## Partitioned Cellular Automata

For discussion of other cellular automata.
bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

PCA_12 is a reversible PCA rule that supports guns.

The rule:

Code: Select all

``````  /* Put your state count, neighbor count, and function here */
final static int numStates = 16;
final static int numNeighbors = 4;
private int rule[] = {0,4,2,3,14,6,11,5,8,7,9,13,10,12,1,15};

/* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */
/* order for five neighbors is n, w, e, s, c */
int f(int[] a)
{
int s = 0;
if ((a[3] & 4) > 0)
s = s | 1;
if ((a[1] & 8) > 0)
s = s | 2;
if ((a[0] & 1) > 0)
s = s | 4;
if ((a[2] & 2) > 0)
s = s | 8;
return rule[s];
}
``````

Code: Select all

``````@RULE PCA_12
@TREE
num_states=16
num_neighbors=4
num_nodes=31
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
2 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
1 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
2 3 3 3 3 4 4 4 4 3 3 3 3 4 4 4 4
3 2 2 5 5 2 2 5 5 2 2 5 5 2 2 5 5
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
2 7 7 7 7 8 8 8 8 7 7 7 7 8 8 8 8
1 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
1 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
2 10 10 10 10 11 11 11 11 10 10 10 10 11 11 11 11
3 9 9 12 12 9 9 12 12 9 9 12 12 9 9 12 12
4 6 6 6 6 6 6 6 6 13 13 13 13 13 13 13 13
1 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
1 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 15 15 15 15 16 16 16 16 15 15 15 15 16 16 16 16
1 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
1 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
2 18 18 18 18 19 19 19 19 18 18 18 18 19 19 19 19
3 17 17 20 20 17 17 20 20 17 17 20 20 17 17 20 20
1 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
2 22 22 22 22 23 23 23 23 22 22 22 22 23 23 23 23
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
2 25 25 25 25 26 26 26 26 25 25 25 25 26 26 26 26
3 24 24 27 27 24 24 27 27 24 24 27 27 24 24 27 27
4 21 21 21 21 21 21 21 21 28 28 28 28 28 28 28 28
5 14 29 14 29 14 29 14 29 14 29 14 29 14 29 14 29
``````
The reverse rule:

Code: Select all

``````  /* Put your state count, neighbor count, and function here */
final static int numStates = 16;
final static int numNeighbors = 4;
private int rule[] = {0,14,2,3,1,7,5,9,8,10,12,6,13,11,4,15};

/* order for nine neighbors is nw, ne, sw, se, n, w, e, s, c */
/* order for five neighbors is n, w, e, s, c */
int f(int[] a)
{
int s = 0;
if ((rule[a[3]] & 4) > 0)
s = s | 1;
if ((rule[a[1]] & 8) > 0)
s = s | 2;
if ((rule[a[0]] & 1) > 0)
s = s | 4;
if ((rule[a[2]] & 2) > 0)
s = s | 8;
return s;
}
``````

Code: Select all

``````@RULE PCA_12R
@TREE
num_states=16
num_neighbors=4
num_nodes=31
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1
1 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
1 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
2 3 4 3 3 3 4 4 3 3 3 4 4 4 3 4 4
3 2 5 5 5 2 5 2 2 2 5 2 5 2 5 2 5
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
2 7 8 7 7 7 8 8 7 7 7 8 8 8 7 8 8
1 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
1 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
2 10 11 10 10 10 11 11 10 10 10 11 11 11 10 11 11
3 9 12 12 12 9 12 9 9 9 12 9 12 9 12 9 12
4 6 13 6 6 6 6 6 13 13 13 13 6 13 13 6 13
1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
2 15 16 15 15 15 16 16 15 15 15 16 16 16 15 16 16
1 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
1 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
2 18 19 18 18 18 19 19 18 18 18 19 19 19 18 19 19
3 17 20 20 20 17 20 17 17 17 20 17 20 17 20 17 20
1 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
2 22 23 22 22 22 23 23 22 22 22 23 23 23 22 23 23
1 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
1 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
2 25 26 25 25 25 26 26 25 25 25 26 26 26 25 26 26
3 24 27 27 27 24 27 24 24 24 27 24 27 24 27 24 27
4 21 28 21 21 21 21 21 28 28 28 28 21 28 28 21 28
5 14 14 14 29 29 29 29 29 14 14 14 14 29 29 14 29
``````
An irregular gun:

Code: Select all

``````x = 3, y = 4, rule = PCA_12
H\$BOB\$J\$.A!
``````
Run the gun for 1000 steps, then reverse it using the technique described in the previous two posts.

Brian Prentice

wildmyron
Posts: 1347
Joined: August 9th, 2013, 12:45 am

### Re: Partitioned Cellular Automata

Very interesting Brian. Have you been able to stabilise the growing end of that puffer / gun pattern - or have you found a more regular gun?

I decided to take a foray into the world of NewCA.lua
Here is a script to run 2PCA4 rules which can be used with Golly 3.3 (or one of the earlier 3.3 betas with NewCA.lua included). Save it as a file named PCA.lua

It has similar functionality to the RPCA java application. "alt R" to generate a new rule with a random pattern (restricted to reversible rules), "alt V" to change the direction for reversible rules. Like RPCA.jar the generation counter continues to increment even in reverse (this is a limitation of NewCA.lua). It is a fair bit slower than the Java app, but can be sped up a fair bit for low population patterns by increasing the step. Strobing rules and other rules with "birth" on state 0 will run, but there's no built in strobing support like with Andrew's Margolus.lua.

