o17b2o\$173b2o16bo\$174bo\$
193bo3\$277bo\$278bo\$276b2obo\$277bo\$312bo\$312bo\$312bob2o\$315bo15\$184b3o\$
185b2o232bo\$186bob2o227bob2o\$189bo228bo\$419bo4\$204b3o\$205b2o\$206bob2o\$
209bo31\$324bo\$324b2obo\$327b2o\$327b3o5\$344bo\$344b2obo\$347b2o\$347b3o15\$
218bo\$218b2obo\$221bo\$221bo\$256bo\$254bob2o\$255bo\$256bo4\$359bo\$359b2o\$
359b3o2\$361bo\$248bo112b2o\$246bob2o69bo\$247bo71b2o\$248bo71bo\$319bo2bo
17\$331bo\$331b2o\$332bo\$331bo2bo10\$315bo2\$315b2o\$315b2obo39\$bo\$2bo\$2obo\$
bo4\$425bo\$425bo\$425bob2o\$428bo198\$376b3o2\$378bo\$378b2o!``````

Code: Select all

``````x = 13, y = 15, rule = 22da
bo2\$3bo\$2bo\$2o\$2o5\$11bo\$11b2o\$10bo\$8b2o\$8b2o!``````

### Re: 22da (Hexagonal Grid)

Posted: March 21st, 2014, 3:04 pm

Code: Select all

``````x = 13, y = 15, rule = 22da
bo2\$3bo\$2bo\$2o\$2o5\$11bo\$11b2o\$10bo\$8b2o\$8b2o!``````

Code: Select all

``````x = 12, y = 13, rule = 22da
3bo\$2bo\$2o3bo\$2o5\$10bo\$11bo2\$8b2o\$8b2o!``````
16-cell quadratic growth can be eaten with no more than two p16s.
x = 64, y = 69, rule = 22da
52bo2\$54b2o\$53bo\$51b2o\$51b2o5\$62bo\$62b2o\$61bo\$59b2o\$59b2o43\$2bo\$ob2o\$b
o\$2bo5\$11bo\$9bob2o\$10bo\$11bo!

New superlinear growth pattern:

Code: Select all

``````x = 198, y = 213, rule = 22da
4b2o\$5bo\$4bo2bo\$5bobo27\$4b2o\$5bo\$4bo2bo\$5bobo27\$4b2o\$5bo\$4bo2bo\$5bobo
27\$4b2o\$5bo\$4bo2bo\$5bobo27\$4b2o\$5bo\$4bo2bo\$5bobo4\$66bo\$65bo9\$56bo\$55bo
6\$64bo2\$66b2o\$46bo18bo\$45bo17b2o\$63b2o\$4b2o\$5bo73bo\$4bo2bo72bo\$5bobo4\$
36bo\$35bo3\$69bo\$70bo5\$26bo\$25bo3\$59bo\$60bo5\$16bo\$15bo2\$4b2o\$5bo43bo\$4b
o2bo42bo\$5bobo3\$6bobo\$6b2o\$6b4o2\$8b2o\$39bo\$10bo29bo\$9bo4bo\$8bob2o2bo\$
7bo2bo2\$8bo2bo4\$29bo\$30bo2\$12b2o\$11bo2b2o28b2o28b2o28b2o28b2o28b2o28b
2o\$11b2o\$3bo2bo7bob2o26bob2o26bob2o26bob2o26bob2o26bob2o26bob2o\$3b2o
10bobo27bobo27bobo27bobo27bobo27bobo27bobo\$b2ob3o\$ob2o\$bobo\$2bo!``````
This has the same growth rate as Gotts dots.

### Re: 22da (Hexagonal Grid)

Posted: March 22nd, 2014, 2:40 pm
A rake:

Code: Select all

``````x = 125, y = 128, rule = 22da
o2\$2bo\$2o\$2o2bo\$6b2o\$7bo\$6bo2bo\$7bobo54\$57bo\$57bo\$56bo\$6b2o46b2o3bo\$7b
o26bo19b2o\$6bo2bo25bo\$7bobo2\$64bo2\$66b2o\$65bo\$63b2o\$63b2o11\$14bo\$15bo
7\$62bo\$63bo7\$16bo\$15bo2bo\$15bo\$19b2o\$16bo3bo2bo\$17bo4bo\$21bo\$19b2o2b2o
\$20bo3bo\$6bo19bo\$7b2o13bo\$6b2o15bo3bo\$5bo19b2o15bo\$3b2obo4bo31bo\$2bob
2o4bo\$3bobo6bo\$4bo9bo\$13bo\$61b2o58b2o\$17bo\$16b2o43bob2o56bob2o\$14bobob
o43bobo57bobo\$12b2obo\$11bob2o\$12bobo\$13bo!``````
I will call this rake "Siderake 1".

I still have not found any still lifes in the rule. I wonder if someone might be able to prove that there aren't any.

### Re: 22da (Hexagonal Grid)

Posted: March 23rd, 2014, 9:31 pm
Here is a small puffer that sends gliders backwards. With a little more work, it can probably be transformed into a backrake.

Code: Select all

``````x = 16, y = 16, rule = 22da
7bo\$6bo2\$4bo3b5o\$6bo5bo\$2bo9bo\$7bo4bo\$3bo8bo\$9bo5bo\$11bo2bo\$3bo\$3bo8bo
\$b2ob2o2bo\$ob2o6bo\$bobo\$2bo!``````
Here is a pulling reaction that will prove the existence of a growing spaceship once this backrake is completed:

Code: Select all

``````x = 104, y = 105, rule = 22da
102bo2\$103bo6\$94bo\$93bobo\$92b3obo\$94b2o\$94bo27\$62bobo\$62bob2o2\$64b2o
28\$30bo2b2o\$33b2o\$32bo2\$34bo26\$2bo\$bobo\$3obo\$2b2o\$2bo!``````
Inspired by the Neutronium rule, here is a cross between 22da, Neutronium, and DLA:

Code: Select all

``````@RULE 22daDLA

@TABLE

# Golly rule-table format.
# Each rule: C,N,E,SE,S,W,NW,C'
#
# Default for transitions not listed: no change
#
# Variables are bound within each transition.
# For example, if a={1,2} then 4,a,0->a represents
# two transitions: 4,1,0->1 and 4,2,0->2
# (This is why we need to repeat the variables below.
#  In this case the method isn't really helping.)

n_states:3
neighborhood:hexagonal
symmetries:rotate6reflect
var a={0,1,2}
var b={a}
var c={a}
var d={1,2}
var e={d}
var f={d}
var g={d}
var h={d}
1,d,e,f,g,h,2,2          # aggregation
0,d,e,0,0,0,0,1
0,d,0,e,0,0,0,1
0,d,0,0,e,0,0,1
1,0,0,0,0,0,0,0
1,d,0,0,0,0,0,0
1,d,e,f,a,b,c,0
1,d,e,c,f,a,b,0
1,d,c,e,b,f,a,0
1,d,0,e,0,0,0,0
2,2,2,2,2,2,a,0           # the last two transitions allow junctions of no more than two lines
2,2,2,2,0,0,2,0

@COLORS
1   0   0 255   blue
2   0 255   0   green
3 255   0   0   red
4 255 255   0
5 255   0 255
6 0   255 255``````

### Re: 22da (Hexagonal Grid)

Posted: March 24th, 2014, 10:00 pm
I have completed a backrake, along with a growing ship.

