Triangular & Tripod von Neuman neighborhoods

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EricG
Posts: 199
Joined: August 19th, 2011, 5:41 pm
Location: Chicago-area, USA

Triangular & Tripod von Neuman neighborhoods

Post by EricG » September 9th, 2012, 4:58 pm

I liked the way the rule VN-B1x2/S23 made the von Neuman neighborhood come to life
(see viewtopic.php?f=11&t=808
and viewtopic.php?f=11&t=949).

I thought it would be interesting to see if the same Bx2 trick would work in neighborhoods which were analogous to the von Neuman neighborhood. I identified four such neighborhoods:
fourVNneighborhoods.tiff
fourVNneighborhoods.tiff (15.39 KiB) Viewed 11222 times
1) The three neighbor triangular cell neighborhood.
I had a lot of fun with Carter Bays' 12 neighbor triangualr Moore neighborhood, so the first thing I tried was the 3 neighbor triangular von Neuman neighborhood.

2) The Tripod neighborhood.
Tim Tyler talks about a neighborhood with three neighbors which is rather different.
See his page: http://cell-auto.com/neighbourhood/tripod/index.html
Tyler calls the six neighbor hexagonal neighborhood "the honeycomb neighborhood", and he says of the Tripod neighborhood, "This is a cut-down version of the Honeycomb neighbourhood.
It has the same sort of relationship to this that the von Neumann neighbourhood has to the Moore neighbourhood."

So, that suggests there are (at least) two ways to generalize the von Neuman neighborhood to other tesselations.

One way is to "include side cells, but exclude corner cells", as the triangular von neuman neighborhood does. But that won't work for the hexagonal neighborhood, since there are no corner cells.

Another way is to "cut down" the neighborhood is to eliminate every other neighbor, so that neighbors touch the central cell, and don't touch each other -- this seems to capture the spirit of the von Neuman neighborhood. (Edit: correction, I should have said "so that the neighbors share a side with the central cell but don't share sides with each other". ) So, for triangular cells, cutting down the neighborhood yields two new neighborhoods:

3) The Tri6inner neighborhood
For triangular cells, if you eliminate every other neighbor starting with one particular cell, you get a very pleasant looking neighborhood that has six total neighbors, and this includes the three side neighbors.

4) The Tri6outer neighborhood
Alternatively, for triangular cells, if you eliminate every other neighbor starting with a different particular cell, you get a very different neighborhood -- it also has six total neighbors, but it includes no side cells. This one doesn't seem nearly as von Neuman-like to me, but I have to admit that it is pretty in its own way. 

I'm not crazy about the names "Tri6inner" and "Tri6outer" -- anyone have a better suggestion?
Also, can anyone suggest other neighborhoods that are analogous to the von Neuman neighborhood? Ideally, they'd be easily searchable, as the above four are, with Golly or some other available tool (Ready?)

I'll discuss what I've found so far below.
Last edited by EricG on September 10th, 2012, 11:01 am, edited 1 time in total.

EricG
Posts: 199
Joined: August 19th, 2011, 5:41 pm
Location: Chicago-area, USA

Re: Triangular & Tripod von Neuman neighborhoods

Post by EricG » September 10th, 2012, 12:16 am

Predictably, two state triangular VN rules aren't very interesting (although I didn't try B0 rules).
For the Bx2 trick, the rule table is really simple - here's TriVN-B12x2_S13.table:

Code: Select all

n_states:3
neighborhood:triangularVonNeumann
symmetries:permute

var a={0,1}
var b={a}
var c={a}

# Birth
0,a,b,c,0
0,2,b,c,1
0,2,2,c,1
0,2,2,2,0

# Change
1,a,b,c,0
1,2,b,c,2
1,2,2,c,2
1,2,2,2,0

# Survive
2,a,b,c,0
2,2,b,c,2
2,2,2,c,0
2,2,2,2,2
Golly can't use this table direclty, so after you save the ruletable in a file, click on the RuleTabletoTree.py script and select the ruletable's file to convert it into a rule Golly can use. If you sort by the rules by date, the newest rule is always at the top, and this procedure is hassle-free. The resulting ruletree will be called TriVN-B12x2_S13_emulated.

TriVN-B1x2_S1, TriVN-B12x2_S1 and TriVN-B123x2_S1 are all very busy rules, but if you make a random field, you'll immediately see similarities to the orginal VN-B1x2/S23. Hooray - the Bx2 plan worked! You can isolate many rakes, etc.

Rake:

Code: Select all

x = 14, y = 10, rule = TriVN-B12x2_S1_emulated
8A$GFGFGFB2A$CBEBEBE$.7CHA2.B$4.AECEB.E2FB$4.GFAGA2GAHA$3.FH.F4A2B$3.
CBDF$4.FCF$5.2F!
Quadratic growth with an optional roof:

Code: Select all

x = 38, y = 23, rule = TriVN-B12x2_S1_emulated
5$29.BEC$13.8B8.BAEC$13.BABABABGE7.GF.C$13.FCFCFCFCF.A6.H7B$14.8F.2A
6.BABABAB$31.FCFC.CF$20.3C2F2H5.3FCAF$20.CECECABCB5.2F2B$21.GAG4AFB4.
FCAB$22.AGFGFAF5.2F2B$23.CBEBECF4.FCAB$24.3CF.F4.2F2B$34.FCAB$35.F2B!
Rules with S13 are calmer. TriVN-B1x2_S13 is a very quiet rule except for a very common natural gun.
Here's the gun, and another structure that appears to be an odd sort of gun, but after 4,500 geneations, it runs out of ammunition:

Code: Select all

x = 106, y = 69, rule = TriVN-B1x2_S13_emulated
95.CEA$81.F.F12.BFA$83.BA12.F$81.F.2H2F8.2A$84.GFBA7.AFE$83.F.F.GBH6.
A.C$86.F2.2HBACEBABC$89.2FHBC.HB$92.AFHFA$93.C2FEDF2A$93.CBHDGB2.A$
94.CHBC.F3E$96.A.FACHB.A$95.2AB2.ADBFHA$95.A6.C.GA$96.GBC$97.2C$96.B$
95.CBF$96.CGA46$BDC.2CAB$BF.FH.F.B$F.B.HB.BF$.FC2A.ADF!
TriVN-B12x2_S13 is the most interesting of the Bx2 rules I found in this neighborhood (but I didn't do an exhaustive search). It has long lived chaos that doesn't explode. There are many easily found rakes, puffers, and breeders.
Here's a dirty rake that which makes a funny alien structure over and over:

Code: Select all

x = 93, y = 70, rule = TriVN-B12x2_S13_emulated
27$21.2A$21.BGHA$21.HFCFA$22.GAGA$23.3A2$14.FHC$14.CBEC$15.C.C$15.CEA
32.3A$A14.C2HAFH18.F2HF7.GF2A$FA14.CGA2BC17.2FBDA3.A.B.D2FB$GA17.HFBA
16.F.2FBE2.GEH2BD2B$FA18.HDC16.F2HFBE2.BFC.CBH28.2B$GA13.2A3.HE3CECB
12.FH2FB.DBF.B.CH2.GC3AB20.BAB$B14.3A2.BD2.FBFAB12.2F.HDHGAEHAF3BAEB
2AGE.2A4.2H10.BGFA$A14.AFEDC.F3C.2FB13.FHCBH2.2F2.FCHA.A2.DE4A3.3H7.
2CB.HB$2A13.AG2HEC.2C.CBEB14.FHF2A6.3CFAGEH.2AB2A3.BH7.3CBE$2A14.ADGB
C5.GCGE14.2F9.2CF.GHEC.A2HA2B2.C4.2B2.FCFC$2A16.3C6.2GE18.3A.B3.2C2.H
D2EG2FAG.EFA2F2AHFB2.2F$2.2A15.2C7.FBF17.AGBEFB7.CBHCFA.ADEC2BCH.D.E$
2.GFA12.2C10.2G17.2A3HA8.C2HADBHB.AFBCHGHDGB$2.D.H12.2C30.GE2BF2E9.AG
3CF2AFG.EBEBE$2.A2GA11.2CBA2.A26.CBEHGBH10.G2A.2AG.F2E2FC$3.3A12.CABA
B2A10.B.B13.F4CF10.G2HA2.B.C.AG$17.FCBGHFHA10.BAGE4.2H7.2F.E11.GECF3.
B.H$18.FBFEGBA11.BAGHF2AB.H2A6.DGEH10.G.EC3.BE$13.2CA3.CGFBHA10.2CFA.
D.F2B2GBC5.BGEAE2CE6.AGFE$10.2A.FCGFADE.HEA11.AEHFG.B2EHBDFHE6.HAC.DF
C6.AGA$10.2AB.CA.H2FE2HAB10.GBEGAFHFA2.HBFE5.2C2.AGHFE$10.2AGCH2BG.GD
.F13.2G.AF.HEH.GB2C5.AC2.BHBDC$10.2AB.FH2.AB2A14.2AG.HE3CF.2A6.2A.2C.
F.C$10.GHD3BF.3B5.3C9.AGDHA2.F.2A8.G4C$8.C3HFGEGEH2.2H4.CE2C8.2CEHA
14.AE2.F$8.C2H2BF.HEG2ACF5.HA2E8.CGEF$9.C2HCBE.E3ADE2A3.CBF.E10.F$10.
2CEA2.BGC2.BFAB3.CFAGA$11.C2HB.FC2B.F.HGE4.4A$12.EG2BAFGHA.CH.E5.3A$A
11.BA.GHDHDHB.3C$.B11.2BHB2EBFCF6.2B.2B$CAB10.AG.BCHGH2F3.2A4FBAB$E
12.2A3F2.G2.2B.GFGHB.F2HB!
Here's the alien structure isolated so that it can grow without interfernece:

Code: Select all

x = 25, y = 25, rule = TriVN-B12x2_S13_emulated
2A$GFA$D.H$GFGA$.HBA17$20.AGFE$20.AGEBH$20.2AF.F$21.2A!
Last edited by EricG on September 10th, 2012, 1:11 am, edited 1 time in total.

EricG
Posts: 199
Joined: August 19th, 2011, 5:41 pm
Location: Chicago-area, USA

Re: Triangular & Tripod von Neuman neighborhoods

Post by EricG » September 10th, 2012, 12:24 am

For 2 state Tripod neighborhood rules, Weighted Life can be used, by giving weight to only the North, West, and SouthEast neighbors.
Here's a weightedlife->ruletree.py script: viewtopic.php?f=9&t=933#p6814
Here's a sample rulestring:
name=Tripod-B1_S23 NW0,NN1,NE0,WW1,ME0,EE0,SW0,SS0,SE1,HI0,RB1,RS2,RS3

I thought it was pretty interesting to compare and contrast B1/SV (B1/S in the 4 neighbor von Neuman rule) with Tripod-B1_S and with TriVN-B1_s. Tripod-B1/S looks a lot more like a three neighbor version of the von Neuman rule than the triangular von Neuman rule does.

For Bx2 rules, here's a script that takes a Bnnn/Snnn rule as input and generates a Bx2 rule. As a bonus, this script generates Bx2 rules in four different non-triangular neighborhoods. The default is the Moore neighborhood. Include a "T" for the tripod neighborhood ( for example, "B123/S13T" or "Tripod-B123/S13"), include an "H" for the six neighbor hexagonal neighborhood, and include a "V" or "N" for the von Neuman neighborhood.

Code: Select all

import golly
from glife.RuleTree import *

rulestring = golly.getstring('''Enter a Bnnn/Snnnn rule, and it will run as a Bx2 rule.  
The Moore neighborhood is the default. Include an H for the hexagonal neighorhood, 
include a V or N for the von Neuman neighborhood, and include a T for the Tripod neighborhood.''')

rulestring = rulestring.replace("/", "")
rulestring = rulestring.replace(" ", "")
rulestring = rulestring.upper()

if rulestring.count("H"):
   neighborhood = "Hex-"
elif rulestring.count("V") or rulestring.count("N"):
   neighborhood = "VN-"
elif rulestring.count("T"):
   neighborhood = "Tripod-"
else:
   neighborhood = ""

Brulestring = rulestring.split("S")[0]
Srulestring = rulestring.split("S")[1]

weight_lookup = {
                # NW,NN,NE,WW,EE,SW,SS,SE
  ""           : [1, 1, 1, 1, 1, 1, 1, 1],
  "Hex-"       : [1, 1, 0, 1, 1, 0, 1, 1],
  "VN-"        : [0, 1, 0, 1, 1, 0, 1, 0],
  "Tripod-"    : [0, 1, 0, 1, 0, 0, 0, 1]
 }

neighbor_lookup = {
  ""           : ["0","1","2","3","4","5","6","7","8"],
  "Hex-"       : ["0","1","2","3","4","5","6"],
  "VN-"        : ["0","1","2","3","4"],
  "Tripod-"    : ["0","1","2","3"],

 }

RB = []
RS = []
RB_canonical = ""
RS_canonical = "" 

for i in Brulestring:
    if i in neighbor_lookup[neighborhood]:
       RB.append(int(i))
       RB_canonical = RB_canonical + i

for i in Srulestring:
    if i in neighbor_lookup[neighborhood]:
       RS.append(int(i))
       RS_canonical = RS_canonical + i

name = neighborhood + "B" + RB_canonical + "x2_S" + RS_canonical

n_states = 3
n_neighbors = 8

def transition_function(a):
    NW_weight = weight_lookup[neighborhood][0]
    NN_weight = weight_lookup[neighborhood][1]
    NE_weight = weight_lookup[neighborhood][2]
    WW_weight = weight_lookup[neighborhood][3]
    EE_weight = weight_lookup[neighborhood][4]
    SW_weight = weight_lookup[neighborhood][5]
    SS_weight = weight_lookup[neighborhood][6]
    SE_weight = weight_lookup[neighborhood][7]