Code: Select all

``````--[[
This script lets you explore CA rules using the Partitioned Cellular
Automata scheme.
Author: Arie Paap (wildmyron@gmail.com), October 2019.
Adapted from Margolus.lua and other NewCA.lua scripts by Andrew Treverrow
NextVal() based on Java and Golly RuleTree implementation of PCA rules by Brian Prentice
--]]

local g = golly()
local gp = require "gplus"
local split = gp.split
local floor = math.floor

require "gplus.NewCA"
SCRIPT_NAME = "PCA"
DEFAULT_RULE = "2PCA4,0,4,8,3,1,10,6,7,2,9,5,11,12,13,14,15" -- Model 1
RULE_HELP = [[
This script lets you explore Partitioned Cellular Automata (PCA).
It currently only supports 2-state PCA with 4 neighbours (2PCA4)
Rule strings are of the form kPCAn,s,s,s,s,s,s,s,s,s,s,s,s,s,s,s,s
where 'k' is the number of states (must be 2), 'n' is the number of neighbours
(must be 4) and there must be 16 's' numbers with values from 0 to 15.
<p>
You can enter rules using one of the following aliases (case must match):
<p>
<center>
<table cellspacing=1 border=2 cols=2 width="90%%">
<tr><td align=right> Alias    &nbsp;</td><td>&nbsp; Rule </td></tr>
<tr><td align=right> Model_1 / PCA_1    &nbsp;</td><td>&nbsp; 2PCA4,0,4,8,3,1,10,6,7,2,9,5,11,12,13,14,15 </td></tr>
<tr><td align=right> PCA_2    &nbsp;</td><td>&nbsp; 2PCA4,0,2,4,3,8,10,6,7,1,9,5,11,12,13,14,15 </td></tr>
<tr><td align=right> PCA_3    &nbsp;</td><td>&nbsp; 2PCA4,0,8,1,3,2,5,6,7,4,9,10,11,12,13,14,15 </td></tr>
<tr><td align=right> PCA_4    &nbsp;</td><td>&nbsp; 2PCA4,0,2,4,12,8,5,9,7,1,6,10,11,3,13,14,15 </td></tr>
<tr><td align=right> Model_2 / PCA_5    &nbsp;</td><td>&nbsp; 2PCA4,0,4,8,3,1,10,6,11,2,9,5,13,12,14,7,15 </td></tr>
<tr><td colspan=2> PCA_6 - PCA_12: 2PCA4 rules as defined by Brian Prentice at the link below</td></tr>
</table>
</center>
<p>
For more details about 2D Partitioned Cellular Automata see this link:<br>
<a href="http://www.conwaylife.com/forums/viewtopic.php?f=11&t=4098">
http://www.conwaylife.com/forums/viewtopic.php?f=11&t=4098</a>,<br>
and references therein. Model 1 and Model 2 are two reversible PCA rules shown
to be computation universal by Kenichi Morita <i>et al.</i>
]]

-- the following are non-local so a startup script can change them
DEFWD, DEFHT = 500, 500         -- default grid size
aliases = {
Model_1     = "2PCA4,0,4,8,3,1,10,6,7,2,9,5,11,12,13,14,15",
PCA_1       = "2PCA4,0,4,8,3,1,10,6,7,2,9,5,11,12,13,14,15",
PCA_2       = "2PCA4,0,2,4,3,8,10,6,7,1,9,5,11,12,13,14,15",
PCA_3       = "2PCA4,0,8,1,3,2,5,6,7,4,9,10,11,12,13,14,15",
PCA_4       = "2PCA4,0,2,4,12,8,5,9,7,1,6,10,11,3,13,14,15",
Model_2     = "2PCA4,0,4,8,3,1,10,6,11,2,9,5,13,12,14,7,15",
PCA_5       = "2PCA4,0,4,8,3,1,10,6,11,2,9,5,13,12,14,7,15",
PCA_6       = "2PCA4,0,2,4,3,8,10,6,14,1,9,5,7,12,11,13,15",
PCA_7       = "2PCA4,0,2,4,12,8,5,9,14,1,6,10,7,3,11,13,15",
PCA_8       = "2PCA4,0,2,4,12,8,10,9,14,1,6,5,7,3,11,13,15",
PCA_9       = "2PCA4,0,2,4,12,8,10,9,13,1,6,5,14,3,7,11,15",
PCA_10      = "2PCA4,0,1,2,3,4,5,6,13,8,9,10,14,12,7,11,15",
PCA_11      = "2PCA4,0,4,8,3,1,10,6,11,2,9,5,11,13,12,14,15",
PCA_12      = "2PCA4,0,4,2,3,14,6,11,5,8,7,9,13,10,12,1,15",
}

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

-- Rule variables set by ParseRule and used in NextPattern
NextPattern = function() end    -- ParseRule sets this to SlowPattern or FastPattern
local transition = {}           -- Transition table used to run PCA rules forwards
local inv_transition = {}       -- Lookup table used to run reversible PCA rules backwards
local reversible = false        -- True for reversible PCA (RPCA) rules
local direction = 1             -- >0 if running forwards, <0 if running backwards
local numstates = 2             -- Allowed states for each partition
local numneighbors = 4          -- Neighbourhood is von Neumann (ignoring centre cell)
local maxstate = floor(2^4)-1   -- Cell state representing all partitions (S=1, W=2, N=3, E=4)

function ParseRule(newrule)
-- Parse the given rule string.
-- If valid then return nil, the canonical rule string,
-- the width and height of the grid, and the number of states.
-- If not valid then just return an appropriate error message.
-- Default: 2PCA4,0,4,8,3,1,10,6,7,2,9,5,11,12,13,14,15

if #newrule == 0 then
newrule = DEFAULT_RULE  -- should be a valid rule!
else
-- check for a known alias
local rule = aliases[newrule]
if rule then
newrule = rule
elseif newrule:find(":") then
-- try without the suffix
local p, s = split(newrule,":")
rule = aliases[p]
if rule then newrule = rule..":"..s end
end
end

local prefix, suffix = split(newrule:upper(),":")

-- check for a valid prefix
if prefix:sub(1,5) ~= "2PCA4" then
return "Rule must start with kPCAn. Only k=2 and n=4 are currently supported."
end

-- fill the transition table for use in NextPattern
transition = {}
local i = 0
for n in string.gmatch(prefix, "[,;_](%d+)") do
if tonumber(n) > maxstate then
return "Bad number: "..n.." (must be from 0 to "..maxstate..")."
end
transition[i] = tonumber(n)
i = i + 1
if i > (maxstate + 1) then break end
end
if i ~= (maxstate + 1) then
return string.format("Rule must specify %d comma-separated numbers from 0 to %d.", maxstate + 1, maxstate)
end

-- invert the transition table for reversible rules
inv_transition = {}
reversible = true
direction = 1
for i = 0, maxstate do
inv_transition[i] = -1
end
for i = 0, maxstate do
inv_transition[transition[i]] = i
end
for i = 0, maxstate do
if inv_transition[i] < 0 then
reversible = false
break
end
end

-- check for a valid suffix like T50 or T50,30
local wd, ht = DEFWD, DEFHT
if suffix then
if suffix:find(",") then
wd, ht = suffix:match("^T(%d+),(%d+)\$")
else
wd = suffix:match("^T(%d+)\$")
ht = wd
end
wd = tonumber(wd)
ht = tonumber(ht)
if wd == nil or ht == nil then
return "Rule suffix must be Twd,ht or Twd."
end
end
if wd < 4 then wd = 4 elseif wd > 1000 then wd = 1000 end
if ht < 4 then ht = 4 elseif ht > 1000 then ht = 1000 end

-- given rule is valid

-- create the canonical form of the given rule
local canonrule = numstates.."PCA"..numneighbors
for i = 0, 15 do
canonrule = canonrule..","..transition[i]
end
canonrule = canonrule..":T"..wd..","..ht

if transition[0] == 0 then
NextPattern = FastPattern
else
NextPattern = SlowPattern
end

return nil, canonrule, wd, ht, maxstate + 1
end

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

local function NextVal(x, y, minx, miny, maxx, maxy, emptycells)
-- Calculate the next state of a cell at (x,y)
-- If called with arg <emptycells>, then record coords of empty neighbours

local get = g.getcell
local gridwd = maxx-minx+1
local keepempty = false
if emptycells then keepempty = true end

-- for neighbour coordinates
local xm1 = x-1
local xp1 = x+1
local ym1 = y-1
local yp1 = y+1
-- might need to wrap edges
if xm1 < minx then xm1 = maxx end
if xp1 > maxx then xp1 = minx end
if ym1 < miny then ym1 = maxy end
if yp1 > maxy then yp1 = miny end

local S = get(x, yp1)
local W = get(xm1, y)
local N = get(x, ym1)
local E = get(xp1, y)
if direction < 0 then
S = inv_transition[S]
W = inv_transition[W]
N = inv_transition[N]
E = inv_transition[E]
end
local state = 0
if S == 0 then
if keepempty then emptycells[(yp1 - miny) * gridwd + (x - minx)] = 1 end
elseif (S & 4) > 0 then
state = state + 1
end
if W == 0 then
if keepempty then emptycells[(y - miny) * gridwd + (xm1 - minx)] = 1 end
elseif (W & 8) > 0 then
state = state + 2
end
if N == 0 then
if keepempty then emptycells[(ym1 - miny) * gridwd + (x - minx)] = 1 end
elseif (N & 1) > 0 then
state = state + 4
end
if E == 0 then
if keepempty then emptycells[(y - miny) * gridwd + (xp1 - minx)] = 1 end
elseif (E & 2) > 0 then
state = state + 8
end

if direction > 0 then
state = transition[state]
end
return state
end

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

function FastPattern(currcells, minx, miny, maxx, maxy)
-- Create the next pattern when transition[0] == 0
-- currcells is a non-empty cell array containing the current pattern.
-- minx, miny, maxx, maxy are the cell coordinates of the grid edges.
-- This function must return the new pattern as a cell array.

local newcells = {}         -- cell array for the new pattern (one-state)
local newlen = 0            -- length of newcells
local emptycells = {}       -- keys are x,y coords for empty cells
local gridwd = maxx-minx+1

local currlen = #currcells  -- currcells is multi-state so currlen is odd
if currlen % 3 > 0 then
currlen = currlen - 1   -- ignore padding int
end
for i = 1, currlen, 3 do
local x = currcells[i]
local y = currcells[i+1]

local newstate = NextVal(x, y, minx, miny, maxx, maxy, emptycells)
if newstate > 0 then
newlen = newlen+1 ; newcells[newlen] = x
newlen = newlen+1 ; newcells[newlen] = y
newlen = newlen+1 ; newcells[newlen] = newstate
end
end

-- now go through emptycells and add any births to newcells
for k,v in pairs(emptycells) do
local x = minx + (k % gridwd)
local y = miny + (k // gridwd)

local newstate = NextVal(x, y, minx, miny, maxx, maxy)
if newstate > 0 then
newlen = newlen + 1 ; newcells[newlen] = x
newlen = newlen + 1 ; newcells[newlen] = y
newlen = newlen + 1 ; newcells[newlen] = newstate
end
end

if newlen > 0 then
-- newcells is a multi-state cell array so ensure length is odd
if newlen & 1 == 0 then newcells[newlen+1] = 0 end
end

-- delete the old pattern and add the new pattern
g.putcells(currcells, 0, 0, 1, 0, 0, 1, "xor")
g.putcells(newcells)
if direction < 0 then
g.show("reverse")
end

return newcells     -- return the new pattern
end

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

function SlowPattern(currcells, minx, miny, maxx, maxy)
-- Create the next pattern when transition[0] > 0 and we have to examine
-- every cell in the grid (so very slow).
-- currcells is a non-empty cell array containing the current pattern.
-- minx, miny, maxx, maxy are the cell coordinates of the grid edges.
-- This function must return the new pattern as a cell array.
-- TODO cache rows to minimise the number of get calls
--      requires completely different NextVal()

local newcells = {}         -- cell array for the new pattern (one-state)
local newlen = 0            -- length of newcells

for y = miny, maxy do
for x = minx, maxx do
local newstate = NextVal(x, y, minx, miny, maxx, maxy)
if newstate > 0 then
newlen = newlen+1 ; newcells[newlen] = x
newlen = newlen+1 ; newcells[newlen] = y
newlen = newlen+1 ; newcells[newlen] = newstate
end
end
end

if newlen > 0 then
-- newcells is a multi-state cell array so ensure length is odd
if newlen & 1 == 0 then newcells[newlen+1] = 0 end
end

-- delete the old pattern and add the new pattern
g.putcells(currcells, 0, 0, 1, 0, 0, 1, "xor")
g.putcells(newcells)
if direction < 0 then
g.show("reverse")
end

return newcells     -- return the new pattern
end

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

-- user's startup script might want to override this
function RandomRule(reversible)
local reversible = reversible or true
local rand = math.random
local rule = numstates.."PCA"..numneighbors..",0"  -- avoid strobing rules
if reversible then
local states = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
for i = 1, 15 do
rule = rule..","..table.remove(states, rand(1,#states))
end
else
for i = 1, 15 do
rule = rule..","..rand(0,15)
end
end
return rule
end

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

-- allow alt-R to create a random pattern with a random rule
local saveHandleKey = HandleKey
function HandleKey(event)
local _, key, mods = split(event)
if key == "r" and mods == "alt" then
SetRule(RandomRule())
RandomPattern(nil, 20, 20)
elseif key == "v" and mods == "alt" then
if reversible then
direction = direction * -1
if direction < 0 then
g.show("reverse")
end
else
g.warn("Rule is not reversible.")
end
else
-- pass the event to the original HandleKey
saveHandleKey(event)
end
end

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

-- and away we go...
StartNewCA()
``````
The following rule can be used to display the icons I posted earlier for PCA_5. This will mean there are some funny icons used for a range 1 LtL rule and other 16 state rules using NewCA.lua, but I don't think it's an issue. Currently there's no built in way for NewCA.lua to change the icons.