Code: Select all

``````x = 8192, y = 7535, rule = 22da
7318bo2\$7320bo\$7318b2o\$7318b2o2bo\$7324b2o\$7325bo\$7324bo2bo\$7325bobo54\$
7375bo\$7375bo\$7374bo\$7324b2o46b2o3bo\$7325bo26bo19b2o\$7324bo2bo25bo\$
7325bobo2\$7382bo2\$7384b2o\$7383bo\$7381b2o\$7381b2o11\$7332bo\$7333bo7\$
7380bo\$7381bo7\$7334bo\$7333bo2bo\$7333bo\$7337b2o\$7334bo3bo2bo\$7335bo4bo\$
7339bo\$7337b2o2b2o\$7338bo3bo\$7324bo19bo\$7325b2o13bo\$7324b2o15bo3bo\$
7323bo19b2o15bo\$7321b2obo4bo31bo\$7320bob2o4bo\$7321bobo6bo\$7322bo9bo\$
7331bo\$7379b2o58b2o\$7335bo\$7334b2o43bob2o56bob2o\$7332bobobo43bobo57bob
o\$7330b2obo\$7329bob2o854bo\$7330bobo\$7331bo857bo\$8187b2o\$8187b2o2bo789\$
6437bo2\$6439bo\$6437b2o\$6437b2o2bo\$6443b2o\$6444bo\$6443bo2bo\$6444bobo54\$
6494bo\$6494bo\$6493bo\$6443b2o46b2o3bo\$6444bo26bo19b2o\$6443bo2bo25bo\$
6444bobo2\$6501bo2\$6503b2o\$6502bo\$6500b2o\$6500b2o11\$6451bo\$6452bo7\$
6499bo\$6500bo7\$6453bo\$6452bo2bo\$6452bo\$6456b2o\$6453bo3bo2bo\$6454bo4bo\$
6458bo\$6456b2o2b2o\$6457bo3bo\$6443bo19bo\$6444b2o13bo\$6443b2o15bo3bo\$
6442bo19b2o15bo\$6440b2obo4bo31bo\$6439bob2o4bo\$6440bobo6bo\$6441bo9bo\$
6450bo\$6498b2o58b2o\$6454bo\$6453b2o43bob2o56bob2o\$6451bobobo43bobo57bob
o\$6449b2obo\$6448bob2o854bo\$6449bobo\$6450bo857bo\$7306b2o\$7306b2o2bo972\$
5575bo2\$5577bo\$5575b2o\$5575b2o2bo\$5581b2o\$5582bo\$5581bo2bo\$5582bobo54\$
5632bo\$5632bo\$5631bo\$5581b2o46b2o3bo\$5582bo26bo19b2o\$5581bo2bo25bo\$
5582bobo2\$5639bo2\$5641b2o\$5640bo\$5638b2o\$5638b2o11\$5589bo\$5590bo7\$
5637bo\$5638bo7\$5591bo\$5590bo2bo\$5590bo\$5594b2o\$5591bo3bo2bo\$5592bo4bo\$
5596bo\$5594b2o2b2o\$5595bo3bo\$5581bo19bo\$5582b2o13bo\$5581b2o15bo3bo\$
5580bo19b2o15bo\$5578b2obo4bo31bo\$5577bob2o4bo\$5578bobo6bo\$5579bo9bo\$
5588bo\$5636b2o58b2o\$5592bo\$5591b2o43bob2o56bob2o\$5589bobobo43bobo57bob
o\$5587b2obo\$5586bob2o854bo\$5587bobo\$5588bo857bo\$6444b2o\$6444b2o2bo
1263\$3791bo2\$3793bo\$3791b2o\$3791b2o2bo\$3797b2o\$3798bo\$3797bo2bo\$3798bo
bo54\$3848bo\$3848bo\$3847bo\$3797b2o46b2o3bo\$3798bo26bo19b2o\$3797bo2bo25b
o\$3798bobo2\$3855bo2\$3857b2o\$3856bo\$3854b2o\$3854b2o11\$3805bo\$3806bo7\$
3853bo\$3854bo7\$3807bo\$3806bo2bo\$3806bo\$3810b2o\$3807bo3bo2bo\$3808bo4bo\$
3812bo\$3810b2o2b2o\$3811bo3bo\$3797bo19bo\$3798b2o13bo\$3797b2o15bo3bo\$
3796bo19b2o15bo\$3794b2obo4bo31bo\$3793bob2o4bo\$3794bobo6bo\$3795bo9bo\$
3804bo\$3852b2o58b2o\$3808bo\$3807b2o43bob2o56bob2o\$3805bobobo43bobo57bob
o\$3803b2obo\$3802bob2o854bo\$3803bobo\$3804bo857bo\$4660b2o\$4660b2o2bo751\$
2741bo2\$2743bo\$2741b2o\$2741b2o2bo\$2747b2o\$2748bo\$2747bo2bo\$2748bobo54\$
2798bo\$2798bo\$2797bo\$2747b2o46b2o3bo\$2748bo26bo19b2o\$2747bo2bo25bo\$
2748bobo2\$2805bo2\$2807b2o\$2806bo\$2804b2o\$2804b2o11\$2755bo\$2756bo7\$
2803bo\$2804bo7\$2757bo\$2756bo2bo\$2756bo\$2760b2o\$2757bo3bo2bo\$2758bo4bo\$
2762bo\$2760b2o2b2o\$2761bo3bo\$2747bo19bo\$2748b2o13bo\$2747b2o15bo3bo\$
2746bo19b2o15bo\$2744b2obo4bo31bo\$2743bob2o4bo\$2744bobo6bo\$2745bo9bo\$
2754bo\$2802b2o58b2o\$2758bo\$2757b2o43bob2o56bob2o\$2755bobobo43bobo57bob
o\$2753b2obo\$2752bob2o854bo\$2753bobo\$2754bo857bo\$3610b2o\$3610b2o2bo
1043\$1745bo2\$1747bo\$1745b2o\$1745b2o2bo\$1751b2o\$1752bo\$1751bo2bo\$1752bo
bo54\$1802bo\$1802bo\$1801bo\$1751b2o46b2o3bo\$1752bo26bo19b2o\$1751bo2bo25b
o\$1752bobo2\$1809bo2\$1811b2o\$1810bo\$1808b2o\$1808b2o11\$1759bo\$1760bo7\$
1807bo\$1808bo7\$1761bo\$1760bo2bo\$1760bo\$1764b2o\$1761bo3bo2bo\$1762bo4bo\$
1766bo\$1764b2o2b2o\$1765bo3bo\$1751bo19bo\$1752b2o13bo\$1751b2o15bo3bo\$
1750bo19b2o15bo\$1748b2obo4bo31bo\$1747bob2o4bo\$1748bobo6bo\$1749bo9bo\$
1758bo\$1806b2o58b2o\$1762bo\$1761b2o43bob2o56bob2o\$1759bobobo43bobo57bob
o\$1757b2obo\$1756bob2o854bo\$1757bobo\$1758bo857bo\$2614b2o\$2614b2o2bo467\$
1143bo2\$1145bo\$1143b2o\$1143b2o2bo\$1149b2o\$1150bo\$1149bo2bo\$1150bobo54\$
1200bo\$1200bo\$1199bo\$1149b2o46b2o3bo\$1150bo26bo19b2o\$1149bo2bo25bo\$
1150bobo2\$1207bo2\$1209b2o\$1208bo\$1206b2o\$1206b2o11\$1157bo\$1158bo7\$
1205bo\$1206bo7\$1159bo\$1158bo2bo\$1158bo\$1162b2o\$1159bo3bo2bo\$1160bo4bo\$
1164bo\$1162b2o2b2o\$1163bo3bo\$1149bo19bo\$1150b2o13bo\$1149b2o15bo3bo\$
1148bo19b2o15bo\$1146b2obo4bo31bo\$1145bob2o4bo\$1146bobo6bo\$1147bo9bo\$
1156bo\$1204b2o58b2o\$1160bo\$1159b2o43bob2o56bob2o\$1157bobobo43bobo57bob
o\$1155b2obo\$1154bob2o854bo\$1155bobo\$1156bo857bo\$2012b2o\$2012b2o2bo547\$
491bo2\$493bo\$491b2o\$491b2o2bo\$497b2o\$498bo\$497bo2bo\$498bobo54\$548bo\$
548bo\$547bo\$497b2o46b2o3bo\$498bo26bo19b2o\$497bo2bo25bo\$498bobo2\$555bo
2\$557b2o\$556bo\$554b2o\$554b2o11\$505bo\$506bo7\$553bo\$554bo7\$507bo\$506bo2b
o\$506bo\$510b2o\$507bo3bo2bo\$508bo4bo\$512bo\$510b2o2b2o\$511bo3bo\$497bo19b
o\$498b2o13bo\$497b2o15bo3bo\$496bo19b2o15bo\$494b2obo4bo31bo\$493bob2o4bo\$
494bobo6bo\$495bo9bo\$504bo\$552b2o58b2o\$508bo\$507b2o43bob2o56bob2o\$505bo
bobo43bobo57bobo\$503b2obo\$502bob2o854bo\$503bobo\$504bo857bo\$1360b2o\$
1360b2o2bo300\$o2\$2bo\$2o\$2o2bo\$6b2o\$7bo\$6bo2bo\$7bobo54\$57bo\$57bo\$56bo\$
6b2o46b2o3bo\$7bo26bo19b2o\$6bo2bo25bo\$7bobo2\$64bo2\$66b2o\$65bo\$63b2o\$63b
2o11\$14bo\$15bo7\$62bo\$63bo7\$16bo\$15bo2bo\$15bo\$19b2o\$16bo3bo2bo\$17bo4bo\$
21bo\$19b2o2b2o\$20bo3bo\$6bo19bo\$7b2o13bo\$6b2o15bo3bo\$5bo19b2o15bo\$3b2ob
o4bo31bo\$2bob2o4bo\$3bobo6bo\$4bo9bo\$13bo\$61b2o58b2o\$17bo\$16b2o43bob2o
56bob2o\$14bobobo43bobo57bobo\$12b2obo\$11bob2o854bo\$12bobo\$13bo857bo\$
869b2o\$869b2o2bo130\$301bo2\$303bo\$301b2o\$301b2o2bo81\$319bo\$318bo2\$316bo
3b5o\$318bo5bo\$314bo9bo\$319bo4bo\$315bo8bo\$321bo5bo\$323bo2bo\$315bo\$315bo
8bo\$313b2ob2o2bo\$312bob2o6bo\$313bobo\$314bo7\$408bo2\$410bo\$408b2o\$408b2o
2bo!``````

Code: Select all

