I suspect that a rulestring's sensitivity correlates tightly with the soup propagation speed.
could be used to define the classes of CA more formally?
# soup-propagation-distance.py
# Estimates the soup propagation distance of a rule. Estimates approaching 4 digits are unrealiable.
# Tanner Jacobi, August 2015
import golly as g
# Clear out layer 0 for use
g.setlayer(0)
g.addlayer()
g.setlayer(0)
g.dellayer()
# Pick your desired rule and level of patience
g.setrule(g.getstring("Which rule to use?", "B3/S23"))
tedium = int(g.getstring("How many soups to average over?", "10"))
disttotal = 0
g.show("Performing trial 1 of " + str(tedium) + ". Current Mean: 0.000")
for x in range(1, tedium+1):
# Set up layer 1. Empty layer 0 already here.
g.addlayer()
g.setlayer(1)
# Run two random 1999x1999 soups that differ only by the central cell for 30,000 generations
g.select([-999,-999,1999,1999])
g.randfill(50)
soup = g.getcells(g.getselrect())
g.setcell(0,0,1)
g.setlayer(0)
g.putcells(soup,0,0)
g.setcell(0,0,0)
g.run(30000)
g.setlayer(1)
g.run(30000)
# Xor the results.
WhereToXor = g.getrect()
LayerOneAsh = g.getcells(WhereToXor)
g.setlayer(0)
g.putcells(LayerOneAsh,0,0,1,0,0,1,"xor")
# Find propagation distance from the xor result and accumulate
dist = g.getrect()
bugdist = g.getrect()
if dist: # If dist is empty, propagation was zero, so we'll skip evaluating and accumulating
dist[2] = dist[0] + dist[2] - 1
dist[3] = dist[1] + dist[3] - 1
dist[0] = abs(dist[0])
dist[1] = abs(dist[1])
disttotal = disttotal + max(dist)
# Progress update before next trial
g.show("Performing trial " + str(x+1) + " of " + str(tedium) + ". Current Mean: " + '%.3f'%(disttotal/float(x)))
# Remove layers; it's faster than deleting everything for large patterns. Leave with an empty layer 0.
g.addlayer()
g.movelayer(g.getlayer(),0)
g.setlayer(2)
g.dellayer()
g.dellayer()
# When all the tedium is done, report average
g.show("Done. Estimate for rule " + g.getrule() + ": " + str('%.3f'%(disttotal/float(tedium))))
Kazyan wrote:From running this script, Life seems to have a soup propagation distance of about 444.8, from 1,000 trials.
Kiran wrote:The average maximum Moore distance a 1 achieves from {0,0} is the soup propagation distance of that rule.
Kazyan wrote:However, Golly does not "support" toruses so much as it "tolerates" them
By superimposing 338 xored results, it is shown that that the probability for a 1 to appear at some place only depends on its Euclidean distance to the center.
Kiran wrote:Also, to better visualize the effect a four state rule can be used with black (0,0) cells, red (0,1) cells, green (1,0) cells and white (1,1) cells that together simulate two independent universes at once.