Code: Select all

``````@RULE R1,C16,M0,S1..1,B1..1,NM
Icons for Partitioned Cellular Automata (PCA) rules which are simulated with
PCA.lua (and NewCA.lua which relies on the LtL Golly algo)
These icons are for 2 state PCA with 4 neighbours

@ICONS

XPM
/* width height num_colors chars_per_pixel */
"31 465 2 1"
/* colors */
". c #000000"
"B c #FFFFFF"
/* icon for state 1 */
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"...............B..............."
"..............BBB.............."
".............BBBBB............."
"............BBBBBBB............"
"...........BBBBBBBBB..........."
"..........BBBBBBBBBBB.........."
".........BBBBBBBBBBBBB........."
"........BBBBBBBBBBBBBBB........"
".......BBBBBBBBBBBBBBBBB......."
"......BBBBBBBBBBBBBBBBBBB......"
".....BBBBBBBBBBBBBBBBBBBBB....."
"....BBBBBBBBBBBBBBBBBBBBBBB...."
"...BBBBBBBBBBBBBBBBBBBBBBBBB..."
"..BBBBBBBBBBBBBBBBBBBBBBBBBBB.."
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
/* icon for state 2 */
"..............................."
"B.............................."
"BB............................."
"BBB............................"
"BBBB..........................."
"BBBBB.........................."
"BBBBBB........................."
"BBBBBBB........................"
"BBBBBBBB......................."
"BBBBBBBBB......................"
"BBBBBBBBBB....................."
"BBBBBBBBBBB...................."
"BBBBBBBBBBBB..................."
"BBBBBBBBBBBBB.................."
"BBBBBBBBBBBBBB................."
"BBBBBBBBBBBBBBB................"
"BBBBBBBBBBBBBB................."
"BBBBBBBBBBBBB.................."
"BBBBBBBBBBBB..................."
"BBBBBBBBBBB...................."
"BBBBBBBBBB....................."
"BBBBBBBBB......................"
"BBBBBBBB......................."
"BBBBBBB........................"
"BBBBBB........................."
"BBBBB.........................."
"BBBB..........................."
"BBB............................"
"BB............................."
"B.............................."
"..............................."
/* icon for state 3 */
"..............................."
"B.............................."
"BB............................."
"BBB............................"
"BBBB..........................."
"BBBBB.........................."
"BBBBBB........................."
"BBBBBBB........................"
"BBBBBBBB......................."
"BBBBBBBBB......................"
"BBBBBBBBBB....................."
"BBBBBBBBBBB...................."
"BBBBBBBBBBBB..................."
"BBBBBBBBBBBBB.................."
"BBBBBBBBBBBBBB................."
"BBBBBBBBBBBBBBB................"
"BBBBBBBBBBBBBB.B..............."
"BBBBBBBBBBBBB.BBB.............."
"BBBBBBBBBBBB.BBBBB............."
"BBBBBBBBBBB.BBBBBBB............"
"BBBBBBBBBB.BBBBBBBBB..........."
"BBBBBBBBB.BBBBBBBBBBB.........."
"BBBBBBBB.BBBBBBBBBBBBB........."
"BBBBBBB.BBBBBBBBBBBBBBB........"
"BBBBBB.BBBBBBBBBBBBBBBBB......."
"BBBBB.BBBBBBBBBBBBBBBBBBB......"
"BBBB.BBBBBBBBBBBBBBBBBBBBB....."
"BBB.BBBBBBBBBBBBBBBBBBBBBBB...."
"BB.BBBBBBBBBBBBBBBBBBBBBBBBB..."
"B.BBBBBBBBBBBBBBBBBBBBBBBBBBB.."
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
/* icon for state 4 */
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
"..BBBBBBBBBBBBBBBBBBBBBBBBBBB.."
"...BBBBBBBBBBBBBBBBBBBBBBBBB..."
"....BBBBBBBBBBBBBBBBBBBBBBB...."
".....BBBBBBBBBBBBBBBBBBBBB....."
"......BBBBBBBBBBBBBBBBBBB......"
".......BBBBBBBBBBBBBBBBB......."
"........BBBBBBBBBBBBBBB........"
".........BBBBBBBBBBBBB........."
"..........BBBBBBBBBBB.........."
"...........BBBBBBBBB..........."
"............BBBBBBB............"
".............BBBBB............."
"..............BBB.............."
"...............B..............."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
"..............................."
/* icon for state 5 */
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
"..BBBBBBBBBBBBBBBBBBBBBBBBBBB.."
"...BBBBBBBBBBBBBBBBBBBBBBBBB..."
"....BBBBBBBBBBBBBBBBBBBBBBB...."
".....BBBBBBBBBBBBBBBBBBBBB....."
"......BBBBBBBBBBBBBBBBBBB......"
".......BBBBBBBBBBBBBBBBB......."
"........BBBBBBBBBBBBBBB........"
".........BBBBBBBBBBBBB........."
"..........BBBBBBBBBBB.........."
"...........BBBBBBBBB..........."
"............BBBBBBB............"
".............BBBBB............."
"..............BBB.............."
"...............B..............."
"..............................."
"...............B..............."
"..............BBB.............."
".............BBBBB............."
"............BBBBBBB............"
"...........BBBBBBBBB..........."
"..........BBBBBBBBBBB.........."
".........BBBBBBBBBBBBB........."
"........BBBBBBBBBBBBBBB........"
".......BBBBBBBBBBBBBBBBB......."
"......BBBBBBBBBBBBBBBBBBB......"
".....BBBBBBBBBBBBBBBBBBBBB....."
"....BBBBBBBBBBBBBBBBBBBBBBB...."
"...BBBBBBBBBBBBBBBBBBBBBBBBB..."
"..BBBBBBBBBBBBBBBBBBBBBBBBBBB.."
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
/* icon for state 6 */
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
"B.BBBBBBBBBBBBBBBBBBBBBBBBBBB.."
"BB.BBBBBBBBBBBBBBBBBBBBBBBBB..."
"BBB.BBBBBBBBBBBBBBBBBBBBBBB...."
"BBBB.BBBBBBBBBBBBBBBBBBBBB....."
"BBBBB.BBBBBBBBBBBBBBBBBBB......"
"BBBBBB.BBBBBBBBBBBBBBBBB......."
"BBBBBBB.BBBBBBBBBBBBBBB........"
"BBBBBBBB.BBBBBBBBBBBBB........."
"BBBBBBBBB.BBBBBBBBBBB.........."
"BBBBBBBBBB.BBBBBBBBB..........."
"BBBBBBBBBBB.BBBBBBB............"
"BBBBBBBBBBBB.BBBBB............."
"BBBBBBBBBBBBB.BBB.............."
"BBBBBBBBBBBBBB.B..............."
"BBBBBBBBBBBBBBB................"