``````x = 8192, y = 7879, rule = 22da
8177bo2\$8178bo6\$8169bo\$8168bobo\$8167b3obo\$8169b2o\$8169bo236\$7929bo\$
7928bobo\$7927b3obo\$7929b2o\$7929bo92\$7318bo2\$7320bo\$7318b2o\$7318b2o2bo
16\$7324b2o\$7325bo\$7324bo2bo\$7325bobo26\$7384b2o\$7385bo2bo2bo\$7368bo17bo
\$7367bo21bobo\$7388bo5bo\$7387bobobobo2\$7389bobobobobo2\$7391bobobo\$7394b
o2bo\$7393bo\$7373bo22bo\$7397b2o\$7375b2o21bo\$7374bo\$7372b2o\$7372b2o5\$
7348bo35bo\$7347bo36bo\$7383bo\$7381b2o3bo\$7381b2o4\$7396bo\$7324b2o69bo\$
7325bo\$7324bo2bo\$7325bobo8\$7328bo\$7327bo3\$7331bo\$7330bo2bo\$7330bo\$
7331bo\$7376bo\$7375bo8\$7322bo3bo5bo\$7323bo4bo3bo\$7322bo3bo\$7329b7o\$
7330bo4b2o\$7325bo5bo4bo\$7323bobo2bo4bo2bo14bo\$7321b2obo11bob2o\$7320bob
2o6bo3bobo12bo2bo\$7321bobo5b3o3b2o13b2o\$7322bo7bo5bo\$7333bo4bo17bo\$
7355bo8b2o58b2o58b2o58b2o58b2o58b2o58b2o58b2o58b2o118b2o58b2o58b2o58b
2o\$7337bobo\$7333b2o29bob2o56bob2o56bob2o56bob2o56bob2o56bob2o56bob2o
56bob2o56bob2o116bob2o56bob2o56bob2o56bob2o\$7332bo32bobo57bobo57bobo
57bobo57bobo57bobo57bobo57bobo57bobo117bobo57bobo57bobo57bobo\$7330b2ob
o4bo\$7329bob2o4bobo847bo\$7330bobo\$7331bo857bo\$8187b2o\$8187b2o2bo15\$
7689bo\$7688bobo\$7687b3obo\$7689b2o\$7689bo36\$7670bo\$7671bo119\$7550bo\$
7551bo79\$7449bo\$7448bobo\$7447b3obo\$7449b2o\$7449bo36\$7430bo\$7431bo119\$
7310bo\$7311bo79\$7209bo\$7208bobo\$7207b3obo\$7209b2o\$7209bo36\$7190bo\$
7191bo119\$7070bo\$7071bo79\$6969bo\$6968bobo\$6967b3obo\$6969b2o\$6969bo36\$
6950bo\$6951bo13\$6437bo2\$6439bo\$6437b2o\$6437b2o2bo16\$6443b2o\$6444bo\$
6443bo2bo\$6444bobo26\$6503b2o\$6504bo2bo2bo\$6487bo17bo\$6486bo21bobo\$
6507bo5bo\$6506bobobobo2\$6508bobobobobo2\$6510bobobo\$6513bo2bo\$6512bo\$
6492bo22bo\$6516b2o\$6494b2o21bo\$6493bo\$6491b2o\$6491b2o5\$6467bo35bo\$
6466bo36bo\$6502bo\$6500b2o3bo\$6500b2o4\$6515bo\$6443b2o69bo\$6444bo\$6443bo
2bo\$6444bobo8\$6447bo\$6446bo3\$6450bo\$6449bo2bo\$6449bo\$6450bo\$6495bo\$
6494bo6\$6830bo\$6831bo\$6441bo3bo5bo\$6442bo4bo3bo\$6441bo3bo\$6448b7o\$
6449bo4b2o\$6444bo5bo4bo\$6442bobo2bo4bo2bo14bo\$6440b2obo11bob2o\$6439bob
2o6bo3bobo12bo2bo\$6440bobo5b3o3b2o13b2o\$6441bo7bo5bo\$6452bo4bo17bo\$
6474bo8b2o58b2o58b2o58b2o58b2o58b2o118b2o58b2o118b2o58b2o118b2o\$6456bo
bo\$6452b2o29bob2o56bob2o56bob2o56bob2o56bob2o56bob2o116bob2o56bob2o
116bob2o56bob2o116bob2o\$6451bo32bobo57bobo57bobo57bobo57bobo57bobo117b
obo57bobo117bobo57bobo117bobo\$6449b2obo4bo\$6448bob2o4bobo847bo\$6449bob
o\$6450bo857bo\$7306b2o\$7306b2o2bo39\$6762bo\$6763bo17\$6729bo\$6728bobo\$
6727b3obo\$6729b2o\$6729bo31\$6682bo\$6681bo\$6683bo3\$6710bo\$6711bo61\$6642b
o\$6643bo52\$6562bo\$6561bo\$6563bo3\$6590bo\$6591bo61\$6522bo\$6523bo17\$6489b
o\$6488bobo\$6487b3obo\$6489b2o\$6489bo31\$6442bo\$6441bo\$6443bo3\$6470bo\$
6471bo61\$6402bo\$6403bo52\$6322bo\$6321bo\$6323bo3\$6350bo\$6351bo61\$6282bo\$
6283bo17\$6249bo\$6248bobo\$6247b3obo\$6249b2o\$6249bo31\$6202bo\$6201bo\$
6203bo3\$6230bo\$6231bo61\$6162bo\$6163bo52\$6082bo\$6081bo\$6083bo3\$6110bo\$
6111bo61\$6042bo\$6043bo17\$6009bo\$6008bobo\$6007b3obo\$6009b2o\$6009bo31\$
5962bo\$5961bo\$5963bo3\$5990bo\$5991bo61\$5922bo\$5923bo52\$5842bo\$5841bo\$
5843bo3\$5870bo\$5871bo34\$5575bo2\$5577bo\$5575b2o\$5575b2o2bo16\$5581b2o\$
5582bo\$5581bo2bo\$5582bobo4\$5802bo\$5803bo17\$5769bo\$5768bobo\$5767b3obo\$
5769b2o\$5641b2o126bo\$5642bo2bo2bo\$5625bo17bo\$5624bo21bobo\$5645bo5bo\$
5644bobobobo2\$5646bobobobobo2\$5648bobobo\$5651bo2bo\$5650bo\$5630bo22bo\$
5654b2o\$5632b2o21bo\$5631bo\$5629b2o\$5629b2o5\$5605bo35bo\$5604bo36bo\$
5640bo\$5638b2o3bo\$5638b2o4\$5653bo\$5581b2o69bo69bo\$5582bo138bo\$5581bo2b
o138bo\$5582bobo2\$5750bo\$5751bo5\$5585bo\$5584bo3\$5588bo\$5587bo2bo\$5587bo
\$5588bo\$5633bo\$5632bo8\$5579bo3bo5bo\$5580bo4bo3bo\$5579bo3bo\$5586b7o\$
5587bo4b2o\$5582bo5bo4bo\$5580bobo2bo4bo2bo14bo\$5578b2obo11bob2o\$5577bob
2o6bo3bobo12bo2bo\$5578bobo5b3o3b2o13b2o\$5579bo7bo5bo\$5590bo4bo17bo\$
5612bo8b2o58b2o58b2o118b2o58b2o118b2o58b2o118b2o58b2o118b2o\$5594bobo\$
5590b2o29bob2o56bob2o56bob2o116bob2o56bob2o116bob2o56bob2o116bob2o56bo
b2o116bob2o\$5589bo32bobo57bobo57bobo117bobo57bobo117bobo57bobo117bobo
57bobo117bobo\$5587b2obo4bo\$5586bob2o4bobo847bo\$5587bobo\$5588bo857bo\$
6444b2o\$6444b2o2bo7\$5656bo\$5657bo10\$5682bo\$5683bo43\$5605b2o\$5605bo\$
5606bo3bo\$5611bo\$5610b2o10\$5630bo\$5631bo50\$5536bo\$5537bo10\$5562bo\$
5563bo17\$5529bo\$5528bobo\$5527b3obo\$5529b2o\$5529bo22\$5485b2o\$5485bo\$
5486bo3bo\$5491bo\$5490b2o10\$5510bo\$5511bo50\$5416bo\$5417bo10\$5442bo\$
5443bo43\$5365b2o\$5365bo\$5366bo3bo\$5371bo\$5370b2o10\$5390bo\$5391bo50\$
5296bo\$5297bo10\$5322bo\$5323bo17\$5289bo\$5288bobo\$5287b3obo\$5289b2o\$
5289bo22\$5245b2o\$5245bo\$5246bo3bo\$5251bo\$5250b2o10\$5270bo\$5271bo50\$
5176bo\$5177bo10\$5202bo\$5203bo43\$5125b2o\$5125bo\$5126bo3bo\$5131bo\$5130b
2o10\$5150bo\$5151bo50\$5056bo\$5057bo10\$5082bo\$5083bo17\$5049bo\$5048bobo\$
5047b3obo\$5049b2o\$5049bo22\$5005b2o\$5005bo\$5006bo3bo\$5011bo\$5010b2o10\$
5030bo\$5031bo50\$4936bo\$4937bo10\$4962bo\$4963bo43\$4885b2o\$4885bo\$4886bo
3bo\$4891bo\$4890b2o10\$4910bo\$4911bo50\$4816bo\$4817bo10\$4842bo\$4843bo17\$
4809bo\$4808bobo\$4807b3obo\$4809b2o\$4809bo22\$4765b2o\$4765bo\$4766bo3bo\$
4771bo\$4770b2o10\$4790bo\$4791bo50\$4696bo\$4697bo10\$4722bo\$4723bo43\$4645b
2o\$4645bo\$4646bo3bo\$4651bo\$4650b2o10\$4670bo\$4671bo50\$4576bo\$4577bo10\$
4602bo\$4603bo17\$4569bo\$4568bobo\$4567b3obo\$4569b2o\$4569bo22\$4525b2o\$
4525bo\$4526bo3bo\$4531bo\$4530b2o10\$4550bo\$4551bo50\$4456bo\$4457bo10\$
4482bo\$4483bo43\$4405b2o\$3791bo613bo\$4406bo3bo\$3793bo617bo\$3791b2o617b
2o\$3791b2o2bo9\$4430bo\$4431bo6\$3797b2o\$3798bo\$3797bo2bo\$3798bobo26\$
3857b2o\$3858bo2bo2bo\$3841bo17bo\$3840bo21bobo\$3861bo5bo\$3860bobobobo2\$
3862bobobobobo2\$3864bobobo\$3867bo2bo\$3866bo\$3846bo22bo\$3870b2o\$3848b2o
21bo\$3847bo488bo\$3845b2o490bo\$3845b2o5\$3821bo35bo\$3820bo36bo\$3856bo\$
3854b2o3bo\$3854b2o506bo\$4363bo3\$3869bo\$3797b2o69bo\$3798bo\$3797bo2bo\$
3798bobo8\$3801bo\$3800bo\$4329bo\$4328bobo\$3804bo522b3obo\$3803bo2bo522b2o
\$3803bo525bo\$3804bo\$3849bo\$3848bo8\$3795bo3bo5bo\$3796bo4bo3bo\$3795bo3bo
\$3802b7o\$3803bo4b2o\$3798bo5bo4bo\$3796bobo2bo4bo2bo14bo\$3794b2obo11bob
2o\$3793bob2o6bo3bobo12bo2bo\$3794bobo5b3o3b2o13b2o\$3795bo7bo5bo\$3806bo
4bo17bo455b2o\$3828bo8b2o58b2o58b2o58b2o58b2o58b2o58b2o58b2o26bo31bo59b
2o58b2o58b2o58b2o\$3810bobo473bo3bo\$3806b2o29bob2o56bob2o56bob2o56bob2o
56bob2o56bob2o56bob2o56bob2o30bo85bob2o56bob2o56bob2o56bob2o\$3805bo32b
obo57bobo57bobo57bobo57bobo57bobo57bobo57bobo29b2o86bobo57bobo57bobo
57bobo\$3803b2obo4bo\$3802bob2o4bobo847bo\$3803bobo\$3804bo857bo\$4660b2o\$
4660b2o2bo4\$4276bo33bo\$4277bo33bo50\$4216bo\$4217bo10\$4242bo\$4243bo43\$
4165b2o\$4165bo\$4166bo3bo\$4171bo\$4170b2o22bo\$4195bo9\$4156bo33bo\$4157bo
33bo50\$4096bo\$4097bo10\$4122bo\$4123bo17\$4089bo\$4088bobo\$4087b3obo\$4089b