    # As specified in glife.RuleTree, a's order for the cell "C" and its
    # 8 neighbors is:  NW, NE, SW, SE, N, W, E, S, C

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

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

    if a[8] == 1 and n in RB:
        return 2
         
    if  a[8] == 2 and n in RS:
        return 2 
      
    return 0


golly.show("Please wait while ruletree 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" )
   golly.setalgo("RuleTree")   # in case name.table exists
   golly.setrule(name)
   golly.show("Created "+name+".tree in "+golly.getdir("rules"))
   
except:
   import sys
   import traceback
   exception, msg, tb = sys.exc_info()
   golly.warn(\
'''There was an error.'''+ '\n'.join(traceback.format_exception(exception, msg, tb)))
   golly.exit()
Tripod-B12x2_S1 and Tripod-B12x2_S13 both have spaceships, but the best Tripod rule I've found is Tripod-B123x2_S13

Spaceships have a triangular nature:

Code: Select all

x = 54, y = 22, rule = Tripod-B123x2_S13
A.A$.BA2B$BA3B.B$.2B.2A.A18.2A$.B2.B.A20.3B4.A$2.2ABA.B19.A.A.B4.A$4.
A.BA20.B.A4.A2.A$3.A2BA.BA18.AB.A3.B.A2.A$6.B2A.B19.A2.A3.A.A2.A$5.B.
B.BA18.B2.A3.2BAB.A2.A$7.3B2.B5.A4.A.A5.B5.4BA.A.B$6.3B3.A2B5.A4.A.B
2.B6.2ABA.A2.A.B$7.A2.B.A.B.B2.A2.A.2A.BA9.3BA2.A.BABA$9.B.4BA.2B2.A
2.AB2.B.A8.B.2BA2.A.3B$11.B.2A2.B2.A2.A.A2B.A9.2B.A2.A2.A4B$10.B.BAB.
A.BA2.A3.B.A11.BA2.A.2AB.AB$12.BA4BA.2A8.A9.A4.A4.4B$13.B2.A.BA9.A2.A
14.2A.2AB$14.BA2BA12.A14.A2.B.B$14.2B2.A11.A17.A.B$17.A29.A$16.A!
Many of the spaceships are vast, as they very slowly fail to become puffers.
What looks like a breeder turns out to be a rake.