"BBBBBBBBBBBBBB................."
"BBBBBBBBBBBBB.................."
"BBBBBBBBBBBB..................."
"BBBBBBBBBBB...................."
"BBBBBBBBBB....................."
"BBBBBBBBB......................"
"BBBBBBBB......................."
"BBBBBBB........................"
"BBBBBB........................."
"BBBBB.........................."
"BBBB..........................."
"BBB............................"
"BB............................."
"B.............................."
"..............................."
/* icon for state 7 */
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
"B.BBBBBBBBBBBBBBBBBBBBBBBBBBB.."
"BB.BBBBBBBBBBBBBBBBBBBBBBBBB..."
"BBB.BBBBBBBBBBBBBBBBBBBBBBB...."
"BBBB.BBBBBBBBBBBBBBBBBBBBB....."
"BBBBB.BBBBBBBBBBBBBBBBBBB......"
"BBBBBB.BBBBBBBBBBBBBBBBB......."
"BBBBBBB.BBBBBBBBBBBBBBB........"
"BBBBBBBB.BBBBBBBBBBBBB........."
"BBBBBBBBB.BBBBBBBBBBB.........."
"BBBBBBBBBB.BBBBBBBBB..........."
"BBBBBBBBBBB.BBBBBBB............"
"BBBBBBBBBBBB.BBBBB............."
"BBBBBBBBBBBBB.BBB.............."
"BBBBBBBBBBBBBB.B..............."
"BBBBBBBBBBBBBBB................"
"BBBBBBBBBBBBBB.B..............."
"BBBBBBBBBBBBB.BBB.............."
"BBBBBBBBBBBB.BBBBB............."
"BBBBBBBBBBB.BBBBBBB............"
"BBBBBBBBBB.BBBBBBBBB..........."
"BBBBBBBBB.BBBBBBBBBBB.........."
"BBBBBBBB.BBBBBBBBBBBBB........."
"BBBBBBB.BBBBBBBBBBBBBBB........"
"BBBBBB.BBBBBBBBBBBBBBBBB......."
"BBBBB.BBBBBBBBBBBBBBBBBBB......"
"BBBB.BBBBBBBBBBBBBBBBBBBBB....."
"BBB.BBBBBBBBBBBBBBBBBBBBBBB...."
"BB.BBBBBBBBBBBBBBBBBBBBBBBBB..."
"B.BBBBBBBBBBBBBBBBBBBBBBBBBBB.."
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
/* icon for state 8 */
"..............................."
"..............................B"
".............................BB"
"............................BBB"
"...........................BBBB"
"..........................BBBBB"
".........................BBBBBB"
"........................BBBBBBB"
".......................BBBBBBBB"
"......................BBBBBBBBB"
".....................BBBBBBBBBB"
"....................BBBBBBBBBBB"
"...................BBBBBBBBBBBB"
"..................BBBBBBBBBBBBB"
".................BBBBBBBBBBBBBB"
"................BBBBBBBBBBBBBBB"
".................BBBBBBBBBBBBBB"
"..................BBBBBBBBBBBBB"
"...................BBBBBBBBBBBB"
"....................BBBBBBBBBBB"
".....................BBBBBBBBBB"
"......................BBBBBBBBB"
".......................BBBBBBBB"
"........................BBBBBBB"
".........................BBBBBB"
"..........................BBBBB"
"...........................BBBB"
"............................BBB"
".............................BB"
"..............................B"
"..............................."
/* icon for state 9 */
"..............................."
"..............................B"
".............................BB"
"............................BBB"
"...........................BBBB"
"..........................BBBBB"
".........................BBBBBB"
"........................BBBBBBB"
".......................BBBBBBBB"
"......................BBBBBBBBB"
".....................BBBBBBBBBB"
"....................BBBBBBBBBBB"
"...................BBBBBBBBBBBB"
"..................BBBBBBBBBBBBB"
".................BBBBBBBBBBBBBB"
"................BBBBBBBBBBBBBBB"
"...............B.BBBBBBBBBBBBBB"
"..............BBB.BBBBBBBBBBBBB"
".............BBBBB.BBBBBBBBBBBB"
"............BBBBBBB.BBBBBBBBBBB"
"...........BBBBBBBBB.BBBBBBBBBB"
"..........BBBBBBBBBBB.BBBBBBBBB"
".........BBBBBBBBBBBBB.BBBBBBBB"
"........BBBBBBBBBBBBBBB.BBBBBBB"
".......BBBBBBBBBBBBBBBBB.BBBBBB"
"......BBBBBBBBBBBBBBBBBBB.BBBBB"
".....BBBBBBBBBBBBBBBBBBBBB.BBBB"
"....BBBBBBBBBBBBBBBBBBBBBBB.BBB"
"...BBBBBBBBBBBBBBBBBBBBBBBBB.BB"
"..BBBBBBBBBBBBBBBBBBBBBBBBBBB.B"
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
/* icon for state 10 */
"..............................."
"B.............................B"
"BB...........................BB"
"BBB.........................BBB"
"BBBB.......................BBBB"
"BBBBB.....................BBBBB"
"BBBBBB...................BBBBBB"
"BBBBBBB.................BBBBBBB"
"BBBBBBBB...............BBBBBBBB"
"BBBBBBBBB.............BBBBBBBBB"
"BBBBBBBBBB...........BBBBBBBBBB"
"BBBBBBBBBBB.........BBBBBBBBBBB"
"BBBBBBBBBBBB.......BBBBBBBBBBBB"
"BBBBBBBBBBBBB.....BBBBBBBBBBBBB"
"BBBBBBBBBBBBBB...BBBBBBBBBBBBBB"
"BBBBBBBBBBBBBBB.BBBBBBBBBBBBBBB"
"BBBBBBBBBBBBBB...BBBBBBBBBBBBBB"
"BBBBBBBBBBBBB.....BBBBBBBBBBBBB"
"BBBBBBBBBBBB.......BBBBBBBBBBBB"
"BBBBBBBBBBB.........BBBBBBBBBBB"
"BBBBBBBBBB...........BBBBBBBBBB"
"BBBBBBBBB.............BBBBBBBBB"
"BBBBBBBB...............BBBBBBBB"
"BBBBBBB.................BBBBBBB"
"BBBBBB...................BBBBBB"
"BBBBB.....................BBBBB"
"BBBB.......................BBBB"
"BBB.........................BBB"
"BB...........................BB"
"B.............................B"
"..............................."
/* icon for state 11 */
"..............................."
"B.............................B"
"BB...........................BB"
"BBB.........................BBB"
"BBBB.......................BBBB"
"BBBBB.....................BBBBB"
"BBBBBB...................BBBBBB"
"BBBBBBB.................BBBBBBB"
"BBBBBBBB...............BBBBBBBB"
"BBBBBBBBB.............BBBBBBBBB"
"BBBBBBBBBB...........BBBBBBBBBB"
"BBBBBBBBBBB.........BBBBBBBBBBB"
"BBBBBBBBBBBB.......BBBBBBBBBBBB"
"BBBBBBBBBBBBB.....BBBBBBBBBBBBB"
"BBBBBBBBBBBBBB...BBBBBBBBBBBBBB"
"BBBBBBBBBBBBBBB.BBBBBBBBBBBBBBB"
"BBBBBBBBBBBBBB.B.BBBBBBBBBBBBBB"