2o\$4089bo22\$4045b2o\$4045bo\$4046bo3bo\$4051bo\$4050b2o22bo\$4075bo9\$4036bo
33bo\$4037bo33bo50\$3976bo\$3977bo10\$4002bo\$4003bo43\$3925b2o\$3925bo\$3926b
o3bo\$3931bo\$3930b2o22bo\$3955bo9\$3916bo33bo\$3917bo33bo50\$3856bo\$3857bo
10\$3882bo\$3883bo17\$3849bo\$3848bobo\$3847b3obo\$3849b2o\$3849bo22\$3805b2o\$
3805bo\$3806bo3bo\$3811bo\$3810b2o22bo\$3835bo9\$3796bo33bo\$3797bo33bo50\$
3736bo\$3737bo10\$3762bo\$3763bo43\$3685b2o\$3685bo\$3686bo3bo\$3691bo\$3690b
2o22bo\$3715bo9\$3676bo33bo\$3677bo33bo50\$3616bo\$3617bo10\$3642bo\$3643bo
17\$3609bo\$3608bobo\$3607b3obo\$3609b2o\$3609bo22\$3565b2o\$3565bo\$3566bo3bo
\$3571bo\$3570b2o22bo\$3595bo9\$3556bo33bo\$3557bo33bo26\$2741bo2\$2743bo\$
2741b2o\$2741b2o2bo16\$2747b2o\$2748bo\$2747bo2bo\$2748bobo\$3496bo\$3497bo
10\$3522bo\$3523bo13\$2807b2o\$2808bo2bo2bo\$2791bo17bo\$2790bo21bobo\$2811bo
5bo\$2810bobobobo679bo\$3495bo\$2812bobobobobo\$3489bo\$2814bobobo672bo\$
2817bo2bo\$2816bo\$2796bo22bo\$2820b2o\$2798b2o21bo\$2797bo\$2795b2o\$2795b2o
5\$2771bo35bo\$2770bo36bo\$2806bo\$2804b2o3bo\$2804b2o2\$3465bo\$3464bobo\$
2819bo625b2o16b3obo\$2747b2o69bo626bo19b2o\$2748bo697bo3bo14bo\$2747bo2bo
700bo\$2748bobo699b2o22bo\$3475bo7\$2751bo\$2750bo\$3436bo33bo\$3437bo33bo\$
2754bo\$2753bo2bo\$2753bo\$2754bo\$2799bo\$2798bo8\$2745bo3bo5bo\$2746bo4bo3b
o\$2745bo3bo\$2752b7o\$2753bo4b2o\$2748bo5bo4bo\$2746bobo2bo4bo2bo14bo\$
2744b2obo11bob2o\$2743bob2o6bo3bobo12bo2bo\$2744bobo5b3o3b2o13b2o\$2745bo
7bo5bo\$2756bo4bo17bo\$2778bo8b2o58b2o58b2o58b2o58b2o58b2o58b2o58b2o58b
2o58b2o58b2o58b2o58b2o58b2o\$2760bobo\$2756b2o29bob2o56bob2o56bob2o56bob
2o56bob2o56bob2o56bob2o56bob2o56bob2o56bob2o56bob2o56bob2o56bob2o56bob
2o\$2755bo32bobo57bobo57bobo57bobo57bobo57bobo57bobo57bobo57bobo57bobo
57bobo57bobo57bobo57bobo\$2753b2obo4bo\$2752bob2o4bobo654bo192bo\$2753bob
o660bobo\$2754bo660b3obo192bo\$3417b2o191b2o\$3417bo192b2o2bo15\$3376bo2\$
3377bo9\$3402bo\$3403bo13\$3354bo\$3355bo3\$3369bo\$3368bobo\$3367b3obo\$3369b
2o\$3369bo2\$3378bo\$3379bo19\$3325b2o\$3325bo\$3326bo3bo\$3331bo\$3330b2o22bo
\$3355bo9\$3316bo33bo\$3317bo33bo7\$3321bo\$3320bobo\$3319b3obo\$3321b2o\$
3321bo39\$3256bo2\$3257bo3\$3273bo\$3272bobo\$3271b3obo\$3273b2o\$3273bo2\$
3282bo\$3283bo13\$3234bo\$3235bo9\$3258bo\$3259bo17\$3225bo\$3224bobo\$3205b2o
16b3obo\$3205bo19b2o\$3206bo3bo14bo\$3211bo\$3210b2o22bo\$3235bo9\$3196bo33b
o\$3197bo33bo31\$3177bo\$3176bobo\$3175b3obo\$3177b2o\$3177bo15\$3136bo2\$
3137bo9\$3162bo\$3163bo13\$3114bo\$3115bo3\$3129bo\$3128bobo\$3127b3obo\$3129b
2o\$3129bo2\$3138bo\$3139bo19\$3085b2o\$3085bo\$3086bo3bo\$3091bo\$3090b2o22bo
\$3115bo9\$3076bo33bo\$3077bo33bo7\$3081bo\$3080bobo\$3079b3obo\$3081b2o\$
3081bo39\$3016bo2\$3017bo3\$3033bo\$3032bobo\$3031b3obo\$3033b2o\$3033bo2\$
3042bo\$3043bo13\$2994bo\$2995bo9\$3018bo\$3019bo17\$2985bo\$2984bobo\$2965b2o
16b3obo\$2965bo19b2o\$2966bo3bo14bo\$2971bo\$2970b2o22bo\$2995bo9\$2956bo33b
o\$2957bo33bo31\$2937bo\$2936bobo\$2935b3obo\$2937b2o\$2937bo15\$2896bo2\$
2897bo9\$2922bo\$2923bo13\$2874bo\$2875bo3\$2889bo\$2888bobo\$2887b3obo\$2889b
2o\$2889bo2\$2898bo\$2899bo19\$2845b2o\$2845bo\$2846bo3bo\$2851bo\$2850b2o22bo
\$2875bo9\$2836bo33bo\$2837bo33bo7\$2841bo\$2840bobo\$2839b3obo\$2841b2o\$
2841bo39\$2776bo2\$2777bo3\$2793bo\$2792bobo\$2791b3obo\$2793b2o\$2793bo2\$
2802bo\$2803bo13\$2754bo\$2755bo9\$2778bo\$2779bo17\$2745bo\$2744bobo\$2725b2o
16b3obo\$2725bo19b2o\$2726bo3bo14bo\$2731bo\$2730b2o22bo\$2755bo9\$2716bo33b
o\$2717bo33bo31\$2697bo\$2696bobo\$2695b3obo\$2697b2o\$2697bo15\$2656bo2\$
2657bo9\$2682bo\$2683bo13\$2634bo\$2635bo3\$2649bo\$2648bobo\$2647b3obo\$2649b
2o\$2649bo2\$2658bo\$2659bo19\$2605b2o\$2605bo\$2606bo3bo\$2611bo\$2610b2o22bo
\$2635bo9\$2596bo33bo\$2597bo33bo7\$2601bo\$2600bobo\$2599b3obo\$2601b2o\$
2601bo39\$2536bo2\$2537bo3\$2553bo\$2552bobo\$2551b3obo\$2553b2o\$2553bo2\$
2562bo\$2563bo13\$2514bo\$2515bo9\$2538bo\$2539bo17\$2505bo\$2504bobo\$2485b2o
16b3obo\$2485bo19b2o\$2486bo3bo14bo\$2491bo\$2490b2o22bo\$2515bo9\$2476bo33b
o\$2477bo33bo31\$2457bo\$2456bobo\$2455b3obo\$2457b2o\$2457bo15\$2416bo2\$
2417bo9\$2442bo\$2443bo13\$2394bo\$2395bo3\$2409bo\$2408bobo\$2407b3obo\$2409b
2o\$2409bo2\$2418bo\$2419bo19\$2365b2o\$2365bo\$2366bo3bo\$2371bo\$2370b2o22bo
\$2395bo8\$1745bo\$2356bo33bo\$1747bo609bo33bo\$1745b2o\$1745b2o2bo5\$2361bo\$
2360bobo\$2359b3obo\$2361b2o\$2361bo7\$1751b2o\$1752bo\$1751bo2bo\$1752bobo
26\$1811b2o\$1812bo2bo2bo\$1795bo17bo\$1794bo21bobo477bo\$1815bo5bo\$1814bob
obobo476bo2\$1816bobobobobo\$2313bo\$1818bobobo489bobo\$1821bo2bo486b3obo\$
1820bo492b2o\$1800bo22bo489bo\$1824b2o\$1802b2o21bo496bo\$1801bo521bo\$
1799b2o\$1799b2o5\$1775bo35bo\$1774bo36bo\$1810bo\$1808b2o3bo\$1808b2o2\$
2274bo\$2275bo\$1823bo\$1751b2o69bo\$1752bo\$1751bo2bo\$1752bobo4\$2298bo\$
2299bo3\$1755bo\$1754bo3\$1758bo\$1757bo2bo\$1757bo\$1758bo\$1803bo\$1802bo5\$
2265bo\$2264bobo\$2245b2o16b3obo\$1749bo3bo5bo485bo19b2o\$1750bo4bo3bo486b
o3bo14bo\$1749bo3bo497bo\$1756b7o487b2o22bo\$1757bo4b2o511bo\$1752bo5bo4bo
\$1750bobo2bo4bo2bo14bo\$1748b2obo11bob2o\$1747bob2o6bo3bobo12bo2bo\$1748b
obo5b3o3b2o13b2o\$1749bo7bo5bo\$1760bo4bo17bo\$1782bo8b2o58b2o58b2o58b2o
58b2o58b2o58b2o58b2o118b2o58b2o58b2o118b2o\$1764bobo469bo33bo\$1760b2o
29bob2o56bob2o56bob2o56bob2o56bob2o56bob2o56bob2o56bob2o22bo33bo59bob
2o56bob2o56bob2o116bob2o\$1759bo32bobo57bobo57bobo57bobo57bobo57bobo57b
obo57bobo117bobo57bobo57bobo117bobo\$1757b2obo4bo\$1756bob2o4bobo847bo\$
1757bobo\$1758bo857bo\$2614b2o\$2614b2o2bo20\$2202bo\$2203bo3\$2217bo\$2216bo
bo\$2215b3obo\$2217b2o\$2217bo15\$2176bo2\$2177bo9\$2202bo\$2203bo13\$2154bo\$
2155bo3\$2169bo\$2168bobo\$2167b3obo\$2169b2o\$2169bo2\$2178bo\$2179bo23\$
2125bo28bo\$2124bo30bo9\$2116bo33bo\$2117bo33bo7\$2121bo\$2120bobo\$2119b3ob
o\$2121b2o\$2121bo16\$2082bo\$2083bo22\$2056bo2\$2057bo3\$2073bo\$2072bobo\$
2071b3obo\$2073b2o\$2073bo2\$2082bo\$2083bo13\$2034bo\$2035bo9\$2058bo\$2059bo
17\$2025bo\$2024bobo\$2023b3obo\$2025b2o\$2025bo2\$2005bo28bo\$2004bo30bo9\$
1996bo33bo\$1997bo33bo27\$1962bo\$1963bo3\$1977bo\$1976bobo\$1975b3obo\$1977b
2o\$1977bo15\$1936bo2\$1937bo9\$1962bo\$1963bo13\$1914bo\$1915bo3\$1929bo\$
1928bobo\$1927b3obo\$1929b2o\$1929bo2\$1938bo\$1939bo23\$1885bo28bo\$1884bo
30bo9\$1876bo33bo\$1877bo33bo7\$1881bo\$1880bobo\$1879b3obo\$1881b2o\$1881bo
16\$1842bo\$1843bo22\$1816bo2\$1817bo3\$1833bo\$1832bobo\$1831b3obo\$1833b2o\$
1833bo2\$1842bo\$1843bo13\$1794bo\$1795bo9\$1818bo\$1819bo17\$1785bo\$1784bobo
\$1783b3obo\$1785b2o\$1785bo2\$1765bo28bo\$1764bo30bo4\$1143bo2\$1145bo\$1143b
2o\$1143b2o2bo\$1756bo33bo\$1757bo33bo14\$1149b2o\$1150bo\$1149bo2bo\$1150bob
o10\$1722bo\$1723bo3\$1737bo\$1736bobo\$1735b3obo\$1737b2o\$1737bo8\$1209b2o\$
1210bo2bo2bo\$1193bo17bo\$1192bo21bobo\$1213bo5bo\$1212bobobobo2\$1214bobob
obobo473bo2\$1216bobobo476bo\$1219bo2bo\$1218bo\$1198bo22bo\$1222b2o\$1200b