Code: Select all

x = 1584, y = 1679, rule = Tripod-B123x2_S13
196.BA$191.B4.B2.A$193.B.B2.A.BA$192.B2.2BA2BA$194.B.2B.BA$193.2B.2BA
B$194.ABA.B2.B.2B$195.4B.B2.4B5.BA2.A$195.A.B2A2.B3.BA5.4B.A$197.AB.
2A2.2BA2.A3.3B.BABA$199.2B2.B.ABAB3.A.BA.2BA.B$198.2A.2B3.A2.2B.A.A.B
A3B$199.3BA2.A2.ABA3.ABA.B.BA$199.AB.2BA2.A.B3.A.3BA.BA272.A$200.2B.A
2.A.BA4.2BA.B2.B.A272.A2.A84.B$201.BA5.A5.4ABA.2A.BA165.A103.A.2B.BA
84.B$203.BA2.A8.2BA2B3.B167.BA101.3B.A3BA81.B2.B$202.BA2.B8.3A.A2BABA
167.AB.A7.B92.2BA2.A3B81.2B.A$203.BA2.2B11.B.AB164.A7.BA4.BA.B90.BA2.
B.B2.2B.A73.A3.3B2.A$203.A.B.B.2B7.A.A4BA163.BA2.A.ABA5.B.A90.2A.B.B
2.AB.A2.A72.BA4.AB.BA$205.A.2BA10.A3.A164.AB.A.B.2BA2.A.A.A.A87.A.B.A
5B.2ABA2.A68.B.A2.A3B2A2BA$204.A.BA.BA8.B.BAB2.A163.B3.A2BA.BA2.2B.B
2.A84.2ABAB2.3BABA2.2BA71.3B.3BAB.A.BA$205.BA2.A10.BA2.BA164.ABA2.BA
2.2A.A2.A.BAB89.A2B2.3B.2BA71.B2.B.3BA.3BA$205.A.BA11.B.2BA165.2B.3B.
BA2B.A.B.BA3.A83.3A.ABA.3B2.BA71.B2.BAB2.A2B2.A$207.A13.AB169.B3.B.3B
2A.A.2A.2A2.A83.4BABA.B2AB.BA70.2B3.3A2B.A$206.A184.2B.BA.3B.A3.B.B.A
B.AB82.A.BA.2B.4B.BA71.2B.3A.2B2A$392.2B4.B.A.2B2.B.3B.2B.BA.B79.2BA.
AB.BA.BA51.A21.6BABA59.B4.A$314.A77.B5.B2A5B.BA3B.B.6B76.A.A2B.B2AB.B
.B2.A42.A6.A19.2B.3BAB60.A2B.2B.A$316.A82.2B2.A2.4BAB2AB.B2A2B.A76.BA
BAB.BABA3.B.BA41.BA3.3BA18.2A.2A.B61.2B.2B.ABA$314.2A2.A2.A77.2BAB.BA
.B.2BAB2.B.A.BAB.B74.2A2.2B.A.B3.B2.A.BA39.A.BA2.B.BA17.B.A2.2B.B46.A
4.A2.A4.B2A.B.B2.BA15.B$316.2B2.A2.A71.A2.A.2B2AB4.B2.B2.A2B.AB.B.B.A
74.4A3B3.2AB.BA.BA39.A2.A2B2AB17.3B2A.BA.B46.A4.A2BA4.ABA3B2.A.B15.B$
315.2AB.B2.BA.A71.A.2BA2.A.A4.3B.3B.A2.ABA.B.A70.A3B.B.2B.B2.2B.A2.A.
BA36.A4B2A.3BA15.B2.3B3.A45.A2.A.B3.3B3.BAB2ABA2.A2B2.A3.B.B2.4AB$
316.4B.A.2BA70.A2.A.ABAB2ABA5.B.3B.AB.A2BA.ABA73.B2A2B.A.ABA2.A.2B40.
A3BA2BA18.2B2.2BA48.B3.B2A.BA.4ABA4.A.4B.BAB2.B.B3.4B$313.A2.ABAB.B.
4BA70.A.B.BAB.2B.B2.BAB.A3.A3BAB.B3.B69.BABABABABABA5B.B39.A.A2BA2.2A
17.B3.B2.A47.A2.B.B.2B3.B2.2BA.A.2B.3A.2A.3B2.A3B.AB$315.A6.BABAB67.A
2.BA.B.A2BA.AB2.B3.BA2BAB2.A2.A.B2A.BA67.A.A.B.A2.A2B.A.2AB2.B38.B.BA
6.A18.A2.A50.ABA3BA2B.ABA.ABA.B2ABA3BA.2BA.BA2B.AB.2B$237.B.A74.B2.A.
4B.2B2AB66.B2A.BABAB.2AB2A2.4BA2B.2BA2.4B3.A69.BAB2A.BA2.BA2.B.5B38.B
A2.A3.A2.A18.A50.AB2.2BA.4B.BA.2BAB2.2B2.B.2A4B.B.A.BAB$239.A.A73.AB
4.B3.5BA64.A3BA.2BA.A.ABAB2.B2A.2BA.B.B.A2B.BA2BA68.A.B.B2A2.B2.BABA.
BAB39.A.BA2.A3.A.BA68.B.BAB.2A2.A2B.2BA3.2B.A2B3.B.A.B.A2.A4B$238.B.A
B.A73.AB.ABABA.B2.A67.BA.BA.2B.B2.B3AB2.B.B.A.4B.A2BABA.BA68.BA.A2.A
2.BA.A.B.B41.BA.A3.3ABA.A67.A3B2.A.2B.B2AB.A2B.ABAB.B.BAB2.A.A.6B$
238.3A2.A72.B.2B.BA.B.ABA67.A2.3B2.BA.2ABA.B.BA.B2A.2B2.B.BAB3.BA46.A
2.A18.AB2.A2B2.A2.A2.2A38.BA4.B2.AB2.B.2B2.A66.BA.BA.2B2.A3.B.B.A.2B
2.A.A.2B3.A.ABA.B$241.BA2.A71.BAB.B2.A2BA69.2B2.A3B.B.BA2.A2.B.A3BAB.
AB2A2.B3A44.B3.2B.2BA8.B7.B.A.B2.A47.B.A.B2.A.BA2B2A2.A2.A64.A2.B.B2A
.A2.AB.A2.3BA2BAB2.6BA.A.B$239.2AB.BA2.A69.2BA2B.B2.A70.2A4B.AB.BA.AB
A3BA.B.A.2BA.A.A.A.B.A44.2B2A.AB.2BA5.A.2B5.A3B2.A48.2B2.A.B4.5B2A.A
2.A66.BA2B.A7.B.BAB.B.2ABA.A.BA3.B$241.2ABA.A2.A68.A2.B.5B71.B2A.2B.A
BA2B.2BA.B.2A.ABA3B.2BAB2.ABA42.3B.BAB.AB2.A5.B.AB4.BA54.AB.BA.B.ABAB
A3B.B.A67.A2.BA10.2B2.AB2.A.A$240.2A2B.A2.A70.2B.2B2.A.A69.A2.3B.4B3.
A3B3.BA.3B.B.2A3BA2B.B44.4B.BA.A2.A2.A2.A3B2.A54.B.2A3B2.BAB3.B2.2B
69.B2A12.B2.B$243.B.A.A72.A2B.3BA72.BA3.2BA.B2A.BA4.A.A2B.B3A.A2B.B.B
2.A40.A.AB2.ABABABA2BA2.A2.BA58.2B.2B2.B2.2BA.BA2B73.B11.A2B$241.A3B.
A73.4B.BA2.A69.A8.BA11.BAB.A.B.BA2BA.2ABA42.A.2BAB2.3B.B.B.B.2BA.B57.
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A.4B1034.A5.A2.2BABA$22.BA.B2.BA2.3A2.A1034.A5.ABA.A.BA$19.3A.A.A2BA
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BA.A.BA.B1032.2A2B3.B3.2BA.BABABAB$25.B.A2.A2.A2.BA2.A.BA1031.A2.A4.
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A.A2B2.A11.B.B$1069.3BA2BA9.A.B$74.A993.B2.BABA.3B8.A2B$74.A.A993.B.B
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BA3B1007.BA.A2B$75.B.AB1007.B.B.AB.B$62.A3.B9.A1011.2BAB.A.B$64.A2.2B
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397.5B599.2BA2.B.A$65.A.3B.A.A5.B.B.AB2.A.2B396.BA2B.B598.2B2A2BABA$
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A.3B3.A395.2B.A.BA600.ABA.B$68.AB3.2BA4.A.2B.5B.B2.A393.B4.A604.B$71.
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A.B2.A963.3B$73.A.BA6.B2A2.AB4.ABAB.3BA2.A.A2.A961.A4B$72.A2.A6.A.A2B
A.BA4.6BA2.ABA2BA963.B.B3.A$74.A9.B2.ABA5.A2.2B3.2A2.B2.BA961.3B.BA2.
A$73.A9.A.B.BA9.2B2A.4B3ABA963.ABA.BA$85.ABA2.A9.B.2B3A.B.A.BA.A958.B
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955.A.2A$90.A2.A6.A5.BA.3B2.2BA.A2.A953.B4.A$89.A2.A12.2B.A2.B2A.A.BA
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A.5BA2B$109.BA.2B.BA2BA2.A954.B2.BA3B4.2B$112.3ABA.A2.A2.A954.BA3BAB
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954.2BABA.2B$116.AB.B4.2A954.B.5BABAB$115.A7.A2.A3.A951.B2.B.5BA$125.
A2BA3.A948.BA2.3BAB.A$124.2A4B.A2.A949.A2.B.BA$127.3BAB.A2.A946.A5.A$
125.3A2BA2BABA952.A$127.BABA4B.B947.A$126.2A.3B.A.BA.B947.A$127.2B2AB
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2BA.BA945.2B2.A$128.AB2AB2.B.A2.A941.A.B.AB$127.A.A.BA.2BA2.A944.2BA
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943.BA4B.A$130.A.5B944.ABA3.B$132.BA5B938.A3.3B2AB$131.A.AB2.B941.2A.
2BA$132.B.BAB941.A2.3B.B$1080.BA3B$1079.A2.3B$1081.B.BA$1080.A2.A$
1081.2BA$1082.2B.B$1082.2BA.2B$1083.4B$1083.B.B7$165.A$167.2AB$165.2B
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10.B.B.2B2A2.B$136.A2.A.B6.A.BABA10.B.AB3.B$137.BA.B2AB3.A2.5BA3.A3.B
2A2.B2A.B$137.B.2B3.2B2.B.2A3.B5.2A.B.BA.B.A2.A$137.A.A2.ABA4.BAB.AB
4.BA2.BA.A.B.A2.A.A$132.A.A6.2BA5.2BA.ABA5.B2A.AB.A3.A4.A$134.ABA.B3.
4B4.B.AB.BA3.3A.A3.2B.A4.A2.A$133.A.2B.2ABA2B.A5.A.A.2AB2.2BABA.A.A.B
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2BA2.ABAB5.A6B.A.BA3B.4B.BA.A.BA2B.A$135.BABAB.3B10.2BABA2.2AB3A.3BAB
A.ABA2.BA.B$137.A.4BA8.A4BA.B.A2.3B.A3.B2.B.A.ABAB$139.2AB.B9.2B3.B2.
B.AB2.2B.AB2.AB.2B.BA3B$138.A.BABA9.A3.A2.B.A.3B.3BA.B2A.3BA.ABA$140.
A2.B15.A5.B2.BAB.B2.B2.3BA.2B$141.2B21.A2.B.2B.2A2BAB.3B.B2.B$141.A
21.A.B2ABA.A.2BA.AB2A2.A.B348.B$165.A.A3B.2AB.2B.2B.A2.A349.2B$164.A
2.3B.A2.A.A.5ABA349.5B$166.ABA.A2.A.2BA.3BA.B.A348.BA2B.B$164.2A.A2B
2.A.BA2.BA.B.B.A.B347.B2.ABA.B$166.A2.3B.BA.2BA2.2B.B.3BA346.2B.A.BA$
165.A2.A.A2.A2.B2.BA2.AB2.B.2B345.B4.A$167.A.B.B2ABAB2.A2.A2.A2BAB
350.A$166.A3.BA.2BA2.B4.2B2.2B2.A$170.2A2BA.2B5.A3.B3.ABA$173.A2.B15.
B.2BA$171.2A2.A16.2A.B2.A$173.BA14.A2.A.A.BA.BA$173.A16.BA.4B2.A$188.
A.AB.A.BABA$190.A2.2BA$189.A2.BABABA$191.A2BAB.2BA$190.A.2BA2.BA2.A$
192.A.B2.A.BA$191.A2.3B.B2.B$193.A.BAB2.B$192.A2.A3.B$194.A3.B16$209.
A.B$211.A2B$210.A.B2.B$212.2A2.A$211.A2.AB.B$213.B.2B.A$212.A2.B.BABA
$216.2BAB.BA$216.B.A2.A2.A$217.BABA.BA2.A$217.A2.2BA2BA2.A$216.A.2ABA
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B$217.A.B.A.2BA5B$217.AB.B2.B.2B.2A.B$218.B.B.A.2AB.2A4B$218.A3B2.7BA
2.2B$219.BA.AB3.2B.A4.A$219.A2.B.4B2.B.ABA$223.BA3.B2.2A.A.A$223.2B.
2A2B.BAB.B$224.B.A2.2BA.2B2.A$224.3BA.A2.AB.BA.B$225.BA4.A2.3AB.A$
225.A5.ABA3.2B2.A$233.B.2ABA.A$232.2BA3B6.A6.B$233.ABABA.B3.A2.B2.A3.
B$234.A2.2BA.2B2.B2.B.BAB2.B$235.BABA.2B2.B2.2B.B.B.B2.B$235.AB2.2B2.
4B.A.B.2ABAB$238.2A2.BA2.4BA.BA2BA.A$237.A2.2AB.4B.A.B.A.4BA$239.A2.A
BA.2B4.B.B3.A.BA$241.A.A2.AB.B3.3B2.B.A$240.A4.BAB.2BA.A.ABABA$243.B.
B.BABA4.BA2.A11.A$245.A2B.2B6.BA13.BA$244.A.B.2B6.BA14.A.2BA$247.2A2B
23.A.A.A$251.A21.A.B.3BA$248.2AB.A21.BABA.3BA$251.B18.B3.2BA.3AB$269.
A2.B4.B2.BA$268.A2.B.A3BA2BA.BA$269.2B.AB.3B2.ABA$269.AB.B.BA2BAB.B$
269.AB.2BABA.B.B$268.BA.B.A.A.2BA.BA$271.AB.A.B.A.BA3B$269.B2ABA5.B2A
B.A$270.A.2B.A3.A.2B.2B$271.B3A.B4.ABAB$271.4BA3B3.B$272.B.A4.BAB300.
B$272.BA2.A.3B.2B299.2B$275.B.AB.A.4B296.5B$274.A.ABA7B297.BA2B.B$
276.B2.A.BA.BA297.B2.ABA.B$275.A2.B2.A2.A299.2B.A.BA$277.B2.A2.A300.B
4.A$279.A308.A14$282.A$284.B$283.A2.B$283.A.B$282.A2.A.B$283.BA2.A.BA
$281.A.A.BA.B.3B.A$283.ABA.B2.B.A.B.A$282.A2.2B2.B.A.BA.A.A$284.AB5.
2BA.B.3BA$283.A9.BA.2A.A.B$291.AB2.A2.A.A$291.A2BA.AB2.B$290.B.B2.A2.
2A2.A$291.2B2AB.2A2.A$291.B.2A.3B.B2.A$292.B.2B.BA4B2.2AB$293.BA2BA.
2A2.2B4.B$293.A.B2.A2.BABA.2AB.AB$294.B2.A2.B2.3BA.BABA.A$299.B.2B2A
2B.B.A.A2.A$300.BA.A.B.B2A3B.A$300.B.A.BAB2.2B.AB$301.2B.A.B.BABA$
303.BAB2.2A2BA$302.2B.A.A.2B.2B$304.B2.A.A.AB$303.B2.B2A.2BA$305.B2.
2B3.B$307.B3AB.BA$311.3BA.A$310.3A2.B2.A$311.2BA.3B2.A$311.A.3BABAB$
312.BABABA3BA$314.B.A2.2BA.A$313.BAB2.BA2B.A$316.B2ABA.A2.A$315.A2.6B
A$316.5BABA2.A$317.2B.B.BABA$317.3B.A3B.B$318.B2.B.3B2.A$320.B2.2A2.A
$319.A2.B3.A$321.B3.A$356.A$346.AB6.A2.BA$348.2BA5.2A.BA$347.2A.2BA2.
A.5BA$349.2A.A4.ABA2.2BA$348.A3B2.A.A3.BABA$351.B2.BA2.A2BA.A$349.2A
3BA2.A.BA.A.BA$350.B.2B2.A2.A.4B$352.2A2B2.A2.A.BA.B$351.A.B3.B2.A2.A
2.A$353.A2B.BAB4.4B$355.A3B2.B2.B.3B$354.A2.A.2B2.BABA2BA$355.BA.BA2.
B.A2BA2.BA$355.A5.A2.3B2.AB$360.A5.A.A$365.B.A$366.2B$366.B4$366.A$
365.A2.B$367.A2.B$363.A2.A2.B2.B$365.B2.A.BA2.B$364.BA.B2.2B2A$366.BA
.B.A2B256.B$365.BA.BA.B2.2B255.2B$368.A6.A254.5B$372.2BA256.BA2B.B$
370.A2.A2.A254.B2.ABA.B$371.BA2.A2.A253.2B.A.BA$370.2A.B.2BA2.A251.B
4.A$372.BAB.B.BA256.A$371.BA.A2BA.ABA$369.BA2.BAB.AB.A.B$370.3B4.ABA
2BA.A$370.B.A.2BA.AB.B.B$372.2BA.A.A3B.2B$371.B.B2.2B.BA.2BA.A2.A$
372.A.BA.B.A.BA.B3.B2.A$370.2ABA.5BABA3B.ABAB2.A$371.2B.B2.B.A.B2.A.
5B.B2.A$368.A2.A.A.2BA.2A.AB.2BA3.B.2B2.A$370.A2.BAB3.6B2AB.BA2BAB.B$
369.A2.A.A2.BA.ABA.BA3.BA.2B.BA$371.A.4B3.2BA2BA2B2A2.2A.A$370.A2.2AB
2.BA.3BABA.4B3.A$372.A.B2.B2.BA.A.B.A.A.B.2A.BA$371.AB3.B2.A2.A3.2ABA
B.BA.BA.B$374.BA5.A5.2B.A.A2.A2.A$373.B2.B3.A7.BA.3BA2.A$375.B2.B9.A
2.2A2B.A$374.B2.B12.A.BABA$376.B14.2A.2A$375.B20.BA$396.A2BA$396.2B.B
.A$396.A.A.BABA$395.A3.2A4.A$395.B.A2B.6B$386.A2.A6.3B2A.3B.A$387.BA.
BA4.BA2B.3B2A.A$387.B2.A.BA3.A2BA.A.2BA$386.B.BAB.A2.A.B.B.4BA$387.3B
A.A2BA.A.BAB.A$387.2B.BA3BABA2BA.A2.A$386.B4.2B.2BA.A.BA2.A$384.2B2.
3B.A2BA.A.2B.2A$384.A2BA.AB.B.B2.A.2BA.A$385.2BA6B.BA.BA2.A$385.AB.3B
.BAB.B.A2.A$386.4BAB.B2.A2.BA8.A$386.3BA.2B2.B.2B.B9.BA$386.A2B2.A2.B
3.2B10.A.BA$387.3BA2.B4.A2.B8.2BA2.A$387.A.4B2.B.A2.A2.B6.A.B.B2.A$
389.BABA.B4.A2.B2.B5.BA.A.B$388.A2.A.BA3.A2.A2.B2.A3.A.2B.A$393.A6.A
2.A2.A6.A3B$392.A6.2A.A2.A.BA5.3BA26.B$401.BABA2.A2B2.B2.A2B28.B$400.
A3B.2A.A2.B2.BA.2BA25.B.AB$402.ABA4.BA.2A3.BA26.B.2B.B$403.A.B3.B2.B.
6B18.A2.A5.A2.BA$404.A6.B.BA.A3B18.B.A2.A2.B.ABA2.A$412.B.2BAB.A19.BA
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20.AB.2BA2B$416.2BA23.2BA.B$417.A24.BA2B2A$444.2BA.2B$443.3B.BAB$440.
A4.2B.4B$440.3BA2.2A.A.B.B$441.4B2A.B.B.BA.B$441.BA.A.2B4ABABA$442.AB
ABA2B.3B.A$442.3BA2.B2.B.A$443.BA3.BAB.BA$443.A7.BAB.A$450.A.2B.BA$
452.ABABAB$451.2A4B2.B$452.2BAB2.B$452.A3B.B$453.2A2B.A$456.BA2.A$
454.2A.B.A$455.B.BA$455.ABA$456.A10$678.B$679.2B$678.5B$463.A215.BA2B
.B$461.A2.BA213.B2.ABA.B$463.A3BA212.2B.A.BA$462.A.B2.2BA3.A206.B4.A$
464.A2B.A.BA2.BA208.A$463.A.BA2.BA3.A2BA$465.A2.BA7.B.A$459.B7.A2.A4.
A.3A$461.B4.A2.A6.B.B.BAB$458.A.B.BA4.2A.B2.A.2A4BA.B$460.A2B.A3.A.BA
4.A.B.BA2.A$459.A.2BA2.A2.B2ABA.BABA.B.BA$461.2A.BA2.A3B.2BA.BAB2.A$
460.A2.B.4B.A4B.A3B.B$463.A.B.B2.BA.B3.A3B$462.A.B2A.2BA2.A4.2B$464.
2B.B2A2.A5.A$462.BA2.BA2.BA$464.2BA2.2A.B17.B$463.BA2.B2A2B2.A15.A.B$
465.BAB2.2B.A17.B2AB$464.BA2.3BAB.B16.B3.BA$466.3BA.BA.ABA15.BABA$
465.BA.B2.A.A.B.B14.B.2B$467.B2AB.A2.ABA.B13.2B$466.B3.B.A.A.B.2B13.B
$469.ABABA.BA.B$474.BA.BA$471.BA2.B.A$461.BA7.5B2A$462.B.A6.B.2B$462.
2B.BA4.A2B$464.ABA.A.2A.A$463.B.A.BA.AB.B.A$464.A2.2B2AB.2A.BA$467.2A
2B.AB2.B$464.A2.2B.2BA2B.3B$466.BA2BA.A.BA.A.BA$465.A3.3B.BABA.BA$
467.2B2.2BA.B.BA2.A$470.2BA2.2AB2.A$469.B.A2.A4.A$476.A.A$475.A42$
893.B$895.B$894.2ABA$894.2B.2B$890.A2.B.B.B$892.2A.BA$891.A3.ABA$892.
B2A.2B.A$726.B165.B.BA.4BA$727.2B163.A.2A3B.A2.AB$726.5B162.2BAB.B.2B
A3.B$727.BA2B.B160.2A4BAB3.2B2.B$727.B2.ABA.B159.2B.2ABA2.A2.2B2.B$
728.2B.A.BA159.A.2A3.2B2.BA2.B$728.B4.A163.A.BA2B.B2.AB$732.A162.A3BA
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A$903.A.A4BA2.A$901.A3.BA2BA.2A$903.2B.BA.B3.B$902.B3.A.B3.A$907.B30$
899.A$895.2B4.A$897.2B.A2.A$896.BAB3.B2.A$894.A2.BA2B2A.B$896.BA2.B.
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2B$900.2B.A.3BA$897.A2BA.B2A5BA$900.BA2.3B2.A$898.2AB2.AB2A2B$899.BA.
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B2.B$887.A6.B$888.2B5.A$888.A3B3.A.A$774.B114.B.B2.A.BAB$775.2B112.AB
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112.A2.BABA.A$776.2B.A.BA111.A2.3ABAB$776.B4.A114.A4.B$780.A114.A3.AB
40$877.A7.A$879.2A5.BA$878.A.2BA3.A2BA$880.A.A.A2.4BA$879.B2.B2AB3ABA
.BA$879.A.3B2.2BA.B.B$881.AB.2ABABA2B$880.A2.A3.4B$882.A2.BAB2A$881.A
2.A2.A$883.A$882.A29$885.B$881.B2.B2.B$883.B2.B$882.B2.A$884.B.BA$
883.B2.2B.A$889.2B$886.A3B$888.A$822.B64.A2.A$823.2B55.A2.A5.A$822.5B
55.B2.A2.A$823.BA2B.B52.A.2B2.A$823.B2.ABA.B51.2B.2B.A$824.2B.A.BA51.
AB.A.A2.A$824.B4.A53.B.2BABAB$828.A42.A10.A.3B.5BA$873.A2.AB6.AB.AB.A
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875.A.BA13.A$877.A22$878.B$877.2A2B$878.B2.BA$878.ABA.ABA$879.B.2BA.B
A$877.2A2.2A.2BA.A$878.2BA.B.B2.2B$878.A.A.A2B.2BA.B$879.B.A2B.A3.BA$
879.A2BA.B2.ABA.B$881.A.B2.A2.2B$880.A.B2.A.B2A.2B$887.AB2AB$888.B.B$
889.A31$877.A$879.A$878.A2.A$879.B2A$879.A.2BA$878.BABA3B$878.A2BA2B$
879.B.BA$879.B2A2.A$870.B12.B2.A$869.B2.B7.3B.ABA2.B$869.A.B2.A6.ABA.
BA2B.2B$871.ABA5.B2.BA5BA3B$870.3B.B5.2BA.BA.BA2.2B.B$871.3B2.A3.B.A.
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A$873.B.B2.A7.AB.B.BA2.A2.A.B$873.A3BA7.A.BA.BA2BA2.A.BABA$874.B12.A
2.2BA.A.A2.A2.2B$886.A2.A.2BA.A4.BAB2.A$891.BA.B2.A2.B.3B$893.B2.A2.B
2.2BA$895.A2.A2.B.A2.A$894.A2.A2.B2.B4.A$896.A5.B4.A$895.A5.A27$869.A
$867.A3.BA$869.2BA2.A$868.A2.B.B2.A$870.BA.3BA.A15.A$869.A2.A.B.A2B.A
14.BA$871.AB.B.3B.A.A2.A7.A.A.BA$870.A.2B.2B2AB.A4.BA7.2BA.BA$872.A2B
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A5.A4.BAB2A.BA2B$872.B3ABA.2BA.2BA.A4.4B2.A2.2BA$871.AB.2BA2.B2.A2B.B
A5.BA2.B.BA.AB.A$874.B.2BA.2B.B2.BA5.B2.2B.A7B$872.2A4B2.ABABA.2B.A2.
2A.BAB.5B2A$873.BA.B2.A3.B.ABA2.BA.3B2.AB.B2.2B$873.A.B7.AB.4B3.A2.A
5B.ABA$874.B10.2AB.BA5B2A2.2BA.A$885.2B.B.B2ABA3B.A2BA$889.B.B.A.BA.A
.BA2.A$886.BA2B.A.B.A4.A.BA$888.ABA.B2.B6.A.B$887.A.B4.B8.B$891.A.B$
890.A23$863.AB$860.A3.B.B$862.B.AB.2B$861.A2.3B.3B$862.2BA.B2.A2.A$
862.A3.6B.BAB$863.BA.2BAB2.2A.3B$865.A.A.A2B.B.B.2B$864.A.B.BA2BA2.AB
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4B.B.2B2.B.A.A$875.A2.BA4.BA.BA3B.B2.2BA.A$877.B2A3B.A2B2.3B.A.BA.2BA
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3B.2A.A2B.A2.BA$883.2A.2BAB.A4.BA.B.2BA$885.B2A.BA3.A2BA.3A.2BA$889.A
5.2A.B.2B.A2B$888.A10.BAB.2B$901.BAB$901.A2.A$903.A$902.A22$876.A$
877.2B$877.A.AB$874.A.2AB2.2B$875.4B3A.A$875.AB2.B.2B$876.B.A.BA2.B$
876.AB2.AB.B2.A$878.2A2.BA.B$875.A2.B.2BA.A.AB$877.A.BA.B.2BA.2B$876.
A2.A2.2B2.3B$878.A2.A.2A.A$877.B2.A4.3BA2.AB$879.B2.A2.2BA2.A3.B$878.
B.2B.BA4.A2.2A.BA$880.2B.2B2ABABA.B.BA$879.B3.B2.AB.A.B2.B2.B$879.BA
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882.B2.BAB.A.A.2B4.A$880.2A.2B2.BA4.ABABA.2B$882.A2.2BA.BA3.B.AB2.A$
884.BA2.BA5.A.ABA$883.A3.BA9.A$886.A3$867.A$869.A$868.A$869.B$871.B$
870.A10$871.A$873.AB$872.A3.B$867.A6.2A.AB$869.A.A.B2.AB2.B$868.A3.BA
.A.A2B$870.A.B.2BA.4B$869.A3.B2.B.2ABA$871.A3.2B2.BA2.A$870.A2.2BAB.
2BA.A$865.A5.B.A2.2BA2B.A$866.BA.B.A.3B2.3BA.B$866.A6BA2BA2B.B.B$867.
B.AB.BA2BAB2.AB.A$866.BABA.AB.A3.BA2.B.B$867.3B.B.A3BA.A.AB3A$867.B.A
2B2A2BA2BABAB.B.2B$869.7B.A2B.A.A.AB$868.A2B2A.A.2BABA.4BA.B$869.B3.
2A.BA2.A.A.A.ABA$872.A2.BA2.A2.ABA2BA$875.BA.A.2B2.2B2A.B$876.ABABA4.
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2.A.A.AB.2BA$879.A2.A.B.BA3.B$881.A2.A.BAB.B$865.A14.A2.A.B3.B$867.A
14.A2B2.AB$863.A2.B2.A11.AB2.BA$865.B2.B.B13.BA$864.A2.B2.A.A10.B$
866.B2.A.BABA$865.2A.A2.B.B.BA$863.A2.2BABA.2ABA$865.2AB.B2.B.2B$864.
A2.BAB3.2B$866.2A2.5B.A$865.A2.2B2.BABA.B$868.A2.BA3.B$873.BAB$856.A
15.BA$855.A2.A$857.A10.A$856.A13.A$869.B2.BA$856.A3.A10.B2.BA$858.A.A
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858.A.B.BA2.AB2.B.A2B.A$857.A2.ABA2B2A4BA2.A3B$859.A.3B.2A2.A2B2.BAB.
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A4B$861.A3.A2B2.B6.A.3B$863.2A.B2.B8.BAB$865.A2.B6.A2.A$867.B.2B5.BA$
866.A2.B.AB3.A.BA$850.B5.B11.B.A.A.BA.BA.BA$852.B5.B8.A2.B2.4B2ABA.B$
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3B2.2AB$863.A.B.BAB.B.BA$863.2BA.A.A.2B.B$866.3B.4B$864.2B2.3B.B$864.
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853.A2.A14.B2.B$855.A2.A13.2B$854.A2.A14.B$851.A4.A$850.A.B3A2.A$851.
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A.A2.BA.A.2B$851.B.A2.BA.2B.B$851.A2BABA.B.B.A$853.A4BA.2A2.A.B$852.A
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2BA2B.A.A$855.3B2.B2.4B3ABA$856.2BA3B2ABA3.A2.B$856.B2.AB3.BAB2A.AB2.
B$858.3BAB2A2.2B.AB.A.A$863.5B2AB.B.A2.A$860.B.B.BA.A2.AB2A.BA$861.AB
.B.B.2B.A.2BA$862.2B2.B.B.3B2.A$862.A.BA.A.2B3.A2.A$864.4B.A.2B3.A$
863.A.2BA.3B3.A$864.B2A.BAB$864.A.B.A$865.BAB2.A$865.A2.2A.BA$867.BA.
BA$866.2A.BA$869.A3.B$867.2A6.B$874.B2.A$874.2AB$876.2B$875.2A20$857.
B4.A$858.2B4.B$858.2B.B.B2.B$860.B.BA2B2.B$859.2B.2BA.AB$857.A.3BA2BA
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2.BA.B4.A$859.2BA2BA2BA2.A$859.2A.2B2.AB$862.A2.A3.B$860.2A.BABA.B$
863.AB2.BA.B$866.BA.BAB$865.B.ABA.3B$867.A.2BA3BA$866.2A.BA.BAB2.A$
868.3B.A.A.A$868.2B.3BA2B$871.B.A.ABA$870.3A2.B.2BA$867.A.B2.3B.B.B$
860.A8.A.BA.B.AB$862.A5.A.BA.BA.B$861.2A.A5.A.BA.B$864.A4.A2.AB.A$
862.ABABA4.A3.B.BA$865.2B.A5.B2.A.BA$861.A.A.ABA.A6.B2.A$862.BA.2ABA
8.BA$862.A.B2A2BA$864.A2B.A2.A$863.A.2BA2.A$864.B2A2.A$864.A5$873.B$
866.B5.B2.A$867.2B5.A2.A$867.4B2.A2.A$866.B.A.BA3.A$868.4B.BA$866.2B.
AB.A.A$867.4BA.BABA$867.2B2AB.2BA.B$868.A3.BA2.B$872.B.2B$872.A2B$
870.A2.BA$871.BAB2.A$870.BAB.2B$868.A.A3B.A$869.BAB.BA$869.A2.A.B$
871.A2.B$870.A.BA.AB$871.2B.A3.B$872.B.B.AB2.B$872.AB.2A.2B$873.4B.B$
873.A.A2B$876.A!
Last edited by EricG on September 10th, 2012, 2:10 am, edited 3 times in total.