@RULE doublelife
@TABLE
n_states:4
neighborhood:Moore
symmetries:permute
var a={3,1}
var a3=a
var a2=a
var a1=a
var a4=a
var a5=a
var a6=a
var a7=a
var b={0,2}
var b3=b
var b2=b
var b1=b
var b4=b
var b5=b
var b6=b
var b7=b
var c={2,1}
var c3=c
var c2=c
var c1=c
var c4=c
var c5=c
var c6=c
var c7=c
var d={0,3}
var d3=d
var d2=d
var d1=d
var d4=d
var d5=d
var d6=d
var d7=d
var x={0,3,2,1}
var x3=x
var x2=x
var x1=x
var x4=x
var x5=x
var x6=x
var x7=x
var x8=x
x,3,3,3,2,2,2,0,0,1
x,3,3,1,2,2,0,0,0,1
x,3,1,1,2,0,0,0,0,1
x,1,1,1,0,0,0,0,0,1
3,2,2,2,3,3,0,0,0,1
3,2,2,1,3,0,0,0,0,1
3,2,1,1,0,0,0,0,0,1
2,3,3,3,2,2,0,0,0,1
2,3,3,1,2,0,0,0,0,1
2,3,1,1,0,0,0,0,0,1
1,3,3,2,2,2,0,0,0,1
1,3,1,2,2,0,0,0,0,1
1,1,1,2,0,0,0,0,0,1
1,3,3,3,2,2,0,0,0,1
1,3,3,1,2,0,0,0,0,1
1,3,1,1,0,0,0,0,0,1
1,3,3,2,2,0,0,0,0,1
1,3,1,2,0,0,0,0,0,1
1,1,1,0,0,0,0,0,0,1
x,a,a3,a2,b3,b2,b1,b4,b5,3
x,a,a3,a2,b3,b2,b1,b4,b5,3
3,a,a3,b3,b2,b1,b4,b5,b6,3
1,a,a3,b3,b2,b1,b4,b5,b6,3
x,c,c3,c2,d3,d2,d1,d4,d5,2
x,c,c3,c2,d3,d2,d1,d4,d5,2
2,c,c3,d3,d2,d1,d4,d5,d6,2
1,c,c3,d3,d2,d1,d4,d5,d6,2
x,x3,x2,x1,x4,x5,x6,x7,x8,0
@COLORS
0 0 0 0
1 255 255 255
2 0 255 0
3 255 0 0
x = 250, y = 250, rule = doublelife
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x = 130, y = 179, rule = doublelife
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5.4B.9B2.A11.A2.A4.36B$4.15B3.3A9.2AB3.27B.9B$3.14B7.A10.14B2A16B2.7B
$2.16B18.13B2A16B2.7B$.3A14B19.29B4.6B$.2BA13B20.17B.B.2B10.7B$2.A2.
11B22.15B4.3B10.6B$4.14B20.15B5.A2B.2A6.7B$4.2B2A11B20.13B5.A.A2B.A7.
5B$5.B2A11B22.13B2.A.AB2.A8.6B34.A9.2A$5.14B21.8B4.2A.A.A3.A7.9B33.3A
6.B2AB$5.4B.8B4.2A16.6B6.2ABA2.4A.A5.2A.7B10.A24.A5.3B$6.2B2.8B4.A17.
5B8.B2.A.A3.A.A5.A5.4B7.3A23.2A3.B.2B7.A$9.8B2.BA.A17.B.B9.2A.2A2.A2.
A.A2.3A7.4B5.A21.B4.3B.6B4.3A$8.9B2.B2A19.3B9.A.A2.2A3.A3.A10.4B4.2A
19.3B5.8B3.A$8.12B20.B2AB9.A.A15.2A6.9B17.6B3.10B2.2A$8.12B21.2A11.A
17.A7.6B13.4B2.7B2.14B$6.2AB.10B52.A.2A5.6B3.B2.2B2.29B$5.A.AB2.8B54.
A2.A4.47B$5.A6.8B54.2AB3.49B$4.2A5.8B56.14B2A13B2A23B$11.7B58.13B2A
13B2A21B$10.11B16.A11.2A26.51B$10.12B14.A.A9.B2AB25.17B.B5.26B$10.12B
6.A3.2A2.A.A9.3B27.15B10.B2.19B$11.11B5.A.A2.A2.2A.2A9.B.B26.15B12.
19B$9.4B.8B5.A.A3.A.A2.B8.5B27.13B12.21B$9.2A4.7B6.A.4A2.AB2A6.6B29.
13B10.8B2.11B$10.A4.7B8.A3.A.A.2A4.8B28.8B4.2A.A6.2AB2.5B2.11B$7.3A6.
6B7.A2.BA.A2.13B29.6B6.2AB3A3.A.AB2.4B3.9B.B2A$7.A8.7B5.A.2BA.A5.13B
27.5B8.B4.A2.A13.8B.BA.A$16.8B4.2A.2BA5.15B26.B.B9.2A.3A2.2A12.9B4.A$
17.8B7.3B4.15B27.3B9.A.A17.9B5.2A$17.9B7.2B.B.17B25.B2AB9.A.A16.4B2.