2o21bo\$1199bo\$1197b2o\$1197b2o\$1722bo\$1723bo3\$1173bo35bo\$1172bo36bo\$
1208bo\$1206b2o3bo\$1206b2o4\$1221bo\$1149b2o69bo\$1150bo523bo\$1149bo2bo
522bo\$1150bobo2\$1689bo\$1688bobo\$1687b3obo\$1689b2o\$1689bo2\$1153bo544bo\$
1152bo546bo3\$1156bo\$1155bo2bo\$1155bo\$1156bo\$1201bo\$1200bo8\$1147bo3bo5b
o479b2o5bo\$1148bo4bo3bo480bob2o4bo\$1147bo3bo488bo4b3o\$1154b7o480bo4bo\$
1155bo4b2o480b3o3bo\$1150bo5bo4bo481bo\$1148bobo2bo4bo2bo14bo\$1146b2obo
11bob2o509bo\$1145bob2o6bo3bobo12bo2bo497bo\$1146bobo5b3o3b2o13b2o\$1147b
o7bo5bo\$1158bo4bo17bo\$1180bo8b2o58b2o58b2o58b2o58b2o58b2o58b2o58b2o
118b2o\$1162bobo\$1158b2o29bob2o56bob2o56bob2o56bob2o56bob2o56bob2o56bob
2o56bob2o116bob2o\$1157bo32bobo57bobo57bobo57bobo57bobo57bobo57bobo57bo
bo117bobo\$1155b2obo4bo\$1154bob2o4bobo471bo33bo341bo\$1155bobo479bo33bo\$
1156bo857bo\$2012b2o\$2012b2o2bo4\$1641bo\$1640bobo\$1639b3obo\$1641b2o\$
1641bo2\$1650bo\$1651bo13\$1602bo\$1603bo9\$1626bo\$1627bo9\$1588bo\$1589bo2\$
1576bo2\$1577bo3\$1593bo\$1592bobo\$1591b3obo\$1593b2o\$1593bo2\$1602bo\$1603b
o13\$1554bo\$1555bo4\$1605bo\$1604bo4\$1578bo\$1579bo17\$1524bo20bo\$1544bobo\$
1525bo17b3obo\$1545b2o\$1545bo2\$1554bo\$1555bo9\$1516bo33bo\$1517bo33bo13\$
1530bo\$1531bo13\$1482bo\$1483bo3\$1497bo\$1496bobo\$1495b3obo\$1497b2o\$1497b
o2\$1506bo\$1507bo9\$1468bo\$1469bo2\$1456bo2\$1457bo9\$1482bo\$1483bo13\$1434b
o\$1435bo3\$1449bo\$1448bobo34bo\$1447b3obo32bo\$1449b2o\$1449bo2\$1458bo\$
1459bo17\$1404bo2\$1405bo4\$1434bo\$1435bo9\$1396bo33bo\$1397bo33bo7\$1401bo\$
1400bobo\$1399b3obo\$1401b2o\$1401bo2\$1410bo\$1411bo13\$1362bo\$1363bo9\$
1386bo\$1387bo9\$1348bo\$1349bo2\$1336bo2\$1337bo3\$1353bo\$1352bobo\$1351b3ob
o\$1353b2o\$1353bo2\$1362bo\$1363bo13\$1314bo\$1315bo4\$1365bo\$1364bo4\$1338bo
\$1339bo17\$1284bo20bo\$1304bobo\$1285bo17b3obo\$1305b2o\$1305bo2\$1314bo\$
1315bo9\$1276bo33bo\$1277bo33bo13\$1290bo\$1291bo13\$1242bo\$1243bo3\$1257bo\$
1256bobo\$1255b3obo\$1257b2o\$1257bo2\$1266bo\$1267bo9\$1228bo\$1229bo2\$1216b
o2\$1217bo9\$1242bo\$1243bo13\$1194bo\$1195bo3\$1209bo\$1208bobo34bo\$1207b3ob
o32bo\$1209b2o\$1209bo2\$1218bo\$1219bo17\$1164bo2\$1165bo4\$1194bo\$1195bo9\$
1156bo33bo\$1157bo33bo7\$1161bo\$1160bobo\$1159b3obo\$1161b2o\$1161bo2\$1170b
o\$1171bo13\$1122bo\$1123bo9\$1146bo\$1147bo9\$1108bo\$1109bo2\$1096bo2\$1097bo
3\$1113bo\$1112bobo\$1111b3obo\$1113b2o\$1113bo2\$1122bo\$1123bo8\$491bo2\$493b
o\$491b2o\$491b2o2bo\$1074bo\$1075bo4\$1125bo\$1124bo4\$1098bo\$1099bo4\$497b2o
\$498bo\$497bo2bo\$498bobo10\$1044bo20bo\$1064bobo\$1045bo17b3obo\$1065b2o\$
1065bo2\$1074bo\$1075bo9\$557b2o477bo33bo\$558bo2bo2bo472bo33bo\$541bo17bo\$
540bo21bobo\$561bo5bo\$560bobobobo2\$562bobobobobo2\$564bobobo\$567bo2bo\$
566bo\$546bo22bo\$570b2o\$548b2o21bo478bo\$547bo503bo\$545b2o\$545b2o5\$521bo
35bo\$520bo36bo\$556bo\$554b2o3bo\$554b2o2\$1002bo\$1003bo\$569bo\$497b2o69bo\$
498bo518bo\$497bo2bo515bobo\$498bobo514b3obo\$1017b2o\$1017bo2\$1026bo\$
1027bo3\$501bo\$500bo3\$504bo\$503bo2bo\$503bo484bo\$504bo484bo\$549bo\$548bo
427bo2\$977bo6\$495bo3bo5bo\$496bo4bo3bo\$495bo3bo\$502b7o493bo\$503bo4b2o
493bo\$498bo5bo4bo\$496bobo2bo4bo2bo14bo\$494b2obo11bob2o\$493bob2o6bo3bob
o12bo2bo\$494bobo5b3o3b2o13b2o\$495bo7bo5bo\$506bo4bo17bo\$528bo8b2o58b2o
58b2o58b2o58b2o58b2o58b2o58b2o238b2o\$510bobo451bo\$506b2o29bob2o56bob2o
56bob2o56bob2o56bob2o56bob2o56bob2o56bob2o4bo231bob2o\$505bo32bobo57bob
o57bobo57bobo57bobo57bobo57bobo57bobo237bobo\$503b2obo4bo\$502bob2o4bobo
441bo405bo\$503bobo449bo\$504bo857bo\$1360b2o\$969bo390b2o2bo\$968bobo34bo\$
967b3obo32bo\$969b2o\$969bo2\$978bo\$979bo9\$940bo\$941bo7\$924bo2\$925bo4\$
954bo\$955bo9\$916bo33bo\$917bo33bo7\$921bo\$920bobo\$919b3obo\$921b2o\$921bo
2\$930bo\$931bo9\$926bo\$927bo3\$882bo\$883bo9\$906bo\$907bo9\$868bo33bo\$869bo
33bo3\$858bo\$859bo3\$873bo\$872bobo\$871b3obo\$873b2o\$873bo2\$882bo\$883bo9\$
844bo\$845bo3\$834bo\$835bo4\$885bo\$884bo4\$858bo\$859bo9\$820bo\$821bo7\$804bo
20bo\$824bobo\$805bo17b3obo\$825b2o\$825bo2\$834bo\$835bo9\$796bo33bo\$797bo
33bo13\$810bo\$811bo9\$806bo\$807bo3\$762bo\$763bo3\$777bo\$776bobo\$775b3obo\$
777b2o\$777bo2\$786bo\$787bo9\$748bo33bo\$749bo33bo3\$738bo\$739bo9\$762bo\$
763bo9\$724bo\$725bo3\$714bo\$715bo3\$729bo\$728bobo34bo\$727b3obo32bo\$729b2o
\$729bo2\$738bo\$739bo9\$700bo\$701bo7\$684bo2\$685bo4\$714bo\$715bo9\$676bo33bo
\$677bo33bo7\$681bo\$680bobo\$679b3obo\$681b2o\$681bo2\$690bo\$691bo5\$o2\$2bo\$
2o\$2o2bo681bo\$687bo3\$642bo\$643bo9\$666bo\$667bo\$6b2o\$7bo\$6bo2bo\$7bobo5\$
628bo33bo\$629bo33bo3\$618bo\$619bo3\$633bo\$632bobo\$631b3obo\$633b2o\$633bo
2\$642bo\$643bo6\$66b2o\$67bo2bo2bo\$50bo17bo\$49bo21bobo530bo\$70bo5bo528bo\$
69bobobobo2\$71bobobobobo514bo\$595bo\$73bobobo\$76bo2bo\$75bo\$55bo22bo566b
o\$79b2o563bo\$57b2o21bo\$56bo\$54b2o\$54b2o562bo\$619bo4\$30bo35bo\$29bo36bo\$
65bo\$63b2o3bo\$63b2o\$580bo\$581bo2\$78bo\$6b2o69bo\$7bo\$6bo2bo\$7bobo\$564bo
20bo\$584bobo\$565bo17b3obo\$585b2o\$585bo2\$594bo\$10bo584bo\$9bo3\$13bo\$12bo
2bo\$12bo\$13bo\$58bo\$57bo498bo33bo\$557bo33bo7\$4bo3bo5bo\$5bo4bo3bo\$4bo3bo
\$11b7o\$12bo4b2o533bo\$7bo5bo4bo\$5bobo2bo4bo2bo14bo518bo17bo\$3b2obo11bob
2o531bo17bo\$2bob2o6bo3bobo12bo2bo519b2o\$3bobo5b3o3b2o13b2o\$4bo7bo5bo\$
15bo4bo17bo\$37bo8b2o58b2o58b2o58b2o58b2o58b2o58b2o58b2o58b2o238b2o58b
2o\$19bobo\$15b2o29bob2o56bob2o56bob2o56bob2o56bob2o56bob2o56bob2o56bob
2o56bob2o236bob2o56bob2o\$14bo32bobo57bobo57bobo57bobo57bobo57bobo57bob
o57bobo57bobo237bobo57bobo\$12b2obo4bo511bo33bo\$11bob2o4bobo511bo33bo
301bo\$12bobo\$13bo857bo\$522bo346b2o\$523bo345b2o2bo3\$537bo\$536bobo\$535b
3obo\$537b2o\$537bo2\$546bo\$547bo9\$508bo33bo\$509bo33bo3\$498bo\$499bo9\$522b
o\$523bo9\$484bo33bo\$485bo33bo3\$474bo\$475bo3\$489bo\$488bobo\$487b3obo\$489b
2o\$489bo2\$498bo\$499bo9\$460bo33bo\$461bo33bo3\$450bo\$451bo9\$474bo\$475bo9\$
436bo33bo\$437bo33bo3\$426bo\$427bo3\$441bo\$440bobo\$439b3obo\$441b2o\$441bo
2\$450bo\$451bo9\$412bo33bo\$413bo33bo3\$402bo\$403bo9\$426bo\$301bo125bo2\$
303bo\$301b2o\$301b2o2bo5\$388bo33bo\$389bo33bo3\$378bo\$311b2o2bo63bo\$312b
2o\$315bo77bo\$391bo\$315bo74bo2b2o\$390b2ob2obo\$386bo\$391bobobo\$393b2o\$
402bo\$403bo2\$392bo7\$364bo33bo\$365bo33bo3\$354bo\$355bo4\$363b3o3bo\$370bo\$
364b2o\$366bo\$362bo4bo\$363bo4bobo7bo\$363bo4bobo8bo\$364b2o4bo\$366bo7\$
374bo\$375bo4\$335b2o2bo\$336b2o\$339bo2\$339bo6bo\$343bo\$341b2obo\$341bobobo
\$341bo2bo\$342b3o2\$346bobobo2\$349bo\$349b2o\$350bo\$329bobo\$324bo3b2o2b2o\$
319bo2bo2bobob5o\$320bo3b3o2bob2obo\$321bo10bo\$331b4o\$321bo11bo\$322bo9bo
\$317bo4b2o2bo4bo\$318bo5b2o5b2o\$323bobo5bobo\$324bobo\$316bo9b2o4bo\$320bo
7bobo\$315b2obob2o9bo\$315b2o15bo\$315b3o2bo4bo\$316b3o7bo\$315bob4obo\$313b
2obob3o73bobobo\$312bob2o\$313bobo81bo\$314bo82b2o\$398bo6\$408bo2\$410bo\$
408b2o\$408b2o2bo!``````
Here is a much slower-growing version of the previous variation on 22da:

Code: Select all

``````@RULE 22dabDLA

@TABLE

# Golly rule-table format.
# Each rule: C,N,NE,E,SE,S,SW,W,NW,C'
#
# Default for transitions not listed: no change
#
# Variables are bound within each transition.
# For example, if a={1,2} then 4,a,0->a represents
# two transitions: 4,1,0->1 and 4,2,0->2
# (This is why we need to repeat the variables below.
#  In this case the method isn't really helping.)

n_states:3
neighborhood:hexagonal
symmetries:rotate6reflect
var a={0,1,2}
var b={a}
var c={a}
var d={1,2}
var e={d}
var f={d}
var g={d}
var h={d}
var i={d}
1,d,e,f,g,h,2,2
0,d,e,0,0,0,0,1
0,d,0,e,0,0,0,1
0,d,0,0,e,0,0,1
1,0,0,0,0,0,0,0
1,d,0,0,0,0,0,0
1,d,e,f,a,b,c,0
1,d,e,c,f,a,b,0
1,d,c,e,b,f,a,0
1,d,0,e,0,0,0,0
2,2,2,2,2,2,a,0
2,2,2,2,0,0,2,0
2,d,e,f,g,h,i,0
2,1,1,0,0,0,0,0
2,1,0,1,0,0,0,0
2,2,0,2,0,0,0,0``````

### Re: 22da (Hexagonal Grid)

Posted: March 25th, 2014, 1:55 pm
c0b0p0 wrote:A rake:

Code: Select all