EricG
Posts: 199
Joined: August 19th, 2011, 5:41 pm
Location: Chicago-area, USA

Re: Triangular & Tripod von Neuman neighborhoods

Post by EricG » September 10th, 2012, 1:01 am

Two state Tri6inner neighborhood rules with B2 often have spaceships, but the rules are explosive.

I haven't tried using decay states, but Tri6inner Generations rules may be worth looking at. (For that matter, regular Triangular Moore neighborhood Generations rules might be good to look at too.)

So, lets try the Bx2 trick once again. Bx2 rules in the Tri6inner neighborhood can be created with this script (and the following script can also be modified to produce two state rules).

Code: Select all

# Tri6inner-Bx2-gen.py
import golly

rulestring = golly.getstring("Enter a Bnnn/Snnnn rule, and it will run as a Bx2 rule in the Tri6inner neighborhood.")
rulestring = rulestring.replace("/", "")
rulestring = rulestring.replace(" ", "")
rulestring = rulestring.upper()

Brulestring = rulestring.split("S")[0]
Srulestring = rulestring.split("S")[1]

rule_name = "Tri6Inner-" + Brulestring + "x2_S" + Srulestring
filename = golly.getdir("rules")+rule_name+".table"
f = open(filename, "w")
f.write("n_states:3"+"\n")
f.write("neighborhood:triangularMoore"+"\n")
f.write("symmetries:rotate"+"\n")
f.write('''

# The following diagram is from EmulateTriangular.py by The Golly Gang
#  (Not sure which individual to credit)


# triangularMoore -> Moore:
#
#      lower         upper 
#    +--+--+--+    +--+--+--+       
#    |\B|\ |\ |    |\6|\7|\ |       where A=10, B=11, C=12
#    |A\|C\| \|    |5\|2\|8\|       
#    +--+--+--+    +--+--+--+
#    |\3|\1|\ |    |\4|\0|\9|
#    |9\|0\|4\|    | \|1\|3\|
#    +--+--+--+    +--+--+--+
#    |\8|\2|\5|    |\ |\C|\A|
#    | \|7\|6\|    | \| \|B\|
#    +--+--+--+    +--+--+--+

#  To implement the Tri6Inner neighborhood, 
#  let the central cell be "0" above. 
#  Only cells 1, 2, 3, 5, 8, and 11 are considered neighbors, 
#  and the others are ignored.
#

''')

f.write('''

var a={0,1}
var b={a}
var c={a}
var d={a}
var e={a}
var f={a}
var g={a}
var h={a}
var i={a}
var j={a}
var k={a}
var l={a}


var m ={0,1,2}
var n = {m}
var o = {m}
var p = {m}
var q = {m}
var r = {m}
var nn = {m}
var oo = {m}
var pp = {m}
var qq = {m}
var rr = {m}
var ss = {m}

''')


Brule_dict = {  
                 "1" : '''
# B1 - Part 1
0, 2, b, c, m, d, n, o, e, p, q, f, r,1
0, a, 2, c, m, d, n, o, e, p, q, f, r,1
0, a, b, 2, m, d, n, o, e, p, q, f, r,1
0, a, b, c, m, 2, n, o, e, p, q, f, r,1
0, a, b, c, m, d, n, o, 2, p, q, f, r,1
0, a, b, c, m, d, n, o, e, p, q, 2, r,1