"BBBBBBBBBBBBB.BBB.BBBBBBBBBBBBB"
"BBBBBBBBBBBB.BBBBB.BBBBBBBBBBBB"
"BBBBBBBBBBB.BBBBBBB.BBBBBBBBBBB"
"BBBBBBBBBB.BBBBBBBBB.BBBBBBBBBB"
"BBBBBBBBB.BBBBBBBBBBB.BBBBBBBBB"
"BBBBBBBB.BBBBBBBBBBBBB.BBBBBBBB"
"BBBBBBB.BBBBBBBBBBBBBBB.BBBBBBB"
"BBBBBB.BBBBBBBBBBBBBBBBB.BBBBBB"
"BBBBB.BBBBBBBBBBBBBBBBBBB.BBBBB"
"BBBB.BBBBBBBBBBBBBBBBBBBBB.BBBB"
"BBB.BBBBBBBBBBBBBBBBBBBBBBB.BBB"
"BB.BBBBBBBBBBBBBBBBBBBBBBBBB.BB"
"B.BBBBBBBBBBBBBBBBBBBBBBBBBBB.B"
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
/* icon for state 12 */
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
"..BBBBBBBBBBBBBBBBBBBBBBBBBBB.B"
"...BBBBBBBBBBBBBBBBBBBBBBBBB.BB"
"....BBBBBBBBBBBBBBBBBBBBBBB.BBB"
".....BBBBBBBBBBBBBBBBBBBBB.BBBB"
"......BBBBBBBBBBBBBBBBBBB.BBBBB"
".......BBBBBBBBBBBBBBBBB.BBBBBB"
"........BBBBBBBBBBBBBBB.BBBBBBB"
".........BBBBBBBBBBBBB.BBBBBBBB"
"..........BBBBBBBBBBB.BBBBBBBBB"
"...........BBBBBBBBB.BBBBBBBBBB"
"............BBBBBBB.BBBBBBBBBBB"
".............BBBBB.BBBBBBBBBBBB"
"..............BBB.BBBBBBBBBBBBB"
"...............B.BBBBBBBBBBBBBB"
"................BBBBBBBBBBBBBBB"
".................BBBBBBBBBBBBBB"
"..................BBBBBBBBBBBBB"
"...................BBBBBBBBBBBB"
"....................BBBBBBBBBBB"
".....................BBBBBBBBBB"
"......................BBBBBBBBB"
".......................BBBBBBBB"
"........................BBBBBBB"
".........................BBBBBB"
"..........................BBBBB"
"...........................BBBB"
"............................BBB"
".............................BB"
"..............................B"
"..............................."
/* icon for state 13 */
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
"..BBBBBBBBBBBBBBBBBBBBBBBBBBB.B"
"...BBBBBBBBBBBBBBBBBBBBBBBBB.BB"
"....BBBBBBBBBBBBBBBBBBBBBBB.BBB"
".....BBBBBBBBBBBBBBBBBBBBB.BBBB"
"......BBBBBBBBBBBBBBBBBBB.BBBBB"
".......BBBBBBBBBBBBBBBBB.BBBBBB"
"........BBBBBBBBBBBBBBB.BBBBBBB"
".........BBBBBBBBBBBBB.BBBBBBBB"
"..........BBBBBBBBBBB.BBBBBBBBB"
"...........BBBBBBBBB.BBBBBBBBBB"
"............BBBBBBB.BBBBBBBBBBB"
".............BBBBB.BBBBBBBBBBBB"
"..............BBB.BBBBBBBBBBBBB"
"...............B.BBBBBBBBBBBBBB"
"................BBBBBBBBBBBBBBB"
"...............B.BBBBBBBBBBBBBB"
"..............BBB.BBBBBBBBBBBBB"
".............BBBBB.BBBBBBBBBBBB"
"............BBBBBBB.BBBBBBBBBBB"
"...........BBBBBBBBB.BBBBBBBBBB"
"..........BBBBBBBBBBB.BBBBBBBBB"
".........BBBBBBBBBBBBB.BBBBBBBB"
"........BBBBBBBBBBBBBBB.BBBBBBB"
".......BBBBBBBBBBBBBBBBB.BBBBBB"
"......BBBBBBBBBBBBBBBBBBB.BBBBB"
".....BBBBBBBBBBBBBBBBBBBBB.BBBB"
"....BBBBBBBBBBBBBBBBBBBBBBB.BBB"
"...BBBBBBBBBBBBBBBBBBBBBBBBB.BB"
"..BBBBBBBBBBBBBBBBBBBBBBBBBBB.B"
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
/* icon for state 14 */
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
"B.BBBBBBBBBBBBBBBBBBBBBBBBBBB.B"
"BB.BBBBBBBBBBBBBBBBBBBBBBBBB.BB"
"BBB.BBBBBBBBBBBBBBBBBBBBBBB.BBB"
"BBBB.BBBBBBBBBBBBBBBBBBBBB.BBBB"
"BBBBB.BBBBBBBBBBBBBBBBBBB.BBBBB"
"BBBBBB.BBBBBBBBBBBBBBBBB.BBBBBB"
"BBBBBBB.BBBBBBBBBBBBBBB.BBBBBBB"
"BBBBBBBB.BBBBBBBBBBBBB.BBBBBBBB"
"BBBBBBBBB.BBBBBBBBBBB.BBBBBBBBB"
"BBBBBBBBBB.BBBBBBBBB.BBBBBBBBBB"
"BBBBBBBBBBB.BBBBBBB.BBBBBBBBBBB"
"BBBBBBBBBBBB.BBBBB.BBBBBBBBBBBB"
"BBBBBBBBBBBBB.BBB.BBBBBBBBBBBBB"
"BBBBBBBBBBBBBB.B.BBBBBBBBBBBBBB"
"BBBBBBBBBBBBBBB.BBBBBBBBBBBBBBB"
"BBBBBBBBBBBBBB...BBBBBBBBBBBBBB"
"BBBBBBBBBBBBB.....BBBBBBBBBBBBB"
"BBBBBBBBBBBB.......BBBBBBBBBBBB"
"BBBBBBBBBBB.........BBBBBBBBBBB"
"BBBBBBBBBB...........BBBBBBBBBB"
"BBBBBBBBB.............BBBBBBBBB"
"BBBBBBBB...............BBBBBBBB"
"BBBBBBB.................BBBBBBB"
"BBBBBB...................BBBBBB"
"BBBBB.....................BBBBB"
"BBBB.......................BBBB"
"BBB.........................BBB"
"BB...........................BB"
"B.............................B"
"..............................."
/* icon for state 15 */
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."
"B.BBBBBBBBBBBBBBBBBBBBBBBBBBB.B"
"BB.BBBBBBBBBBBBBBBBBBBBBBBBB.BB"
"BBB.BBBBBBBBBBBBBBBBBBBBBBB.BBB"
"BBBB.BBBBBBBBBBBBBBBBBBBBB.BBBB"
"BBBBB.BBBBBBBBBBBBBBBBBBB.BBBBB"
"BBBBBB.BBBBBBBBBBBBBBBBB.BBBBBB"
"BBBBBBB.BBBBBBBBBBBBBBB.BBBBBBB"
"BBBBBBBB.BBBBBBBBBBBBB.BBBBBBBB"
"BBBBBBBBB.BBBBBBBBBBB.BBBBBBBBB"
"BBBBBBBBBB.BBBBBBBBB.BBBBBBBBBB"
"BBBBBBBBBBB.BBBBBBB.BBBBBBBBBBB"
"BBBBBBBBBBBB.BBBBB.BBBBBBBBBBBB"
"BBBBBBBBBBBBB.BBB.BBBBBBBBBBBBB"
"BBBBBBBBBBBBBB.B.BBBBBBBBBBBBBB"
"BBBBBBBBBBBBBBB.BBBBBBBBBBBBBBB"
"BBBBBBBBBBBBBB.B.BBBBBBBBBBBBBB"
"BBBBBBBBBBBBB.BBB.BBBBBBBBBBBBB"
"BBBBBBBBBBBB.BBBBB.BBBBBBBBBBBB"
"BBBBBBBBBBB.BBBBBBB.BBBBBBBBBBB"
"BBBBBBBBBB.BBBBBBBBB.BBBBBBBBBB"
"BBBBBBBBB.BBBBBBBBBBB.BBBBBBBBB"
"BBBBBBBB.BBBBBBBBBBBBB.BBBBBBBB"
"BBBBBBB.BBBBBBBBBBBBBBB.BBBBBBB"
"BBBBBB.BBBBBBBBBBBBBBBBB.BBBBBB"
"BBBBB.BBBBBBBBBBBBBBBBBBB.BBBBB"
"BBBB.BBBBBBBBBBBBBBBBBBBBB.BBBB"
"BBB.BBBBBBBBBBBBBBBBBBBBBBB.BBB"
"BB.BBBBBBBBBBBBBBBBBBBBBBBBB.BB"
"B.BBBBBBBBBBBBBBBBBBBBBBBBBBB.B"
".BBBBBBBBBBBBBBBBBBBBBBBBBBBBB."

XPM
/* width height num_colors chars_per_pixel */
"15 225 2 1"
/* colors */
". c #000000"
"B c #FFFFFF"
/* icon for state 1 */
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
".......B......."
"......BBB......"
".....BBBBB....."
"....BBBBBBB...."
"...BBBBBBBBB..."
"..BBBBBBBBBBB.."
".BBBBBBBBBBBBB."
/* icon for state 2 */
"..............."
"B.............."
"BB............."
"BBB............"
"BBBB..........."
"BBBBB.........."
"BBBBBB........."
"BBBBBBB........"
"BBBBBB........."
"BBBBB.........."
"BBBB..........."
"BBB............"
"BB............."