3B$16.6B.32B26.2A11.A16.4B4.B$16.7B.17B2A13B54.4B$17.6B2.16B2A14B52.
4B$17.7B.27B3.B2A50.4B$16.35B4.A2.A48.4B$16.19B2.2B2.B3.6B5.2A.A46.4B
$15.18B13.6B7.A45.4B$11.B3.19B10.9B6.2A43.4B$10.2AB.15B2.4B9.2A4.4B
49.4B$10.2A18B2.4B9.A5.4B47.4B$11.B.3B2A12B3.4B5.3A7.4B45.4B$14.2B2A
11B5.4B4.A10.4B43.4B$15.2B2.10B6.4B15.4B41.4B$14.2B3.6B.B9.4B15.4B39.
4B$13.B2AB2.4B14.4B15.4B37.4B$14.2A3.2B2AB14.4B15.4B35.4B$21.2A16.4B
15.4B33.4B$40.4B15.4B31.4B$41.4B15.4B29.4B$42.4B15.4B27.4B$43.4B15.4B
25.4B$44.4B15.4B23.4B$45.4B15.4B21.4B$46.4B15.4B19.4B$47.4B15.4B6.A
10.4B$48.4B15.4B5.3A7.4B$49.4B15.4B7.A5.4B$50.4B15.4B5.2A4.4B$51.4B
15.4B4.9B$52.4B15.4B5.6B$53.4B15.4B2.8B$54.4B15.15B$55.4B15.14B$56.4B
15.13B$57.4B15.10B.B2A$58.4B16.3B2AB3.BA.A$59.4B15.3B2AB6.A$60.4B16.
4B6.2A$61.4B15.3B$62.4B11.AB.2B$63.4B9.A.AB2AB$64.4B8.A.ABABAB$65.4B
4.2A.A.A.A.A2.A$66.4B3.A2.A2.2A.4A$67.4B4.2A4.A$68.4B9.A.A$69.4B9.2A!
Kiran wrote:Can it be done for other rules?
@RULE DoubleB3S23
@TABLE
n_states:4
neighborhood:Moore
symmetries:permute
# 0x01 bit ON
var a={1,3}
var aa=a
var ab=a
var ac=a
var ad=a
var ae=a
var af=a
var ag=a
# 0x01 bit OFF
var b={0,2}
var ba=b
var bb=b
var bc=b
var bd=b
var be=b
var bf=b
var bg=b
# 0x10 bit ON
var c={2,3}
var ca=c
var cb=c
var cc=c
var cd=c
var ce=c
var cf=c
var cg=c
# 0x10 bit OFF
var d={0,1}
var da=d
var db=d
var dc=d
var dd=d
var de=d
var df=d
var dg=d
# don't-care cells
var x={0,1,2,3}
var xa=x
var xb=x
var xc=x
var xd=x
var xe=x
var xf=x
var xg=x
var xh=x
# birth for both 0x01 and 0x10 bits
x,1,1,1,2,2,2,0,0,3
x,1,1,3,2,2,0,0,0,3
x,1,3,3,2,0,0,0,0,3
x,3,3,3,0,0,0,0,0,3
# survival for 0x01 bit, birth for 0x10 bit
1,2,2,2,1,1,0,0,0,3
1,2,2,3,1,0,0,0,0,3
1,2,3,3,0,0,0,0,0,3
# birth for 0x01 bit, survival for 0x10 bit
2,1,1,1,2,2,0,0,0,3
2,1,1,3,2,0,0,0,0,3
2,1,3,3,0,0,0,0,0,3
# 2-neighbor survival for 0x01 bit, 3-neighbor survival for 0x10 bit
3,1,1,2,2,2,0,0,0,3
3,1,3,2,2,0,0,0,0,3
3,3,3,2,0,0,0,0,0,3
# 3-neighbor survival for 0x01 bit, 2-neighbor survival for 0x10 bit
3,1,1,1,2,2,0,0,0,3
3,1,1,3,2,0,0,0,0,3
3,1,3,3,0,0,0,0,0,3
# 2-neighbor survival for both 0x01 and 0x10 bits
3,1,1,2,2,0,0,0,0,3
3,1,3,2,0,0,0,0,0,3
3,3,3,0,0,0,0,0,0,3
# birth for 0x01 bit, death for 0x10 bit
x,a,aa,ab,ba,bb,bc,bd,be,1
x,a,aa,ab,ba,bb,bc,bd,be,1
1,a,aa,ba,bb,bc,bd,be,bf,1
3,a,aa,ba,bb,bc,bd,be,bf,1
# death for 0x01 bit, birth for 0x10 bit
x,c,ca,cb,da,db,dc,dd,de,2
x,c,ca,cb,da,db,dc,dd,de,2
2,c,ca,da,db,dc,dd,de,df,2
3,c,ca,da,db,dc,dd,de,df,2
# death for both bits
x,xa,xb,xc,xd,xe,xf,xg,xh,0
@COLORS
0 0 0 0
1 255 0 0
2 0 255 0
3 255 255 255
I found it a little confusing that the combined state was mapped onto state 1.