``````x = 125, y = 128, rule = 22da
o2\$2bo\$2o\$2o2bo\$6b2o\$7bo\$6bo2bo\$7bobo54\$57bo\$57bo\$56bo\$6b2o46b2o3bo\$7b
o26bo19b2o\$6bo2bo25bo\$7bobo2\$64bo2\$66b2o\$65bo\$63b2o\$63b2o11\$14bo\$15bo
7\$62bo\$63bo7\$16bo\$15bo2bo\$15bo\$19b2o\$16bo3bo2bo\$17bo4bo\$21bo\$19b2o2b2o
\$20bo3bo\$6bo19bo\$7b2o13bo\$6b2o15bo3bo\$5bo19b2o15bo\$3b2obo4bo31bo\$2bob
2o4bo\$3bobo6bo\$4bo9bo\$13bo\$61b2o58b2o\$17bo\$16b2o43bob2o56bob2o\$14bobob
o43bobo57bobo\$12b2obo\$11bob2o\$12bobo\$13bo!``````
I will call this rake "Siderake 1".

I still have not found any still lifes in the rule. I wonder if someone might be able to prove that there aren't any.
Here is a smaller rake:

Code: Select all

``````x = 52, y = 52, rule = 22da
41bo2\$43bo\$41b2o\$41b2o2bo5\$49bo\$49bo\$48bo\$46b2o3bo\$46b2o25\$o2\$2bo\$2o\$
2o2bo5\$8bo\$8bo\$7bo\$5b2o3bo\$5b2o!``````
I also tried to make 11-cell quadratic growth. Here is my closest result.

Code: Select all

``````x = 9, y = 13, rule = 22da
2bo\$2o\$2o7\$7bo\$8bo\$4b2o\$4b2o!``````
By the way, here is my COLORS section for 22da.

Code: Select all

``````@COLORS
1   0 255   0   green
2   0 255   0   green (again!)
3 255   0   0   red
4 255 255   0
5 255   0 255
6 0   255 255``````

### Re: 22da (Hexagonal Grid)

Posted: March 26th, 2014, 2:45 pm
Here is a smoking ship, which should compress the size of my backrake by around one-and-a-half orders of magnitude.

Code: Select all

``````x = 24, y = 24, rule = 22da
21bo\$17bo3bo\$5bo16b2o\$7bo10bo\$6bob2o\$8b2o10bo\$3bo6bo11bo\$2bo6bo\$3bobo
4b2o\$3bo\$3b3obo2bo2bo\$2bo3bo5bo\$2o13bo\$2o11bobobo\$16bob2o\$18b2o\$13bo6b
o\$12bo6bo\$13bobo5bo\$13bo\$13b3obo\$12bo3bo\$10b2o\$10b2o!``````

### Re: 22da (Hexagonal Grid)

Posted: March 27th, 2014, 5:37 pm
Here is a 3-glider synthesis of half of the smoking ship.

Code: Select all

``````x = 25, y = 27, rule = 22da
19bo\$17b2o\$17b2o17\$20b2o\$21b2o\$24bo3\$b2o\$b2o\$o!``````
The other half will be done shortly.

### Re: 22da (Hexagonal Grid)

Posted: March 28th, 2014, 2:07 pm
The 8-cell puffer turns out to be switchable.

Code: Select all

``````x = 1467, y = 1457, rule = 22da
1312bo\$1311bobo\$1310b3obo\$1312b2o\$1312bo2\$1314bo\$1314b3o2\$1315b3o\$
1316b2o\$1316bobo16\$1436bobo\$1435b2ob2o\$1434b2o\$1434bo3b2o\$1362b3o66b2o
bo2b2o\$1429b2o2b5o\$1363b3o53bo4b3o2bo4bo\$1364b2o59b2o2bo5bo\$1364bobo
54bo4bo8bo\$1422b2o10bo\$1427bo4b3o\$1420bobo3bobo\$1425b3obo\$1424bob3o2b
3o\$1418bo5bo2bo4b2o\$1420bo4b2o6bo\$1419bobo8bo\$1419bo2bo5bobo\$1423bo7bo
\$1420bo3bo3bo\$1422b2o9bo\$1425bo4\$1414bo\$1411b2o\$1408bo4bo\$1407bo3bobo\$
1410bo\$1409bo\$1412bo\$1411bo5\$1381bo\$1382bo7\$1384b2o\$1383bobo\$1377bo7bo
5bo\$1378bo6bo2b3obo\$1387b2ob2o\$1388bo2bo\$1389b3o\$1385b2o3bo\$1387bo\$
1387bo3b4o\$1394bo\$1393bo\$1401bo\$1402bo3\$1357bo33bo\$1358bo33bo6\$1368b2o
2\$1362bo5b2obo\$1353bo9bo5bobo\$1354bo\$1366bo64bo\$1365bo66b2o\$1431b3obo\$
1360bo7bo64bobo\$1369bo65bo\$1361bo\$1363bo2\$1377bo\$1378bo3\$1333bo33bo\$
1334bo33bo9\$1329bo\$1330bo9\$1353bo\$1354bo3\$1309bo33bo\$1310bo33bo8\$1318b
2o\$1305bo\$1306bo11b2obo\$1319bobo133bo\$1456b2o\$1455b3obo\$1457bobo\$1459b
2o3bo\$1463bobo\$1462b3obo\$1464b2o\$1329bo134bo\$1330bo3\$1285bo33bo\$1286bo
33bo9\$1281bo\$1282bo9\$1305bo\$1306bo3\$1261bo33bo\$1262bo33bo8\$1270b2o\$
1257bo\$1258bo11b2obo\$1271bobo8\$1281bo\$1282bo3\$1237bo33bo\$1238bo33bo9\$
1233bo\$1234bo4\$1181bobo\$1180b2ob2o\$1176b2o2bo\$1175bo7b2o\$1182b2o\$1176b
o30bo49bo\$1177b2o27bobo49bo\$1177b2o3bo22b3obo\$1179bo2bo24b2o\$1176bo4bo
25bo5bo33bo\$1174b2obo13bobo20bo33bo\$1173bo3bo12b2ob2o\$1176bo9b2o2bo\$
1177bo7bo7b2o\$1192b2o\$1179bo6bo\$1178bo8b2o\$1181bob2o2b2o3bo\$1182bo2bo
3bo2bo29b2o\$1184bo6bo17bo\$1171bo12bo25bo11b2obo\$1172b2o9bo39bobo\$1169b
o2b2o\$1171bo2bo2\$1172bo4\$1233bo\$1234bo3\$1223bo\$1224bo11bo\$1235bobo\$
1234b3obo\$1236b2o\$1236bo5\$1185bo\$1186bo5\$1230bobo\$1229b2ob2o\$1225b2o2b
o\$1224bo7b2o\$1231b2o\$1225bo\$1226b2o\$1226b2o3bo\$1199bo28bo2bo\$1200bo24b
o4bo\$1223b2obo13bobo\$1222bo3bo12b2ob2o\$1225bo9b2o2bo\$1226bo7bo7b2o\$
1241b2o\$1228bo6bo\$1227bo8b2o\$1174b2o54bob2o2b2o3bo\$1161bo69bo2bo3bo2bo
\$1162bo11b2obo55bo6bo\$1175bobo42bo12bo\$1221b2o9bo\$1218bo2b2o\$1220bo2bo
2\$1221bo7\$1175bo\$1176bo9\$1137bo\$1138bo7\$1088bobo\$1087b2ob2o\$1083b2o2bo
\$1082bo7b2o\$1089b2o\$1083bo\$1084b2o25bo2b2o35bo\$1084b2o3bo24b2o36bo\$
1086bo2bo23bo\$1083bo4bo\$1081b2obo13bobo14bo\$1080bo3bo12b2ob2o\$1083bo9b
2o2bo12bo\$1084bo7bo7b2o10bo\$1099b2o\$1086bo6bo32b2o\$1085bo8b2o\$1088bob
2o2b2o3bo26b2obo\$1089bo2bo3bo2bo27bobo\$1091bo6bo\$1078bo12bo\$1079b2o9bo
\$1076bo2b2o\$1078bo2bo2\$1079bo4\$1134bo2b2o\$1137b2o\$1136bo\$1131bo\$1138bo
\$1132bo9\$1131bobo\$1130b2ob2o\$1126b2o2bo\$1125bo7b2o\$1132b2o\$1126bo\$
1127b2o\$1127b2o3bo\$1129bo2bo\$1126bo4bo\$1124b2obo13bobo\$1123bo3bo12b2ob
2o\$1126bo9b2o2bo\$1127bo7bo7b2o\$1142b2o\$1129bo6bo\$1128bo8b2o\$1131bob2o
2b2o3bo\$1132bo2bo3bo2bo\$1134bo6bo\$1078b2o41bo12bo\$1122b2o9bo\$1078b2obo
37bo2b2o\$1079bobo39bo2bo2\$1122bo43\$1030b2o2\$1030b2obo\$1031bobo45\$982b
2o2\$982b2obo\$983bobo45\$934b2o2\$934b2obo\$935bobo45\$886b2o2\$886b2obo\$
887bobo45\$838b2o2\$838b2obo\$839bobo45\$790b2o2\$790b2obo\$791bobo43\$744b2o
2\$744b2obo\$745bobo17\$715bo\$714bobo\$713b3obo\$715b2o\$715bo42\$669bo\$668bo
bo\$667b3obo\$669b2o\$669bo44\$621bo\$620bobo\$619b3obo\$621b2o\$621bo44\$573bo
\$572bobo\$571b3obo\$573b2o\$573bo44\$525bo\$524bobo\$523b3obo\$525b2o\$525bo
44\$477bo\$476bobo\$475b3obo\$477b2o\$477bo44\$429bo\$428bobo\$427b3obo\$429b2o
\$429bo41\$341b2o\$326bo9bobo4bo\$337b3o3bo\$326bobo10bo41bo\$327bobo10b2o
38bobo\$327bo2bo10b2o36b3obo\$328b2o11bo39b2o\$324b3o3bobo9bo38bo\$324b3o
4b2o\$322b2ob2o4bo\$321bob2o\$322bobo7bo2b2o\$323bo10b2o\$336bobo\$337bobo\$
337bo2bo\$338b2o\$334b3o3bobo\$334b3o\$332b2ob2o\$331bob2o\$332bobo\$333bo10\$
330bo\$327b2o3bo\$334bo\$327b2obo4bo\$328bobobo\$334bo6\$384b2o\$369bo9bobo4b
o\$380b3o3bo\$369bobo10bo\$370bobo10b2o\$370bo2bo10b2o\$371b2o11bo\$367b3o3b
obo9bo\$333bo17bo15b3o4b2o\$332bobo14bo2bo12b2ob2o4bo\$331b3obo28bob2o\$
333b2o15bo2bo11bobo7bo2b2o\$333bo32bo10b2o\$350b2o2bo24bobo\$380bobo\$350b
2obo26bo2bo\$351bobo27b2o\$312bo64b3o3bobo\$311bo65b3o\$375b2ob2o\$374bob2o
\$375bobo\$376bo9\$326bo\$325bo9\$288bo\$287bo8\$242b2o\$227bo9bobo4bo\$238b3o
3bo\$227bobo10bo\$228bobo10b2o\$228bo2bo10b2o58bo\$229b2o11bo42bo15bo\$225b
3o3bobo9bo40bobo\$225b3o4b2o49b3obo\$223b2ob2o4bo52b2o\$222bob2o59bo\$223b
obo7bo2b2o\$224bo10b2o\$237bobo\$238bobo\$238bo2bo22bo\$239b2o22bo\$235b3o3b
obo\$235b3o\$233b2ob2o\$232bob2o\$233bobo\$234bo7\$278bo\$277bo2\$228bo2\$230bo
\$228b2o\$228b2o2bo3\$240bo\$239bo3\$230bo\$229bo5\$291b2o\$276bo9bobo4bo\$287b
3o3bo\$276bobo10bo\$254bo22bobo10b2o\$237bo15bo23bo2bo10b2o\$236bobo39b2o
11bo\$235b3obo34b3o3bobo9bo\$237b2o35b3o4b2o\$237bo34b2ob2o4bo\$271bob2o\$
272bobo7bo2b2o\$257bo15bo10b2o\$286bobo\$216bo33bo8bo27bobo\$215bo33bo7b2o
28bo2bo\$257b2o2bo26b2o\$284b3o3bobo\$206bo77b3o\$205bo76b2ob2o\$281bob2o\$
282bobo\$283bo6\$230bo\$229bo9\$192bo33bo\$191bo33bo3\$182bo\$181bo9\$206bo\$
189bo15bo\$188bobo\$187b3obo\$189b2o\$189bo5\$168bo33bo\$167bo33bo3\$158bo\$
157bo9\$182bo\$181bo9\$144bo33bo\$143bo33bo\$o2\$2bo131bo\$2o131bo\$2o2bo6\$8b
2o2bo\$9b2o\$12bo145bo\$141bo15bo\$12bo127bobo\$139b3obo\$141b2o\$141bo5\$120b
o33bo\$119bo33bo3\$110bo\$109bo9\$134bo\$133bo9\$96bo33bo\$95bo33bo3\$86bo\$85b
o2\$101bo\$101bo\$95bo6b2o\$94bo2\$32b2o2bo60bo\$33b2o63bo\$36bo73bo\$101bo7bo
\$36bo63bo\$91bo\$90bobo\$89b3obo\$91b2o\$91bo3\$72bo33bo\$71bo2bo30bo2\$74b3o\$
62bo13bob2o\$61bo8bo5bo4bo\$74bo\$68bo4b2o7bo\$70bo3bob2o4bo\$75bob2o\$76bob
o2b3o\$77bo5bo\$78b3o2bobo\$79bo\$72bo13bo\$71bo13bo\$78bo2bo2\$79bo6\$82bo\$
81bo3\$50bo\$49bobobo2bo\$50b4ob3o\$49b2o2b4o\$51bo2b2o\$50b3o2b3o\$51b3o2bo\$
52b3ob2o\$53bob2obo\$55bobo5\$37bo\$41b3o\$33b2o4bob3o\$34b2o5b3o\$35b4o\$31bo
5bo4bo\$31bobo4bobo\$29bo9b2o3bo\$28bo11bo53bobobo\$33bobo4b2o\$29bo4bo6b2o
54bo\$35bo2bo3bo54b2o\$98bo\$29bo8b2o\$29bo\$27b2ob2o2bo2bo\$26bob2o6bo\$27bo
bo\$28bo14\$142bobobo2\$145bo\$145b2o\$146bo4\$152bo2\$154bo\$152b2o\$152b2o2bo
!``````
Here is a potential component of a p222 shuttle. After 111 generations, the p126s appear again, this time separated by two more cells.