"B.............."
"..............."
/* icon for state 3 */
"..............."
"B.............."
"BB............."
"BBB............"
"BBBB..........."
"BBBBB.........."
"BBBBBB........."
"BBBBBBB........"
"BBBBBB.B......."
"BBBBB.BBB......"
"BBBB.BBBBB....."
"BBB.BBBBBBB...."
"BB.BBBBBBBBB..."
"B.BBBBBBBBBBB.."
".BBBBBBBBBBBBB."
/* icon for state 4 */
".BBBBBBBBBBBBB."
"..BBBBBBBBBBB.."
"...BBBBBBBBB..."
"....BBBBBBB...."
".....BBBBB....."
"......BBB......"
".......B......."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
/* icon for state 5 */
".BBBBBBBBBBBBB."
"..BBBBBBBBBBB.."
"...BBBBBBBBB..."
"....BBBBBBB...."
".....BBBBB....."
"......BBB......"
".......B......."
"..............."
".......B......."
"......BBB......"
".....BBBBB....."
"....BBBBBBB...."
"...BBBBBBBBB..."
"..BBBBBBBBBBB.."
".BBBBBBBBBBBBB."
/* icon for state 6 */
".BBBBBBBBBBBBB."
"B.BBBBBBBBBBB.."
"BB.BBBBBBBBB..."
"BBB.BBBBBBB...."
"BBBB.BBBBB....."
"BBBBB.BBB......"
"BBBBBB.B......."
"BBBBBBB........"
"BBBBBB........."
"BBBBB.........."
"BBBB..........."
"BBB............"
"BB............."
"B.............."
"..............."
/* icon for state 7 */
".BBBBBBBBBBBBB."
"B.BBBBBBBBBBB.."
"BB.BBBBBBBBB..."
"BBB.BBBBBBB...."
"BBBB.BBBBB....."
"BBBBB.BBB......"
"BBBBBB.B......."
"BBBBBBB........"
"BBBBBB.B......."
"BBBBB.BBB......"
"BBBB.BBBBB....."
"BBB.BBBBBBB...."
"BB.BBBBBBBBB..."
"B.BBBBBBBBBBB.."
".BBBBBBBBBBBBB."
/* icon for state 8 */
"..............."
"..............B"
".............BB"
"............BBB"
"...........BBBB"
"..........BBBBB"
".........BBBBBB"
"........BBBBBBB"
".........BBBBBB"
"..........BBBBB"
"...........BBBB"
"............BBB"
".............BB"
"..............B"
"..............."
/* icon for state 9 */
"..............."
"..............B"
".............BB"
"............BBB"
"...........BBBB"
"..........BBBBB"
".........BBBBBB"
"........BBBBBBB"
".......B.BBBBBB"
"......BBB.BBBBB"
".....BBBBB.BBBB"
"....BBBBBBB.BBB"
"...BBBBBBBBB.BB"
"..BBBBBBBBBBB.B"
".BBBBBBBBBBBBB."
/* icon for state 10 */
"..............."
"B.............B"
"BB...........BB"
"BBB.........BBB"
"BBBB.......BBBB"
"BBBBB.....BBBBB"
"BBBBBB...BBBBBB"
"BBBBBBB.BBBBBBB"
"BBBBBB...BBBBBB"
"BBBBB.....BBBBB"
"BBBB.......BBBB"
"BBB.........BBB"
"BB...........BB"
"B.............B"
"..............."
/* icon for state 11 */
"..............."
"B.............B"
"BB...........BB"
"BBB.........BBB"
"BBBB.......BBBB"
"BBBBB.....BBBBB"
"BBBBBB...BBBBBB"
"BBBBBBB.BBBBBBB"
"BBBBBB.B.BBBBBB"
"BBBBB.BBB.BBBBB"
"BBBB.BBBBB.BBBB"
"BBB.BBBBBBB.BBB"
"BB.BBBBBBBBB.BB"
"B.BBBBBBBBBBB.B"
".BBBBBBBBBBBBB."
/* icon for state 12 */
".BBBBBBBBBBBBB."
"..BBBBBBBBBBB.B"
"...BBBBBBBBB.BB"
"....BBBBBBB.BBB"
".....BBBBB.BBBB"
"......BBB.BBBBB"
".......B.BBBBBB"
"........BBBBBBB"
".........BBBBBB"
"..........BBBBB"
"...........BBBB"
"............BBB"
".............BB"
"..............B"
"..............."
/* icon for state 13 */
".BBBBBBBBBBBBB."
"..BBBBBBBBBBB.B"
"...BBBBBBBBB.BB"
"....BBBBBBB.BBB"
".....BBBBB.BBBB"
"......BBB.BBBBB"
".......B.BBBBBB"
"........BBBBBBB"
".......B.BBBBBB"
"......BBB.BBBBB"
".....BBBBB.BBBB"
"....BBBBBBB.BBB"
"...BBBBBBBBB.BB"
"..BBBBBBBBBBB.B"
".BBBBBBBBBBBBB."
/* icon for state 14 */
".BBBBBBBBBBBBB."
"B.BBBBBBBBBBB.B"
"BB.BBBBBBBBB.BB"
"BBB.BBBBBBB.BBB"
"BBBB.BBBBB.BBBB"
"BBBBB.BBB.BBBBB"
"BBBBBB.B.BBBBBB"
"BBBBBBB.BBBBBBB"
"BBBBBB...BBBBBB"
"BBBBB.....BBBBB"
"BBBB.......BBBB"
"BBB.........BBB"
"BB...........BB"
"B.............B"
"..............."
/* icon for state 15 */
".BBBBBBBBBBBBB."
"B.BBBBBBBBBBB.B"
"BB.BBBBBBBBB.BB"
"BBB.BBBBBBB.BBB"
"BBBB.BBBBB.BBBB"
"BBBBB.BBB.BBBBB"
"BBBBBB.B.BBBBBB"
"BBBBBBB.BBBBBBB"
"BBBBBB.B.BBBBBB"
"BBBBB.BBB.BBBBB"
"BBBB.BBBBB.BBBB"
"BBB.BBBBBBB.BBB"
"BB.BBBBBBBBB.BB"
"B.BBBBBBBBBBB.B"
".BBBBBBBBBBBBB."

XPM
/* width height num_colors chars_per_pixel */
"7 105 3 1"
/* colors */
". c #000000"
"B c #FFFFFF"
"C c #A0A0A0"
/* icon for state 1 */
"......."
"......."
"......."
"...C..."
"..CBC.."
".CBBBC."
"CBBBBBC"
/* icon for state 2 */
"C......"
"BC....."
"BBC...."
"BBBC..."
"BBC...."
"BC....."
"C......"
/* icon for state 3 */
"C......"
"BC....."
"BBC...."
"BBBC..."
"BBBBC.."
"BBBBBC."
"BBBBBBC"
/* icon for state 4 */
"CBBBBBC"
".CBBBC."
"..CBC.."
"...C..."
"......."
"......."
"......."
/* icon for state 5 */
"CBBBBBC"
".CBBBC."
"..CBC.."
"...C..."
"..CBC.."
".CBBBC."
"CBBBBBC"
/* icon for state 6 */
"BBBBBBC"
"BBBBBC."
"BBBBC.."
"BBBC..."
"BBC...."
"BC....."
"C......"
/* icon for state 7 */
"BBBBBBC"
"BBBBBC."
"BBBBC.."
"BBBC..."
"BBBBC.."
"BBBBBC."
"BBBBBBC"
/* icon for state 8 */
"......C"
".....CB"
"....CBB"
"...CBBB"
"....CBB"
".....CB"
"......C"
/* icon for state 9 */
"......C"
".....CB"
"....CBB"
"...CBBB"
"..CBBBB"
".CBBBBB"
"CBBBBBB"
/* icon for state 10 */
"C.....C"
"BC...CB"
"BBC.CBB"
"BBBCBBB"
"BBC.CBB"
"BC...CB"
"C.....C"
/* icon for state 11 */
"C.....C"
"BC...CB"
"BBC.CBB"
"BBBCBBB"
"BBBBBBB"
"BBBBBBB"
"BBBBBBB"
/* icon for state 12 */
"CBBBBBB"
".CBBBBB"
"..CBBBB"
"...CBBB"
"....CBB"
".....CB"
"......C"
/* icon for state 13 */
"CBBBBBB"
".CBBBBB"
"..CBBBB"
"...CBBB"
"..CBBBB"
".CBBBBB"
"CBBBBBB"
/* icon for state 14 */
"BBBBBBB"
"BBBBBBB"
"BBBBBBB"
"BBBCBBB"
"BBC.CBB"
"BC...CB"
"C.....C"
/* icon for state 15 */
"BBBBBBB"
"BBBBBBB"
"BBBBBBB"
"BBBBBBB"
"BBBBBBB"
"BBBBBBB"
"BBBBBBB"
``````
Edit: Fix bug in PCA.lua preventing it from starting up.
Last edited by wildmyron on October 7th, 2019, 11:22 pm, edited 2 times in total.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