# B1 - Part 2
1, 2, b, c, m, d, n, o, e, p, q, f, r,2
1, a, 2, c, m, d, n, o, e, p, q, f, r,2
1, a, b, 2, m, d, n, o, e, p, q, f, r,2
1, a, b, c, m, 2, n, o, e, p, q, f, r,2
1, a, b, c, m, d, n, o, 2, p, q, f, r,2
1, a, b, c, m, d, n, o, e, p, q, 2, r,2
''',
              "2" : '''
# B2 - Part 1
0, 2, 2, c, m, d, n, o, e, p, q, f, r,1
0, 2, b, 2, m, d, n, o, e, p, q, f, r,1
0, 2, b, c, m, 2, n, o, e, p, q, f, r,1
0, 2, b, c, m, d, n, o, 2, p, q, f, r,1
0, 2, b, c, m, d, n, o, e, p, q, 2, r,1
0, a, 2, 2, m, d, n, o, e, p, q, f, r,1
0, a, 2, c, m, 2, n, o, e, p, q, f, r,1
0, a, 2, c, m, d, n, o, 2, p, q, f, r,1
0, a, 2, c, m, d, n, o, e, p, q, 2, r,1
0, a, b, 2, m, 2, n, o, e, p, q, f, r,1
0, a, b, 2, m, d, n, o, 2, p, q, f, r,1
0, a, b, 2, m, d, n, o, e, p, q, 2, r,1
0, a, b, c, m, 2, n, o, 2, p, q, f, r,1
0, a, b, c, m, 2, n, o, e, p, q, 2, r,1
0, a, b, c, m, d, n, o, 2, p, q, 2, r,1
# B2 - Part 2
1, 2, 2, c, m, d, n, o, e, p, q, f, r,2
1, 2, b, 2, m, d, n, o, e, p, q, f, r,2
1, 2, b, c, m, 2, n, o, e, p, q, f, r,2
1, 2, b, c, m, d, n, o, 2, p, q, f, r,2
1, 2, b, c, m, d, n, o, e, p, q, 2, r,2
1, a, 2, 2, m, d, n, o, e, p, q, f, r,2
1, a, 2, c, m, 2, n, o, e, p, q, f, r,2
1, a, 2, c, m, d, n, o, 2, p, q, f, r,2
1, a, 2, c, m, d, n, o, e, p, q, 2, r,2
1, a, b, 2, m, 2, n, o, e, p, q, f, r,2
1, a, b, 2, m, d, n, o, 2, p, q, f, r,2
1, a, b, 2, m, d, n, o, e, p, q, 2, r,2
1, a, b, c, m, 2, n, o, 2, p, q, f, r,2
1, a, b, c, m, 2, n, o, e, p, q, 2, r,2
1, a, b, c, m, d, n, o, 2, p, q, 2, r,2
''',
                 "3" : '''
#  B3 - Part 1
0, 2, 2, 2, m, d, n, o, e, p, q, f, r,1
0, 2, 2, c, m, 2, n, o, e, p, q, f, r,1
0, 2, 2, c, m, d, n, o, 2, p, q, f, r,1
0, 2, 2, c, m, d, n, o, e, p, q, 2, r,1
0, 2, b, 2, m, 2, n, o, e, p, q, f, r,1
0, 2, b, 2, m, d, n, o, 2, p, q, f, r,1
0, 2, b, 2, m, d, n, o, e, p, q, 2, r,1
0, 2, b, c, m, 2, n, o, 2, p, q, f, r,1
0, 2, b, c, m, 2, n, o, e, p, q, 2, r,1
0, 2, b, c, m, d, n, o, 2, p, q, 2, r,1
0, a, 2, 2, m, 2, n, o, e, p, q, f, r,1
0, a, 2, 2, m, d, n, o, 2, p, q, f, r,1
0, a, 2, 2, m, d, n, o, e, p, q, 2, r,1
0, a, 2, c, m, 2, n, o, 2, p, q, f, r,1
0, a, 2, c, m, 2, n, o, e, p, q, 2, r,1
0, a, 2, c, m, d, n, o, 2, p, q, 2, r,1
0, a, b, 2, m, 2, n, o, 2, p, q, f, r,1
0, a, b, 2, m, 2, n, o, e, p, q, 2, r,1
0, a, b, 2, m, d, n, o, 2, p, q, 2, r,1
0, a, 2, c, m, 2, n, o, e, p, q, f, r,1
0, a, b, c, m, 2, n, o, 2, p, q, 2, r,1
# B3 - Part 2
1, 2, 2, 2, m, d, n, o, e, p, q, f, r,2
1, 2, 2, c, m, 2, n, o, e, p, q, f, r,2
1, 2, 2, c, m, d, n, o, 2, p, q, f, r,2
1, 2, 2, c, m, d, n, o, e, p, q, 2, r,2
1, 2, b, 2, m, 2, n, o, e, p, q, f, r,2
1, 2, b, 2, m, d, n, o, 2, p, q, f, r,2
1, 2, b, 2, m, d, n, o, e, p, q, 2, r,2
1, 2, b, c, m, 2, n, o, 2, p, q, f, r,2
1, 2, b, c, m, 2, n, o, e, p, q, 2, r,2
1, 2, b, c, m, d, n, o, 2, p, q, 2, r,2
1, a, 2, 2, m, 2, n, o, e, p, q, f, r,2
1, a, 2, 2, m, d, n, o, 2, p, q, f, r,2
1, a, 2, 2, m, d, n, o, e, p, q, 2, r,2
1, a, 2, c, m, 2, n, o, 2, p, q, f, r,2
1, a, 2, c, m, 2, n, o, e, p, q, 2, r,2
1, a, 2, c, m, d, n, o, 2, p, q, 2, r,2
1, a, b, 2, m, 2, n, o, 2, p, q, f, r,2
1, a, b, 2, m, 2, n, o, e, p, q, 2, r,2
1, a, b, 2, m, d, n, o, 2, p, q, 2, r,2
1, a, 2, c, m, 2, n, o, e, p, q, f, r,2
1, a, b, c, m, 2, n, o, 2, p, q, 2, r,2

''',
                 "4" : '''
# B4 - Part 1
0, a, b, 2, m, 2, n, o, 2, p, q, 2, r,1
0, a, 2, b, m, 2, n, o, 2, p, q, 2, r,1
0, a, 2, 2, m, b, n, o, 2, p, q, 2, r,1
0, a, 2, 2, m, 2, n, o, b, p, q, 2, r,1
0, a, 2, 2, m, 2, n, o, 2, p, q, b, r,1
0, 2, a, b, m, 2, n, o, 2, p, q, 2, r,1
0, 2, a, 2, m, b, n, o, 2, p, q, 2, r,1
0, 2, a, 2, m, 2, n, o, b, p, q, 2, r,1
0, 2, a, 2, m, 2, n, o, 2, p, q, b, r,1
0, 2, 2, a, m, b, n, o, 2, p, q, 2, r,1
0, 2, 2, a, m, 2, n, o, b, p, q, 2, r,1
0, 2, 2, a, m, 2, n, o, 2, p, q, b, r,1
0, 2, 2, 2, m, a, n, o, b, p, q, 2, r,1
0, 2, 2, 2, m, a, n, o, 2, p, q, b, r,1
0, 2, 2, 2, m, 2, n, o, a, p, q, b, r,1
# B4 - Part 2
1, a, b, 2, m, 2, n, o, 2, p, q, 2, r,2
1, a, 2, b, m, 2, n, o, 2, p, q, 2, r,2
1, a, 2, 2, m, b, n, o, 2, p, q, 2, r,2
1, a, 2, 2, m, 2, n, o, b, p, q, 2, r,2
1, a, 2, 2, m, 2, n, o, 2, p, q, b, r,2
1, 2, a, b, m, 2, n, o, 2, p, q, 2, r,2
1, 2, a, 2, m, b, n, o, 2, p, q, 2, r,2
1, 2, a, 2, m, 2, n, o, b, p, q, 2, r,2
1, 2, a, 2, m, 2, n, o, 2, p, q, b, r,2
1, 2, 2, a, m, b, n, o, 2, p, q, 2, r,2
1, 2, 2, a, m, 2, n, o, b, p, q, 2, r,2
1, 2, 2, a, m, 2, n, o, 2, p, q, b, r,2
1, 2, 2, 2, m, a, n, o, b, p, q, 2, r,2
1, 2, 2, 2, m, a, n, o, 2, p, q, b, r,2
1, 2, 2, 2, m, 2, n, o, a, p, q, b, r,2

''',
                 "5" : '''
# B5 - Part 1

0, a, 2, 2, m, 2, n, o, 2, p, q, 2, r,1
0, 2, a, 2, m, 2, n, o, 2, p, q, 2, r,1
0, 2, 2, a, m, 2, n, o, 2, p, q, 2, r,1
0, 2, 2, 2, m, a, n, o, 2, p, q, 2, r,1
0, 2, 2, 2, m, 2, n, o, a, p, q, 2, r,1
0, 2, 2, 2, m, 2, n, o, 2, p, q, a, r,1

# B5 - Part 2

1, a, 2, 2, m, 2, n, o, 2, p, q, 2, r,2
1, 2, a, 2, m, 2, n, o, 2, p, q, 2, r,2
1, 2, 2, a, m, 2, n, o, 2, p, q, 2, r,2
1, 2, 2, 2, m, a, n, o, 2, p, q, 2, r,2
1, 2, 2, 2, m, 2, n, o, a, p, q, 2, r,2
1, 2, 2, 2, m, 2, n, o, 2, p, q, a, r,2

''',
                 "6" : '''
# B6 - Part 1
0, 2, 2, 2, m, 2, n, o, 2, p, q, 2, r,1

# B6 - Part 2
1, 2, 2, 2, m, 2, n, o, 2, p, q, 2, r,2
'''
        }


Srule_dict = {  "0" : '''

#  S0

2, a, b, c, m, d, n, o, e, p, q, f, r,2
''',

                 "1" : '''
#  S1

2, 2, b, c, m, d, n, o, e, p, q, f, r,2
2, a, 2, c, m, d, n, o, e, p, q, f, r,2
2, a, b, 2, m, d, n, o, e, p, q, f, r,2
2, a, b, c, m, 2, n, o, e, p, q, f, r,2
2, a, b, c, m, d, n, o, 2, p, q, f, r,2
2, a, b, c, m, d, n, o, e, p, q, 2, r,2

''',
              "2" : '''
# S2
2, 2, 2, c, m, d, n, o, e, p, q, f, r,2
2, 2, b, 2, m, d, n, o, e, p, q, f, r,2
2, 2, b, c, m, 2, n, o, e, p, q, f, r,2
2, 2, b, c, m, d, n, o, 2, p, q, f, r,2
2, 2, b, c, m, d, n, o, e, p, q, 2, r,2
2, a, 2, 2, m, d, n, o, e, p, q, f, r,2
2, a, 2, c, m, 2, n, o, e, p, q, f, r,2
2, a, 2, c, m, d, n, o, 2, p, q, f, r,2
2, a, 2, c, m, d, n, o, e, p, q, 2, r,2
2, a, b, 2, m, 2, n, o, e, p, q, f, r,2
2, a, b, 2, m, d, n, o, 2, p, q, f, r,2
2, a, b, 2, m, d, n, o, e, p, q, 2, r,2
2, a, b, c, m, 2, n, o, 2, p, q, f, r,2
2, a, b, c, m, 2, n, o, e, p, q, 2, r,2
2, a, b, c, m, d, n, o, 2, p, q, 2, r,2
''',
                 "3" : '''
#  S3
2, 2, 2, 2, m, d, n, o, e, p, q, f, r,2
2, 2, 2, c, m, 2, n, o, e, p, q, f, r,2
2, 2, 2, c, m, d, n, o, 2, p, q, f, r,2
2, 2, 2, c, m, d, n, o, e, p, q, 2, r,2
2, 2, b, 2, m, 2, n, o, e, p, q, f, r,2
2, 2, b, 2, m, d, n, o, 2, p, q, f, r,2
2, 2, b, 2, m, d, n, o, e, p, q, 2, r,2
2, 2, b, c, m, 2, n, o, 2, p, q, f, r,2
2, 2, b, c, m, 2, n, o, e, p, q, 2, r,2
2, 2, b, c, m, d, n, o, 2, p, q, 2, r,2
2, a, 2, 2, m, 2, n, o, e, p, q, f, r,2
2, a, 2, 2, m, d, n, o, 2, p, q, f, r,2
2, a, 2, 2, m, d, n, o, e, p, q, 2, r,2
2, a, 2, c, m, 2, n, o, 2, p, q, f, r,2
2, a, 2, c, m, 2, n, o, e, p, q, 2, r,2
2, a, 2, c, m, d, n, o, 2, p, q, 2, r,2
2, a, b, 2, m, 2, n, o, 2, p, q, f, r,2
2, a, b, 2, m, 2, n, o, e, p, q, 2, r,2
2, a, b, 2, m, d, n, o, 2, p, q, 2, r,2
2, a, 2, c, m, 2, n, o, e, p, q, f, r,2
2, a, b, c, m, 2, n, o, 2, p, q, 2, r,2
''',
                 "4" : '''
# S4
2, a, b, 2, m, 2, n, o, 2, p, q, 2, r,2
2, a, 2, b, m, 2, n, o, 2, p, q, 2, r,2
2, a, 2, 2, m, b, n, o, 2, p, q, 2, r,2
2, a, 2, 2, m, 2, n, o, b, p, q, 2, r,2
2, a, 2, 2, m, 2, n, o, 2, p, q, b, r,2
2, 2, a, b, m, 2, n, o, 2, p, q, 2, r,2
2, 2, a, 2, m, b, n, o, 2, p, q, 2, r,2
2, 2, a, 2, m, 2, n, o, b, p, q, 2, r,2
2, 2, a, 2, m, 2, n, o, 2, p, q, b, r,2
2, 2, 2, a, m, b, n, o, 2, p, q, 2, r,2
2, 2, 2, a, m, 2, n, o, b, p, q, 2, r,2
2, 2, 2, a, m, 2, n, o, 2, p, q, b, r,2
2, 2, 2, 2, m, a, n, o, b, p, q, 2, r,2
2, 2, 2, 2, m, a, n, o, 2, p, q, b, r,2
2, 2, 2, 2, m, 2, n, o, a, p, q, b, r,2
''',
                 "5" : '''
# S5 
2, a, 2, 2, m, 2, n, o, 2, p, q, 2, r,2
2, 2, a, 2, m, 2, n, o, 2, p, q, 2, r,2
2, 2, 2, a, m, 2, n, o, 2, p, q, 2, r,2
2, 2, 2, 2, m, a, n, o, 2, p, q, 2, r,2
2, 2, 2, 2, m, 2, n, o, a, p, q, 2, r,2
2, 2, 2, 2, m, 2, n, o, 2, p, q, a, r,2

''',
                 "6" : '''
#  S6

2, 2, 2, 2, m, 2, n, o, 2, p, q, 2, r,2

'''        }


for i in Brulestring:
   if i in ["1", "2", "3", "4", "5", "6"]:
       f.write(Brule_dict[i])

f.write("# Death otherwise" + "\n")
f.write(" 1, nn, oo,pp, m, qq, n, o, rr, p, q, ss, r,0" + "\n")

       
for i in Srulestring:
   if i in ["0", "1", "2", "3", "4", "5", "6"]:
       f.write(Srule_dict[i])

f.write("# Death otherwise"+"\n")
f.write("2, nn, oo,pp, m, qq, n, o, rr, p, q, ss, r,0" + "\n")


f.flush()
f.close()


#  All code below this line is from RuleTableToTree.py by the Golly Gang

import golly
import os
from glife.ReadRuleTable import *
from glife.RuleTree import *
from glife.EmulateTriangular import *
from glife.EmulateMargolus import *
from glife.EmulateOneDimensional import *
from glife.EmulateHexagonal import *


if len(filename) == 0: golly.exit()    # user hit Cancel

# add new converters here as they become available:
Converters = {
    "vonNeumann":ConvertRuleTableTransitionsToRuleTree,
    "Moore":ConvertRuleTableTransitionsToRuleTree,
    "triangularVonNeumann":EmulateTriangular,
    "triangularMoore":EmulateTriangular,
    "Margolus":EmulateMargolus,
    "square4_figure8v":EmulateMargolus,
    "square4_figure8h":EmulateMargolus,
    "square4_cyclic":EmulateMargolus,
    "oneDimensional":EmulateOneDimensional,
    "hexagonal":EmulateHexagonal,
}

golly.show("Reading from rule table file...")
n_states, neighborhood, transitions = ReadRuleTable(filename)

if not neighborhood in Converters:
    golly.warn("Unsupported neighborhood: "+neighborhood)
    golly.show('')
    golly.exit()
    
golly.show("Building rule tree...")
rule_name = Converters[neighborhood]( neighborhood, 
                                      n_states, 
                                      transitions, 
                                      filename )

golly.setalgo('RuleTree')
golly.setrule(rule_name)
golly.show('Created '+rule_name+'.tree and selected that rule.')