Kiran wrote:I found it a little confusing that the combined state was mapped onto state 1.
This makes it easier to set up a soup propagation test because the soup can be generated using golly's random fill in a 2-state rule then the rule can be changed and finally the origin is changed to a green or red cell.
import golly as g
import itertools
answer = g.getstring("Enter x y half-diameters for soup propagation trial:",
"100 100",
"Soup size")
xy = answer.split()
# extract x and y amounts
if len(xy) == 0: xy = [100,100]
if len(xy) == 1: g.exit("Supply x and y amounts separated by a space.")
x = int(xy[0])
y = int(xy[1])
if x==0: x=100
if y==0: y=100
if g.getname()!="DoubleSoupTest":
g.addlayer()
g.setname("DoubleSoupTest")
else:
g.new("DoubleSoupTest")
g.select([-x,-y,x*2+1, y*2+1])
g.setrule("B3S23")
g.randfill(50)
g.setrule("DoubleB3S23")
cells=g.getcells(g.getselrect())
coords = zip(cells[0::3],cells[1::3],[3]*len(cells[2::3]))
flatclist = list(itertools.chain.from_iterable(coords))
if len(coords)%2==0: flatclist += [0]
# if the above line is not included, the list gets interpreted
# as a two-state list half the time -- very weird when you first see it!
g.putcells(g.join(flatclist, [0,0,1]))
import golly as g
import itertools
import os
# Blazingly fast way to convert one state to another
# -- used in this case to move DoubleB3S23 state 1, from g.randfill(), to state 3
def CreateRule():
fname = os.path.join(g.getdir("rules"), "Double123StateFixer.rule")
if not os.path.exists(fname):
with open(fname, 'wb') as f:
f.write('@RULE Double123StateFixer\n\n')
f.write('@TABLE\nn_states:4\nneighborhood:vonNeumann\nsymmetries:none\n\n')
f.write('var a={0,1,2,3}\nvar b={a}\nvar c={a}\nvar d={a}\nvar f={a}\n\n')
f.write('1,a,b,c,d,3\n')
CreateRule()
answer = g.getstring("Enter x y half-diameters for soup propagation trial:",
"500 500",
"Soup size")
xy = answer.split()
# extract x and y amounts
if len(xy) == 0: xy = [500,500]
if len(xy) == 1: g.exit("Supply x and y amounts separated by a space.")
x = int(xy[0])
y = int(xy[1])
if x==0: x=500
if y==0: y=500
if g.getname()!="DoubleSoupTest":
g.addlayer()
g.setname("DoubleSoupTest")
else:
g.new("DoubleSoupTest")
g.select([-x,-y,x*2+1, y*2+1])
g.setrule("B3S23")
g.randfill(50)
oldrule = g.setrule("Double123StateFixer")
g.run(1)
step = g.getstep()
g.setrule("DoubleB3S23")
g.setstep(step)
g.setgen("-1")
g.setcell(0,0,1)
...Life is almost always lightspeed for connected clusters of cells, and dominated by cluster growth rate outside of them.
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