wildmyron wrote:
October 4th, 2019, 7:18 am
Very interesting Brian. Have you been able to stabilise the growing end of that puffer / gun pattern - or have you found a more regular gun?
No to both questions, I will probably explore PCA_12 today.
wildmyron wrote:
October 4th, 2019, 7:18 am
I decided to take a foray into the world of NewCA.lua ...
A very good start. The pattern editing functions, in particular rotations, need work. Look at rotateClockwise and rotateAntiClockwise in Selector.java.

My preference is an implementation of PCA on LifeViewer. Although that program has become so complex that each addition or improvement seems to break older capability.

Brian Prentice

wildmyron
Posts: 1347
Joined: August 9th, 2013, 12:45 am

### Re: Partitioned Cellular Automata

bprentice wrote:
October 4th, 2019, 8:49 am
wildmyron wrote:
October 4th, 2019, 7:18 am
I decided to take a foray into the world of NewCA.lua ...
A very good start. The pattern editing functions, in particular rotations, need work. Look at rotateClockwise and rotateAntiClockwise in Selector.java.
Thanks for trying it out. I had thought about needing to bitshift the cell states when rotating patterns but didn't get around to implementing it. I don't have access to the copy of RPCA I downloaded previously atm, and bprentice.webenet.net seems to be unavailable currently. But I think I know how to deal with rotations and the NewCA.lua functions for doing so can be replaced by PCA.lua. I'll give it a go later this weekend.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

rowett
Moderator
Posts: 1984
Joined: January 31st, 2013, 2:34 am
Location: UK
Contact:

### Re: Partitioned Cellular Automata

bprentice wrote:
October 4th, 2019, 8:49 am
My preference is an implementation of PCA on LifeViewer.
I'll put it on the backlog.
bprentice wrote:
October 4th, 2019, 8:49 am
Although that program has become so complex that each addition or improvement seems to break older capability.
I'm not sure it's every addition. Perhaps 1 in 3...

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

An archived collection of patterns using an assortment of RPCA rules:

Golly.zip
(5.91 KiB) Downloaded 24 times

Run each of the 21 patterns using the lua script here:

posting.php?mode=reply&f=11&t=4098#pr83734

To get a good feel of the behavior of the RPCA rule family, run each pattern in both the forward and backward direction by toggling the alt V key. Watching the evolution of these rules has the same appeal as watching 1D CA's evolve.

Brian Prentice

wildmyron
Posts: 1347
Joined: August 9th, 2013, 12:45 am

### Re: Partitioned Cellular Automata

A 2c/1488 diagonal spaceship in PCA_4:

Code: Select all

``````x = 3, y = 6, rule = PCA_4
.B\$B.B\$.D\$B2\$2.B!``````
Interestingly, this pattern is also a high period spaceship in PCA_7 - because PCA_4 and PCA_7 are so similar - but in this case it is 3c/6534

Code: Select all

``````x = 3, y = 6, rule = PCA_7
.B\$B.B\$.D\$B2\$2.B!``````
There are probably many more corresponding interesting patterns to be found.
bprentice wrote:
October 5th, 2019, 8:16 pm
An archived collection of patterns using an assortment of RPCA rules:
My favourites:

I really like the interaction on a torus here.

Code: Select all

``````x = 1, y = 1, rule = 2PCA4,0,1,11,6,4,5,7,10,12,13,9,14,3,2,8,15:T512,512
L!``````
Strange Sierpinski generator - even stranger in reverse

Code: Select all

``````x = 1, y = 1, rule = 2PCA4,0,12,4,8,2,9,10,7,6,14,1,3,11,5,13,15:T512,512
A!``````
Edit: Some more spaceships in PCA_8 removed some patterns which actually come from PCA_9

8c/12544 orthogonal

Code: Select all

``````x = 2, y = 4, rule = PCA_8
.B\$C\$.I\$J!``````
And a few oscillators:

p7248

Code: Select all

``````x = 5, y = 4, rule = PCA_8
3.A\$H.D.B\$.B\$D!``````
p10216

Code: Select all

``````x = 4, y = 3, rule = PCA_8
B.J\$.B.D\$2.D!``````
Edit: Some of the PCA_8 ships I posted above actually belong in PCA_9. The c/39 and c/71 were already known, here are the other two.

2c/120 orthogonal

Code: Select all