To my surprise Tri6Inner-B1x2_S1 has spaceships. It is a very sparse rule, but it has a rather rare natural rake, and while oscillators are also rare, there is a sparky oscillator looks like it might be useful:

Code: Select all

x = 30, y = 9, rule = Tri6Inner-B1x2_S1_emulated
.3F18.B2.B$.F2.F18.HFB$CHBA.G2A15.CBE$C.A2C3.A14.C2.C$C2.2AFA2.A12.A
6.A$.CA2BEBA15.A5.A$2.C2ABH2A15.6A$4.GFHA.A$7.A!
=====

Tri6inner-B16x2_S156 is a richer version of the rule.

Here is a rake composed of various other rakes:

Code: Select all

x = 397, y = 214, rule = Tri6Inner-B16_x2_S156_emulated
213.3C7$224.3A$224.A$224.A$225.G$225.CB$225.C$226.C$227.3C7$238.3A$
238.A$238.A$239.G$239.CB$239.C$240.C$241.3C7$252.3A$252.A$252.A$253.G
$253.CB$159.3F91.C$159.F94.C$159.F3.B2A89.3C$162.E3.B$161.C.A.FE$161.
3CE2DC$161.3C2.3C3$266.3A$266.A$266.A$267.G$267.CB$151.3A113.C$154.A
113.C$155.A113.3C$154.FA$155.E$156.C$154.2BD$154.2FCA$153.F2.FA$153.F
C.CE122.3A$153.5CF121.A$280.A$281.G$281.CB$137.3A141.C$140.A141.C$
141.A141.3C$140.FA$141.E$142.C$142.C$140.3C2$294.3A68.2CF$294.A70.C.B
F.A$294.A70.C.CBFA2.C$295.G70.C2.DA2.C$147.3A145.CB70.3F3.C$123.3A24.
A144.C78.C.B3.A$126.A19.F2.FA145.C78.2CG2.A$127.A18.FC.CE146.3C51.2CF
24.3A$126.FA18.5CF199.C.BF.A$127.E223.C.CBFA$128.C223.C2.DA$128.C224.
3F$126.3C2$308.3A26.2CF$309.BA26.C.BF.A$308.A3.B24.C.CBFA$309.G2.B25.
C2.DA$146.3A11.3A11.3A11.3A11.3A11.3A11.3A11.3A11.3A11.3A11.3A11.3A6.
CE2B26.3F$109.3A33.C3.A9.C3.A9.C3.A9.C3.A9.C3.A9.C3.A9.C3.A9.C3.A9.C
3.A9.C3.A9.C3.A9.C3.A5.3C$112.A32.C4.B8.C4.B8.C4.B8.C4.B8.C4.B8.C4.B
8.C4.B8.C4.B8.C4.B8.C4.B8.C4.B8.C4.B$113.A31.C4.B8.C4.B8.C4.B8.C4.B8.
C4.B8.C4.B8.C4.B8.C4.B8.C4.B8.C4.B8.C4.B8.C4.B.A2.A13.2CF$112.FA32.C
3.B9.C3.B9.C3.B9.C3.B9.C3.B9.C3.B9.C3.B9.C3.B9.C3.B9.C3.B9.C3.B9.C3.B
2.A.A13.C.BF.A$113.E33.3F11.3F11.3F11.3F11.3F11.3F11.3F11.3F11.3F11.
3F11.3F11.3F4.2A13.C.CBFA$114.C19.2CF187.C2.DA$114.C19.CB.F.4A182.3F$
112.3C19.C.H.FA3.A162.2AB.B.C.2A$135.C.BDG2.FA162.B4.HFC2.A$136.3CFC.
CE162.B.C2.CBGB2.B$139.5CF162.BC.A2CDCE.B$308.H2.A.AC2FB$120.2CF185.B
3E$120.C.BF.A183.BD.BA$94.A2.A22.C.CBFA184.EB3.A$95.A2.A22.C2.DA184.F
.B2.A$96.A2.A22.3F186.2CG2A$91.B2.A3.FA$91.B2.A4.E$92.A.A.C3.C5.2CF$
92.CA2.2FCFC5.C.BF.A62.C$92.2F.ADGC7.C.CBFA62.C$92.FAG3A9.C2.DA62.C$
93.EF2.A10.3F64.C.B3.A$93.EFC.A2D76.2CG2.A$94.B4.BF78.3A$98.AB.F$95.B
2.CABF31.3A$96.BC.HDC34.A$97.E2B32.F2.FA$97.F.BA31.FC.CE$98.2CG31.5CF
8$160.2CF$160.C.BF.A$93.3A64.C.CBFA2.C$96.A64.C2.DA2.C$97.A64.3F3.C$
96.FA71.C.B3.A$97.B72.2CG2.A$146.2CF24.3A$125.3A18.C.BF.A$96.2C2.B3.A
23.A17.C.CBFA$99.2CG2.A24.A17.C2.DA$102.3A23.FA18.3F$129.E$130.F$130.
C.2CF$128.3C.C.BF.A$79.3A50.C.CBFA$82.A50.C2.DA$83.A50.3F$82.FA$83.E$
84.C33.2CF15.C$84.C26.3A4.C.BF.A12.C$82.3C29.A3.C.CBFA12.C$115.A3.C2.
DA13.C.B3.A$114.FA4.3F15.2CG2.A$115.E25.3A$116.C$104.2CF9.C$104.C.BF.
A4.3C$65.3A36.C.CBFA$68.A36.C2.DA$69.A36.3F$68.FA$69.E$70.C19.2CF$70.
C19.C.BF.A.3A$68.3C19.C.CBFA4.A$91.C2.DA5.A$92.3F5.FA$101.E20.2CF$
102.C19.C.BF.A$76.2CF23.C19.C.CBFA2.C$76.C.BF.A18.3C20.C2.DA2.C$50.A
2.A22.C.CBFA42.3F3.C$51.A2.A22.C2.DA49.C.B3.A$52.A2.A22.3F51.2CG2.A$
47.B2.A3.FA52.2CF24.3A$47.B2.A4.E52.C.BF.A$48.A.A.C3.C5.2CF43.C.CBFA$
48.CA2.2FCFC5.C.BF.A41.C2.DA$48.2F.ADGC7.C.CBFA14.3C3A22.3F$48.FAG3A
9.C2.DA14.C2.C2A$49.EF2.A10.3F15.C3.FD$49.EFC.A2D28.B2.EC5.2CF$50.B4.
BF26.2B2.3C.A2.C.BF.A$54.AB.F26.HBD4.A2.C.CBFA$51.B2.CABF26.FEC2.F5.C
2.DA$52.BC.HDC26.F3.BFHCB3.3F$53.E2B29.C4B2.E$53.F.BA28.DAFB.3BC$54.
2CG28.BF.B4.C$86.B.2F$87.E2B4A$87.F.BA.2A$88.2CG2.A!
Here's a knightship:

Code: Select all

x = 10, y = 9, rule = Tri6inner-B16x2_S156_emulated
2$3.3A$3.A2.A$3.BFA.B$4.BF.B$5.BDB$4.3C!
=====

Here's a whole other sort of rule.
Want to see something different? Watch what happens around generation 2,700.