Code: Select all

``````x = 11, y = 10, rule = 22da
obo\$3o7\$8b3o\$8bobo!``````

### Re: 22da (Hexagonal Grid)

Posted: March 30th, 2014, 7:03 pm
As part of my "Project Breeder", I decided to try my hand at SMM and MSM breeders. Here is a worry-free synthesis of the 8-cell glider-emitting puffer for the rake gun.

Code: Select all

``````x = 25, y = 42, rule = 22da
11bo\$9b2o\$9b2o13\$19bo\$17b2o\$17b2o17\$20b2o\$21b2o\$24bo3\$b2o\$b2o\$o!``````
For the MSM breeder, here is a synthesis of the p16 from a p4 that can in turn be synthesized with two gliders.

Code: Select all

``````x = 69, y = 66, rule = 22da
42bobobo2\$45bo\$45b2o\$46bo17bo2\$66bo\$64b2o\$64b2o2bo5\$57bo\$57bo\$58b2o\$
54b2o\$56bo\$56bo7\$40bo2b2o\$43b2o\$42bo2\$44bo7\$29bo2b2o\$32b2o\$31bo2\$33bo
7\$14bo2b2o\$17b2o\$16bo2\$18bo10\$o2b2o\$3b2o\$2bo2\$4bo!``````
Here is the p4's synthesis. Curiously enough, the bounding box is 16x16.

Code: Select all

``````x = 16, y = 16, rule = 22da
13bo\$12b2o\$11bob3o\$12bobo\$13bo7\$o2b2o\$3b2o\$2bo2\$4bo!``````

### Re: 22da (Hexagonal Grid)

Posted: March 31st, 2014, 5:52 pm
For the rake gun, this method is the only one I found to resolve the puffer synchronization problem. (Try running the 8-cell glider-emitting puffer for 960 generations, and then paste another 8-cell glider-emitting puffer in the place the original one was. You will see the problem immediately.)

Code: Select all

``````x = 29, y = 60, rule = 22da
26bo\$25b2o\$24bob3o\$25bobo\$26bo47\$bo2\$3b2o\$2bo\$2o\$2o\$17bo\$15b2o\$15b2o!
``````
Following DivusIulius, I decided to make long-lasting glider collisions. Here is a three-glider mess. (DivusIulius could probably do much better, but at least it's a start.)

Code: Select all

``````x = 118, y = 76, rule = 22da
o2\$o\$2b2o\$o2b2o49\$113b2o2bo\$114b2o\$117bo2\$117bo16\$24b2o\$24b2o\$23bo!
``````

### Re: 22da (Hexagonal Grid)

Posted: April 1st, 2014, 8:42 pm
Here is an improved rake synthesis.

Code: Select all

``````x = 45, y = 45, rule = 22da
12bo2\$14bo\$12b2o\$12b2o2bo24\$40bo2\$42bo\$40b2o\$40b2o2bo7\$bo2\$3b2o\$2bo\$2o
\$2o!``````
A glider pusher:

Code: Select all

``````x = 215, y = 110, rule = 22da
48b2o\$2o46bobo\$obo44bo3bo\$o3bo42b2ob2o\$b2ob2o41b3o\$4b3o\$22b3o\$23b2ob2o
\$24bo3bo\$26bobo\$27b2o9\$53b3o\$53bo2bo\$54bobo2\$55b3o\$56b2o\$57bo14\$61b3o\$
61bo2bo\$62bobo2\$63b3o\$64b2o\$65bo10\$210bo2\$212bo\$210b2o\$210b2o2bo8\$183b
3o2\$185bo\$185b2o17\$195b3o2\$197bo\$197b2o11\$181bo\$179bob2o\$180bo\$181bo\$
162bo\$163bo44bo\$161b2obo43bo\$162bo45bob2o\$211bo!``````