Code: Select all

x = 239, y = 119, rule = Tri6Inner-B1x2_S3456_emulated
11$24.3A$18.D2A2C2.2A$17.C.F.E2.FC2D2.A7.D2B6.3A$20.HC2A5B9.CF.A6.2A$
16.2A.FBHC.6FH7.DAHF.EC2.FHBCB109.3A$18.CFB5H2B2HBF6.BFB2HC2.CABFH.C.
F103.ADBA2.A$19.FBF5HAFHBA8.2FHBA2.B2H3BE.FBA101.A.CA.A7.C.C5.3A$17.C
AFB2.B3.DCFHBC8.HFH2B.8F2BA103.BHF10.GC5.AD.C$10.C3A3.C2FB4.FCA.2FHBD
6.C.HFHFHB2HC.F2HBH102.C.3FH7.B.H.FA.2ADCB.E.A$14.A.CDGF2BHB.C2.2A.2H
.A6.B3.B2HFHBH.FH2B.D102.D2HBHA5.CFB2H.BAB.BFHF.B.C$12.H2C2.EAFB2FHBH
.DABAB.HBA2.3A2B.FH3BFHB2HFH3.C101.CFHB.B6.C2FHB.BDB2H3BEFAC$10.G.5HB
2FB.BFHF3B.DFHFHB2.A2.BHFH.3F.FHB.HF3H.C101.2FHB8.CHFH2B.8FB.E$11.F6H
BFB3.2B.HFH2.H.H.F2.B.FBHBHB.B.FH2BFB2H2BG102.2FH2B6.CAHFHFHB2HF2.2HB
FC$10.A.H.2B2.FHBHBH.2FHBHBFHBH2F2.CAFB2H2B.HFBHBH.H.A2FD104.2H.A6.A
3.B2HFHBH.FHB2.2A$11.A2.2H3BH.2HBH.HB.2H.FBH2.B2CB.2F2HFH.HBAHB2HB3AB
103.F2.HBA5.AB2FH3BFHB2HFH.F2.A$12.2AC.2F2HF2H.FB2HB2H.H2FH.3HFHBH.2B
.HF2.2HBF.2A106.2HFHB3.D2.HFH.3F.FHB.HF3H.A$16.AHFHFBH.HBFHF.HFB2H.H
2FHBHB.H2F2.2HB2HFBG.A104.A2.H.H.C.ADBFBHBHC.ECFHB.FB2H2B$16.D.2HBH.A
2.HB2C.FB3H2.HFHFBA2.2HBF2HFHFB.F106.AFHB.2CA2.CFB2H2B.HFBHBH.H2.2FG$
17.2ABF2.B2.2HB3.2F2HB.BHFH2.2B3HFBH.BHF2.C100.3A4.FBHC.B2.B.2F2HFH.H
2BHB2HBDA.E.B$18.A4.FH.2HFH.HFHB.HBHF.BH.2F3HFB5F2.C98.GAD2A2.BAH2FH.
3HFHBH.2B.HF2.2HBF.AD.G.B$23.H2B2H.AH.H.3FHBH.HFB.HF2BHFB.2H4C98.F4.
2ABFB2H.H2FHBHB.H2F2.2HB2HFBC.A2.2A$22.F2HF2H3.HC.4H2.HBH.A.H.G2F2B.H
BC98.CF2C.HB.A.FB3HCAHFHFB3.2HBF2HFHFB.C$20.2CFBF.H.3H.BF2H2B2.2H2B.B
FBG.C.HFBFBC99.B2.2HB.4F2HB.BHFHC.2B3HFBH.BH$20.F2.HDFB.FH2B2HB.AFHF
2H2FB.FB3.FBHBHBE99.FH.2HFHCH.HB.HBHF.BHC2F3HFB4F.2C$10.2F2.5F.BH2.B.
3HFH2F2HB2AHBFH.F2BH3.DFB2HBH.B96.G.H2B2H.BH.H.3FHBH.HFBCHF2BHFB.2HC$
9.AF2B.F4BH.HFHFH.3HC.HF2H2.G2H.H.3F2B.EAF2HFB2H95.A.F2HF2H3.HF.4H.AH
BHC.AH.G2F2B.HBC$11.2FH.6FBHBHB3.B.FBH6BFB.4H.FHB.BFHFBF.G95.AFBF.H.
3H.BF2H2BC.2H2BD.FBG.F.HFBFBC$10.A.H2B2H.B2FB2HBFDEBHF2H2B5F.HF4HB2.F
HFHBH.C.A89.AB.DBF.A2HFB.FH2B2HB.BFHF2H2FBAFB3.FBHBHBGC$11.A.A2FHB3HB
FH3.DGFH2B3FBH.CH2BH3.HB2.2HB.F.F.A83.A2G2.2FAE.C.H2.B.3HFH2F2H3BHBFH
CF2BH2.CDFB2HBH.C$12.AFCHFHF3HF.3H.D.2HFBH.H2FBA3FB2F2HC.3BHC2.C83.2A
.2B.C5B.HFHFHA3HF.HF2HA.3H.H.3F2B3.F2HFBHBA$13.C.BH6.HFHBHA2.F.HFBH.F
B2HDHB.BFH.FH3FHB2D83.A.C2FH.6FBHBHB3.B.FBH6BFB.4H.2HBCBFHFBG.B.C$13.
2CFB2HB.B2.HFH3BH.H.H.H2.HF3.2FHFHBHB2.2H2.A84.A.CH2B2H.B.FB2HBFB.BHF
2H2B5F.HF4HBHBFHFHBHFCA3C$14.2AHF2HFBC2B.FH4FBHBHFHFHB4.FBHB2FHB3.H.A
85.AF.A2FHB3HBFH2.CBHFH2B3F2BCFH2BH3.HBA.2HB.2F$15.AD2B2FH2BHFHFBHFBH
F.BH2BFH.B2.CAFHBHFH.3HBA2DA3.G2B77.3ACHFHF3HF.3H.BA2HFBH.H2FB.3FBAF
2HC.3BHF$16.A5.2B2H2BHFHBF.HB.H2FB2H5.H2.HF.3HFB2FC2.BAH.B77.2AEBH3.
3AHFHBHE2AF.HFB.CFBHBFHB.BFH.FH3FHB$18.A2.FH2F2H2F2B.DHFB4HBF.F3.F.G
3.FHB2F2B2.F2.FBHC3A75.A.FB2HE.C2.HFH4B.H.H.HC.HF.A.2FHFHBHB2.2H$19.A
.FB2HB2FH2FHBAHFHBFHBF5.DCB.B.BF.H2.FHBD.C.FHB.2A78.HF2HFBA.B.FH4FBHB
HFHFHB3.BFBHB2FHB3.HFC6.C$20.2AH2.F2H3BF2.A.FHBFHB.C3.C.F2HF4HB.FHFB
2.2B2HB.A77.2F2B2FH2.HFHFBH.BHF2.H2BFH.A2.B.FHBHFH.3HBA4.2CBCA$20.C3.
H2B4F2H.CD.2HBFHB4.2CF2BHBF2HFBHBHFH.3F2H.C82.C.2B2H2BHFH.F.HB.H2FBHE
2.2F.H.AH2.3HFB4.C2.HCA$20.C2.HFB4HCF2.B2F.A.2FH2.B3.C2F2HB.2FB2H2BH
3BHBHF83.AFH2F2H2F2B.BHFB4HBF.C.C4.ACAFHB2F2BFA.C.FBH$20.2CFH2B2H.HB.
3H.B3.B.H.HCB4.HF2H2.HBHFH2F.2F2A2F84.FB2HB2FH2FHB.HFHBFHBF4.C2.B.E.B
F.HC.FHBA.C.FH2BC$22.2FHF2H2.HB3HF2HB.2HBH.H4.2BH.BHFH2FBH2B2H.BC87.H
2.F2H3BF.ACAFHBFHB.C2.C.AF2HF4HBCFHFB.C2B2HBDC$23.F2.FHFB2HF.HFBF2BFH
B2FHB2FAC3FGAHFBH.H.2FH2B.3C83.CA.H2B4FHBDA2.2H.FHBDC3.AF2BHBF2HFBHBH
FH.H2F2H.2C$24.AFHB.HFH2.F.HFB2HBFHB.F2HE.AH2.BAHBFBF.2B.FB87.A.HFB4H
2F2.C2.AB2AFH.D4.A2F2HB.2FB2H2BH3BHBHC$25.AFHB.BHB2H.BHF3H2BF2B.FHCF
2B2C2.2H2.H2F2HCD87.FH2B2H.HB.2HB.BC2AB.H.H4.CAHF2HC.HBHFH2F.2F2.GC$
25.CAH4.2FH2BFBF2.2FHB2HFBHFBHFH.3BHFH2B2FH88.2FHF2H2.HB3HF2HBA2HBH.H
2C.D.BH2.HFH2FBH2B2H3.CA$25.C.FG4.HBH2FBAHA3.2F.2H.HFBH2BH3FBFHF.BHB.
C.H2B82.FC.FHFB2HF.HFBF2BFHB2FHB2.C.2F3.HFBH.F.GFHBGC$25.C6.A.2FC.CF
2BC.C2F.A.A2.F2H3FBHBH.H.HF.CDCBH.A2.A2.A76.A.HB.HFH4.HFB2HBFHB.F3H.B
H.BE.HBFB2.2B.FD$26.3C4.A.A.C.FBHFHC2HBH.C.2BFH.C.HB2FBA5H2CFBHC3F2.
2CA75.AFHB.BHB2H2.HF3H2BF2B.FH2F2B2.A.2HC.H2FD2F$38.C.FBH2BF2HFB.2B2H
BFBF2HBH.A.BFHBHCFB10H.A74.AH.A2.2FH2BFBF2.2FHB2HFBHFBHFH.3BHFHBHC.2C
4.F$37.CDCFB2HFHBF.2FHF3HF3BH.FB3.2FH2BHBF9H76.2CH.A2.HBH2F2BHB.D.2F.
2HAHFBH2BH3FBFHF.BE.A.C2EF$40.CF2H.FHB.C.H.H.BH.2FB2H6.FH2F2.2A2.4BF
82.A.3FH2F2BF.F3.B.B.AF2H3FBHBH.H.HF2.AG.HCD2.A2.A$40.FDFH.HFHBDFH2BH
BFC.FHBF5HBHB5.C2.C4.BA81.A.GC2.FBHFHF2HBH.F2.BFH3.HB2FB.5H.CFBHC3F2.
2CA$40.F.GBHB2HB.DFH2FHB2CHFHBF5HFHBH96.2FC.HFBH2BF2HFB.2B2HBFBG2HBHC
3.FHBH2FB10HA$40.C3.F3.HBHC.B.H.FH.3H.FH.BF.FHFB99.AFB2HFHBF.2FHF3HF
3BH.FB.2CAFH2BHBG9HC$41.C3.CB.FHBH.HF2BFBH2.AFBH2B2.B.H101.AF2H.FHB.C
.H.H.BH.2FB2H2.3C.FH2F4.2B4AFC$42.2CDGF3H2.HBH2FHB.H3.E.F.2BH.FB.C99.
2FH.HFHBDFH2BHB2FDFHBF5HBHB3.C2.C6.A$47.3HFB2H3BFHBFB6.EFB2HBA.C99.GB
HB2HB.DFH2FHB2FHFHBF5HFHBH$46.F.2AHB2H3FB3HBEB2.2CEFB3HBC2.2A96.FBG3.
HBHC.B.H.FH.3HAFH2.F.FHFB$49.CB.2H2.FH2BF.FB5.FBF3HFHB2A99.CB.FHBH.HF
2BFBH2.BD.HB3.B.HCF$49.F.F2HFHF2HFBHB5.2AH2B2HF2BC.A98.CF3H2.HBH2FHB.
H3.F.FA2.H.FB$48.CAB.FHFBF2BH.FHBE4.2A2FA.HFH.H99.2A3HFB2H3BFHBFB5.A.
FB2HBD.C$50.3HB.BH.GFCF2H2.2D2.A.ACBHB.FHB4A95.4AHB2H3FB3HBF6.FB3HB4C
$50.F5HF.BCHF2BHB2.C3.FCF3HBFHB3.A95.A.CB.2H2.FH2BF.D4.2CFBF3HFHD.C$
48.CDBH2.F.2HB2FBA2FHB2.A2.2CAH.F2.3HCBA96.CF.F2HFBF2HFBHBD6.H2B2HF2B
.DE$52.HBH2.FHBFBEBF4HBC.2CFBHBCFB.BH2F2.A93.C.B.FHFBF2BH.FHBC4.C.2FB
.HFH.HC$51.F2HBH2BFHBFB.G2BH3.C3.HFHBFBFH.B3.3C3FEA86.CA3HB.BH.G3F2H.
DC5.BFBHB.FHBC$51.DF2HF.GF3HB2CBHF3.C2.2CF2H.H.HB4HB4HBHBA85.BHF5HF2.
FHF2BHBDC2A3.2F3HBFHBCFA$52.G3BF.A2.F.C2.C.C7.CA.2HB2HBF3HF4HFHB2A83.
A2.H2.F.2HB.F2B2FHB3.A2.2AH.F.A3H.H8.C$52.CA2FB2.A.CB3.C2.C6.AFB2H2F
2HF2BF4.F.H2.A84.AC.HBH.AFHBFB.CF3HE.A3.FBHB.FB.BH2C7.CF$55.F.A.D17.A
F2H.HBHFBF6HFC.2A85.2F2HBH2BFHBFB.H2BH.GA4.HFHBFBFH.B5F3C.BCBA$55.CDC
2A18.GFH2.FBHFBHF4HCABA86.C.F2HF.2F3HBF2.2F.A4.3F2H.H.HB4HB4HBHB.A$
80.H2B.HF.F2B3.HC2A87.C.F3B2.C2.F.FC2.D2A6.G2.2HB2HBF3HF4HFHB.A$79.F.
2FH.3H2F2.DBC.A88.C.AHFC3.A.B15.B2H2F2HF2BF4.F.H.2A$81.CHBH.FHBH.2ACF
90.C2.2CGB.2A16.2F2H.HBHFBF5HBCFG.B$81.C.FBCF2HF2B.3C90.2C.C.CB19.2FH
2.FBH2.HF4HC$84.B.G2BH.C98.3C21.H2B.HF.F2B3.H$86.CAGF123.C.2FH.3H2F2.
DCAC$89.3A123.CHBH.FHBH.2A.F2C$215.C.F.2F2HFB.A$219.CH2BH2.A$217.3CA.
2F2.A$220.CBHGCA$222.B3C!
=====

Tri6Inner-B14x2_S235 is maybe a bit too explosive, but it has some great
ships and some fun blobby chaos. The ship on the left can be used to
make all sorts of rakes.

Code: Select all

x = 142, y = 91, rule = Tri6Inner-B14x2_S235_emulated
17$59.2HE$59.2HB$59.GFDG$61.EHBC.C.C$62.F3.4C$62.A2.HEC.2C$64.2HB.FC$
62.2AGF.HD2C$63.2A.2HCA$62.2A.BDAHA$63.4A2CH8.3A$64.A.A10.C3.A$77.2CB
.A$73.B2.B2CABA$72.F.B2.E2.AF$73.F.A.DC2.EF$74.C.CHCB.G2C$72.F2.A.EA.
DA$70.3AGDHGHEGDE2CA$69.C.2A.2ACG.EHCGFE$69.C.FC2.F.EGHAH2F.C13.3C$
69.C2.FC2.2DHC.EB2ED2A11.C2.C$70.3CBGECGAHG.5B.2HB8.C3.C$74.BA.AEB2F
2.C2F2CFHB.D2A$75.A.A2BGF.HE.ACA2FG.CB.B.C.C$77.CG.GFAG.H.G2CBA2.C.AD
GC2.2A$79.ADFB.2HEA.F3.D.A.AHG2.FA3.C$80.CFBC.G.B.C3.CG2.G.EF2.D2.DFE
A$80.C.2AECFHE.F2D2CD.A.B3.B2.GHAC$81.HACA2.GD.FB.A2.DBFG4.A.CH$81.H
2BABA6.A2.CGBHEBDBA2.2CA$81.FHBF2.2B.DACA3.C3AF2CH2.3C$82.FEC2.DF.C.B
D$42.2HB42.D2.AFHD$42.DHEA36.DA.D2A3C3D$42.C2.C9.2C25.CFA.EA$41.CGAHB
9.C.FA23.C2.C.D$41.C.H2.C8.F.FG24.FC3.DA$41.C.H.A7.2BAFCHC24.DCECFEA$
36.AGB5.2A7.A2.B.2AC22.AEH2.BFC$20.C.GAD10.2AFHB4.C2HB6.A.A.AFBD17.3A
2.AEGFEHC$20.C.C.EF12.HG4.F.2HA6.2A2.A.D17.A3.A2.B2.GC$22.2C.ECD2A6.C
HB.B3.C.C2FB10.2A17.A9.FB$20.DB.H2.2ABC2.2ADC2.AGC2.DBG.C.B30.A3.CB3.
DA11.D2A$20.CGHGD.B.F.CB.2A.BECEDC.C.A2C.B31.A2.2CDF.FA11.C.B$21.C.C.
2B2.DFH2.ACBHFC3.2CD3C39.2CH11.CFD$22.HBA2.C2.F3.C.G.CE$22.F.GE.C2.C
4.FCAC2DF44.DEA$24.F.FA2.F2.C.CFC2F.CF42.AB2H2A$24.F2.A3.3C4.C.C45.GC
.2A17.DC.A$26.2A11.F2.C43.CA.CA17.AHF$109.B.BC$108.C.F2.F$110.A2.BG.C
$111.BFHB.ECA$112.EF3.BD$115.D.FA$112.AG3.C$113.AFBA.EC$113.CDC.G.EC$
117.AGHB.DC$118.AFH.F.C$121.HFC.C$119.D2BH2.C$119.A.A.D2C$120.A2.A$
121.3A!
If anyone wants to do anything further with this neighborhood, the following might be helpful. I much prefer to represent rules as an algorithm rather than a ruletable. Unfortunately, the make-ruletree approach bogs down with more than 8 or so states, and what feels like a three state triangular neighborhood rule to us is really a 9 state rule in Golly. Still, here's how to represent the Tri6inner neighborhood in a make-ruletree algorithm. Take Andrew's TriLife-gen.py, and make the following substitutions:

Code: Select all

prefix = "TriVN6Inner"
name = prefix + '-' + canonrule


def transition_function(s):
   # s[0..8] are cell states in the order NW, NE, SW, SE, N, W, E, S, C
   NW, NE, SW, SE, N, W, E, S, C = s
   
   # count the number of live neighbors for the left and right triangles
   # in the central cell (each triangle has 12 neighbors)
   Lnc = 0
   Rnc = 0
   
   if NW == 1:
      Rnc += 1
   elif NW == 2:
      Lnc +=1
      
   elif NW == 3:
      Lnc += 1
      Rnc += 1
   
   if SE == 1:
      Rnc += 1
   elif SE == 2:
      Lnc += 1
   elif SE == 3:
      Lnc += 1
      Rnc += 1
   
   if SW == 2 or SW == 3: Lnc += 1
   if NE == 1 or NE == 3: Rnc += 1
   
   if N == 1 or N == 3: Rnc += 1
   if E == 1 or E == 3: Rnc += 1

   if S == 2 or S == 3: Lnc += 1
   if W == 2 or W == 3: Lnc += 1
   
   
   
   if C == 0:
      # both triangles are dead, so check for birth(s)
      if Lnc in bset and Rnc in bset: return 3
      if Rnc in bset: return 2
      if Lnc in bset: return 1
      return 0
   elif C == 1:
      # left triangle is alive, right is dead
      Rnc += 1
      if Rnc in bset:
         if Lnc in sset:
            return 3
         else:
            return 2
      else:
         if Lnc in sset:
            return 1
         else:
            return 0
   elif C == 2:
      # left triangle is dead, right is alive
      Lnc += 1
      if Lnc in bset:
         if Rnc in sset:
            return 3
         else:
            return 1
      else:
         if Rnc in sset:
            return 2
         else:
            return 0
   else:
      # C == 3, ie. both triangles are alive, so check if they survive
      Lnc += 1
      Rnc += 1
      if Lnc in sset and Rnc in sset: return 3
      if Rnc in sset: return 2
      if Lnc in sset: return 1
      return 0

EricG
Posts: 199
Joined: August 19th, 2011, 5:41 pm
Location: Chicago-area, USA

Re: Triangular & Tripod von Neuman neighborhoods

Post by EricG » September 10th, 2012, 1:04 am

I haven't gotten to Tri6outer yet. If you look at all those scripts and groan, I don't blame you! I'll gather up some ruletables and ruletrees and icons and put them in a zip file for downloading as I continue this thread.

User avatar
Hektor
Posts: 89
Joined: November 3rd, 2011, 2:37 pm

Re: Triangular & Tripod von Neuman neighborhoods

Post by Hektor » September 10th, 2012, 7:01 am

Very interesting! I love exploring new strange rulespaces, but there seems to be a problem with the General-Bx2 and Tripod-Bx2 rule generators (at least on my computer):

• The rule is succesfully created but I can't load any of your patterns, golly always give me this error
File could not be loaded by any algorithm.

Error from RuleTree:
File not found

Error from QuickLife:
Bad character in rule string.

Error from HashLife:
Bad character in rule string.

Error from Generations:
Missing expected slash in Generations rule

Error from JvN:
This algorithm only supports these rules: JvN29, Nobili32, Hutton32.

Error from RuleTable:
Failed to open file: /Applications/golly-2.4/Rules/Tri6Inner-B1x2_S1_emulated.table
I have no clue on how to fix this...
However great work, as always!

EricG
Posts: 199
Joined: August 19th, 2011, 5:41 pm
Location: Chicago-area, USA

Re: Triangular & Tripod von Neuman neighborhoods

Post by EricG » September 10th, 2012, 10:46 am

Well, for instant gratification (I hope), I'm attaching a folder which contains all the rules mentioned so far. Just move the contents of the folder into your Rules folder, and all of the above rules should work.

My first guess is that your problem is related to your Rules folder. Go to Golly's preferences, go to the Control Preferences, and see which folder is specified for "Your Rules". This folder is where the rules from the zipped folder attached to this post should go. And this folder is where the rules being generated by the Bx2 scripts should be going. Are they actually there, or are they ending up in a different folder?

Once things are working... ...the folder includes the two state rule B1/S in the different neighborhoods, so that they could be compared to B1/S in the four neighbor von Neuman neighborhood.

x = 1, y = 1, rule = B1/SV
o!

x = 1, y = 1, rule = TriVN-2state-B1_S_emulated
A!

x = 1, y = 1, rule = Tripod-2state-B1_S
o!

x = 1, y = 1, rule = Tri6Inner-2state-B1S
A!

Tripod-2state-B1_S is a lot more like B1/SV than the other two are, and yet this similarity does't hold in the Bx2 rules.
Attachments
Triangular_&_Tripod_Rules.zip
(25.82 KiB) Downloaded 315 times

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Tropylium
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Re: Triangular & Tripod von Neuman neighborhoods

Post by Tropylium » September 10th, 2012, 3:18 pm

Tri6Outer is actually a superfluous neighborhood equivalent to two copies of the hexagonal neighborhood running on top of each other: if you color a triangle grid checkerboard-style, then black and white cells can never interact…

—OT for the rulespaces at hand, but one thing I'd like to try sometimes are neighborhoods that are 1) non-connected, and 2) can regardless affect the entire plane. Say, a chess knight neighborhood… Might be simulateable at a slower rate (also using one cell to represent a 2×2 area at least would work, but that'd be one huge kludge).

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Re: Triangular & Tripod von Neuman neighborhoods

Post by EricG » September 10th, 2012, 11:36 pm

Ha! Thank you for pointing that out! I'm rather sorry I didn't implement Tri6outer first though. If I understand your observation correctly, I think I would have been very surprised to see spaceships passing through each other. But that reminds me, I didn't mention the other von Neuman inspired neighborhood I tried out.

The other way to "cut down" the Moore neighborhood is to only consider the the central cell and the NW, NE, SW, and SE corners.
corners-only.jpg
corners-only.jpg (6.35 KiB) Viewed 11143 times
I tried out the Bx2 rules in this "Moore corners only" neighborhood. (Once again, I'm stumped on a good name. Maybe the "Diagonal VN neighborhood"?)

I'm including a ruletree for B1x2/S23 in the "Moore-Corners-Only" neighborhood below. I'm also including the input to make-ruletree.py necessary to generate the ruletree.

You'll also need the original VN-Bx2/S23 ruletree or ruletable for this example, from here: viewtopic.php?f=11&t=949

Here's a fairly simple horizontal structure that produces a complex asymmetric pattern in the original VN-Bx2/S23 rule:

Code: Select all

x = 50, y = 10, rule = VN-B1x2_S23
40B$40B$40B$40B$50B$50B$50B$50B$40B$40B!
Here's the corresponding diagonal sturcture in the corners-only version of the rule:

Code: Select all

x = 57, y = 55, rule = Moore-Corners-Only-B1x2_S23
53.B$52.B.B$51.B.B.B$50.B.B.B.B$49.B.B.B.B$48.B.B.B.B$39.B7.B.B.B.B$
38.B.B5.B.B.B.B$37.B.B.B3.B.B.B.B$36.B.B.B.B.B.B.B.B$35.B.B.B.B.B.B.B
.B$34.B.B.B.B.B.B.B.B$33.B.B.B.B.B.B.B.B$32.B.B.B.B.B.B.B.B$31.B.B.B.
B.B.B.B.B.B$30.B.B.B.B.B.B.B.B.B.B$29.B.B.B.B.B.B.B.B.B.B$28.B.B.B.B.
B.B.B.B.B.B$27.B.B.B.B.B.B.B.B.B.B$26.B.B.B.B.B.B.B.B.B.B$25.B.B.B.B.
B.B.B.B.B.B$24.B.B.B.B.B.B.B.B.B.B$23.B.B.B.B.B.B.B.B.B.B$22.B.B.B.B.
B.B.B.B.B.B$21.B.B.B.B.B.B.B.B.B.B$20.B.B.B.B.B.B.B.B.B.B$19.B.B.B.B.
B.B.B.B.B.B$18.B.B.B.B.B.B.B.B.B.B$17.B.B.B.B.B.B.B.B.B.B$16.B.B.B.B.
B.B.B.B.B.B$15.B.B.B.B.B.B.B.B.B.B$14.B.B.B.B.B.B.B.B.B.B$13.B.B.B.B.
B.B.B.B.B.B$12.B.B.B.B.B.B.B.B.B.B$11.B.B.B.B.B.B.B.B.B.B$10.B.B.B.B.
B.B.B.B.B.B$9.B.B.B.B.B.B.B.B.B.B$8.B.B.B.B.B.B.B.B.B.B$7.B.B.B.B.B.B
.B.B.B.B$6.B.B.B.B.B.B.B.B.B.B$5.B.B.B.B.B.B.B.B.B.B$4.B.B.B.B.B.B.B.
B.B.B$3.B.B.B.B.B.B.B.B.B.B$2.B.B.B.B.B.B.B.B.B.B$.B.B.B.B.B.B.B.B.B.
B$B.B.B.B.B.B.B.B.B.B$.B.B.B.B.B.B.B.B.B$2.B.B.B.B.B.B.B.B$3.B.B.B.B.
B.B.B$4.B.B.B.B.B.B$5.B.B.B.B.B$6.B.B.B.B$7.B.B.B$8.B.B$9.B!
As you can see, the rule looks just like the original VN-B1x2/S23, except titled 45 degrees.

I thought that was pretty neat.

In general, if you make a random field in the corner's only version of the rule, it'll probalby look pretty much like a diagonal version of the original rule. But there is a difference....

Here is an orthogonal ship being destroyed by an oscillator:

Code: Select all

x = 34, y = 12, rule = VN-B1x2_S23
3.2B2.A$3.B4.A18.2B$.3B.4B17.4B$2.B2.4B15.A2.2B2.A$A.BA2B2.A17.4B$3.A
3.A14.AB.2B2.2B.BA$2.B19.AB.2B2.2B.BA$26.4B$24.A2.2B2.A$25.A4.A$27.2B
$27.2A!
And here is the corresponding diagonal ship passing right thorugh the oscillator:

Code: Select all

x = 36, y = 33, rule = Moore-Corners-Only-B1x2_S23
30.B3.A2$30.A.B$31.A.B.B$30.B3.B$29.B3.B$26.A3.B3.B$29.B.B3.B$26.A.B.
B3.B$27.B.B$28.B$29.A.A9$.A3.A.A3.A$A.B7.B.A$.B9.B$4.B.B.B$3.B.B.B.B$
A3.B3.B3.A$3.B5.B$A3.B3.B$3.B.B.B.B.B$4.B.B.B.B$.B7.B.B$A.B5.B.B$.A3.
A!
And I thought that was pretty neat too.


-----

Here's the ruletree for Moore-Corners-Only-B1x2_S23:

Code: Select all

num_states=3
num_neighbors=8
num_nodes=25
1 0 0 0
2 0 0 0
3 1 1 1
4 2 2 2
5 3 3 3
1 1 2 0
2 5 5 5
3 6 6 6
4 7 7 7
5 8 8 8
6 4 4 9
1 0 0 2
2 11 11 11
3 12 12 12
4 13 13 13
5 14 14 14
6 9 9 15
7 10 10 16
6 15 15 15
7 16 16 18
8 17 17 19
6 15 15 4
7 18 18 21
8 19 19 22
9 20 20 23
And here's how the rule can be generated -- select and copy the following onto your clipbard and then click on make-ruletree.py:

Code: Select all

name = "Moore-Corners-Only-B1x2_S23"
n_states = 3
n_neighbors = 8

def transition_function(a):
    NW_weight = 1
    NN_weight = 0
    NE_weight = 1
    WW_weight = 0
    EE_weight = 0
    SW_weight = 1
    SS_weight = 0
    SE_weight = 1

    RB = [1]
    RS = [2, 3]

   # The order for 8 neighbors in a is [NW, NE, SW, SE, N, W, E, S, C]

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

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

    if a[8] == 1 and n in RB:
        return 2
         
    if  a[8] == 2 and n in RS:
        return 2 

      
    return 0

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Tropylium
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Re: Triangular & Tripod von Neuman neighborhoods

Post by Tropylium » September 11th, 2012, 4:53 am

EricG wrote:Ha! Thank you for pointing that out! I'm rather sorry I didn't implement Tri6outer first though. If I understand your observation correctly, I think I would have been very surprised to see spaceships passing through each other. But that reminds me, I didn't mention the other von Neuman inspired neighborhood I tried out.

The other way to "cut down" the Moore neighborhood is to only consider the the central cell and the NW, NE, SW, and SE corners(…)
Yes, as you probably realized but don't say, that's pretty much the same thing as Tri6Outer too: the von Neumann neighborhood, running on squares of one parity.

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Re: Triangular & Tripod von Neuman neighborhoods

Post by EricG » September 11th, 2012, 11:51 am

Right, sorry, I put together most of that post when I thought it would go in one of the VN-B1x2/S23 threads - I should have rewritten it for this context.

About the knight's move neighborhood ( http://www.math.cornell.edu/~numb3rs/li ... t_move.jpg ), do you have any intuition (or predictions) about which kinds of rules would be interesting? (Spaceships, no explosive static, etc.) If two state rules or generations rules are likely to be interesting, I could look at dusting off a homebrewed web-based program and modify it for that neighborhood. Not sure off hand how much extra work Bx2 rules would take.

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Re: Triangular & Tripod von Neuman neighborhoods

Post by Tropylium » September 11th, 2012, 3:15 pm

I actually put together a 32 states, slowdown-by-2 version to test (I suppose a marginally less ugly approach than the 2×2-cell one)… Thus far checked: B2/S and B2/S2 both tend to explode into messes at 5c/2, with no sight of spaceships. B3 should also be able to grow though, I'll check those later (it takes a while to add new conditions under the approach I'm using).

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Re: Triangular & Tripod von Neuman neighborhoods

Post by muzik » July 18th, 2020, 12:28 pm

Tri6inner and Tripod replicators:

Code: Select all

x = 1, y = 1, rule = B135/S135LI
o!

Code: Select all

x = 1, y = 1, rule = B135/S0246LI
o!

Code: Select all

x = 1, y = 1, rule = B13/S13HT
o!

Code: Select all

x = 1, y = 1, rule = B13/S02HT
o!

The Tri6inner replicators can be seen to, when run with a step of 2, be identical to range 2 hexagonal replicators:

Code: Select all

x = 9, y = 5, rule = R2,C2,S1,3,5,7,9,11,13,15,17,B1,3,5,7,9,11,13,15,17,NH
o!

Code: Select all

x = 9, y = 5, rule = R2,C2,S0,2,4,6,8,10,12,14,16,18,B1,3,5,7,9,11,13,15,17,NH
o!

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