``````x = 4, y = 4, rule = PCA_9
.J\$B.D\$3.D\$2.H!``````
6c/1768 diagonal

Code: Select all

``````x = 3, y = 3, rule = PCA_9
A.D\$.L\$B.D!``````
Last edited by wildmyron on October 7th, 2019, 11:49 pm, edited 2 times in total.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

wildmyron,

The collection of assorted patterns can be downloaded from:

http://bprentice.webenet.net/PCA/PCA_Assortment.zip

The collection now includes 42 patterns. All of the patterns were found by Square Cell. To do so the simulation speed was slowed and the random pattern density was set to 1%.

How can I get Golly to accept this:

Code: Select all

``````x = 1, y = 1, rule = 2PCA4,0,1,11,6,4,5,7,10,12,13,9,14,3,2,8,15:T512,512
L!
``````
I would like to see your PCA.lua modified so that a directory can be opened and all the patterns in it can be loaded sequentially. For example, this would provide a convenient way to examine the behavior of each pattern in PCA_Assortment.

I will update the appropriate lists and archives to include your new spaceships.

Brian Prentice

rowett
Moderator
Posts: 1984
Joined: January 31st, 2013, 2:34 am
Location: UK
Contact:

### Re: Partitioned Cellular Automata

bprentice wrote:
October 4th, 2019, 8:49 am
My preference is an implementation of PCA on LifeViewer.
Experimental support for PCA has been added in Build 425. Please let me know if you find any issues.

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

rowett wrote:
October 8th, 2019, 12:22 pm
Experimental support for PCA has been added in Build 425. Please let me know if you find any issues.
No issues, well done!

I would like to see your LifeViewer (especially the standalone version) modified so that a directory can be opened and all the patterns in it can be loaded sequentially. For example, this would provide a convenient way to examine the behavior of each pattern in PCA_Assortment.

Now with Bounded Grid support, this pattern:

Code: Select all

``````x = 1, y = 1, rule = 2PCA4,0,12,4,8,2,9,10,7,6,14,1,3,11,5,13,15:T512,512
A!``````
can be run. Doing so, demonstrates both the beauty of the pattern and the excellent display capability of LifeViewer.

Brian Prentice

Andrew
Moderator
Posts: 769
Joined: June 2nd, 2009, 2:08 am
Location: Melbourne, Australia
Contact:

### Re: Partitioned Cellular Automata

bprentice wrote:
October 7th, 2019, 2:15 pm
How can I get Golly to accept this:

Code: Select all

``````x = 1, y = 1, rule = 2PCA4,0,1,11,6,4,5,7,10,12,13,9,14,3,2,8,15:T512,512
L!
``````
No problems (assuming PCA.lua is running). Copy the pattern to the clipboard, switch to PCA.lua and type shift-O (or select Open Clipboard from the File menu.
I would like to see your PCA.lua modified so that a directory can be opened and all the patterns in it can be loaded sequentially. For example, this would provide a convenient way to examine the behavior of each pattern in PCA_Assortment.
No need to modify PCA.lua. Just do these steps:

1. Create a startup script. Here's the one I use:

Code: Select all

``````-- a startup script for PCA.lua
local g = golly()
-- change the files directory to show Brian's PCA collection
-- (NewCA.lua will restore the original directory when it exits)
g.setdir("files", g.getdir("app").."Test-scripts/NewCA/PCA/Golly")
g.setoption("showfiles", 1)
``````
Call it PCA-startup.lua or whatever you like and put it anywhere you like (next to PCA.lua is a good spot). Modify the above g.setdir path to the desired directory containing your PCA patterns.

2. Start up PCA.lua and use File -> Set Startup Script to find and select the startup script you just created.

3. Quit PCA.lua and run it again. The left panel should now display all your PCA files and you can simply click on them to load them.

You can do lots of other user-specific changes in a startup script. See the Margolus example here.

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Andrew wrote:
October 8th, 2019, 6:56 pm
No problems (assuming PCA.lua is running). Copy the pattern to the clipboard, switch to PCA.lua and type shift-O (or select Open Clipboard from the File menu.
Thank you for this and the startup script. Works well.

Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

The PCA demonstration here:

viewtopic.php?f=3&t=1622&start=1200#p83969

generates three knight ships.

(-1, 4)c1187

Code: Select all

``````x = 3, y = 3, rule = 2PCA4,0,2,4,3,8,5,6,14,1,10,9,11,12,13,7,15
L.B2\$A!
``````
(3, -1)c3330

Code: Select all

``````x = 3, y = 3, rule = 2PCA4,0,2,4,3,8,5,6,14,1,10,9,11,12,13,7,15
A2\$F.H!
``````
(-1, -4)c2721

Code: Select all

``````x = 4, y = 2, rule = 2PCA4,0,2,4,3,8,5,6,14,1,10,9,11,12,13,7,15
3.C\$A.H!
``````
Run them using either PCA.lua or LifeViewer.

Brian Prentice

rowett
Moderator
Posts: 1984
Joined: January 31st, 2013, 2:34 am
Location: UK
Contact:

### Re: Partitioned Cellular Automata

A very slow semi-colon:

Code: Select all

``````x = 2, y = 4, rule = 2PCA4,0,2,4,3,8,9,5,14,1,12,6,11,10,13,7,15
.C2\$.E\$A!
``````

wildmyron
Posts: 1347
Joined: August 9th, 2013, 12:45 am

### Re: Partitioned Cellular Automata

rowett wrote:
October 11th, 2019, 9:58 am
A very slow semi-colon:

Code: Select all

``````x = 2, y = 4, rule = 2PCA4,0,2,4,3,8,9,5,14,1,12,6,11,10,13,7,15
.C2\$.E\$A!
``````
Incredible. 8c/288350 according to oscar.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Two knight ships from the same rule:

(4,7)c/21223

Code: Select all

``````x = 31, y = 6, rule = 2PCA4,0,2,4,3,8,9,5,14,1,12,6,11,10,13,7,15
A26.2A\$.H26.2H\$D.H24.2D2H3\$.H26.2H!
``````
(-11,1)c/75146

Code: Select all

``````x = 35, y = 7, rule = 2PCA4,0,2,4,3,8,9,5,14,1,12,6,11,10,13,7,15
3.L28.2L\$A3.B24.2A2.2B5\$.H28.2H!
``````
Brian Prentice

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Rule 2PCA4,0,2,4,3,8,9,5,14,1,12,6,11,10,13,7,15 is reversible, but does not have rotational symmetry. Each of the ships found so far have two versions, a single cell version and a domino version. The two knight ship patterns shown above include both versions. The domino version of the 8c/288350 diagonal ship is:

(8,-8)c/288350

Code: Select all

``````x = 34, y = 4, rule = 2PCA4,0,2,4,3,8,9,5,14,1,12,6,11,10,13,7,15
.C30.2C2\$.E30.2E\$A30.2A!
``````
The two versions of each of the three orthogonal ships are:

(-1,0)c/1261

Code: Select all

``````x = 32, y = 3, rule = 2PCA4,0,2,4,3,8,9,5,14,1,12,6,11,10,13,7,15
3.B24.2B\$A.D.B20.2A2D2B\$5.B24.2B!
``````
(0,1)c/675

Code: Select all

``````x = 31, y = 4, rule = 2PCA4,0,2,4,3,8,9,5,14,1,12,6,11,10,13,7,15
2.A25.2A\$3.D25.2D\$A.H23.2A2H\$.H25.2H!
``````
(0,-1)c/45

Code: Select all

``````x = 37, y = 3, rule = 2PCA4,0,2,4,3,8,9,5,14,1,12,6,11,10,13,7,15
.H.B28.2H2B\$H3.B26.2H2.2B\$.H30.2H!
``````
Brian Prentice

PHPBB12345
Posts: 730
Joined: August 5th, 2015, 11:55 pm
Contact:

### Re: Partitioned Cellular Automata

PASTET for PCA usage:

Code: Select all

```x = 3, y = 3, rule = PCA_1 #C [[ RLE input H.H! ]] #C [[ PASTET EVERY 32 ]] #C [[ PASTE input -32 0 ]] .IC\$IOF\$LF!```

Code: Select all

```x = 3, y = 3, rule = PCA_1 #C [[ RLE input A2\$A! ]] #C [[ PASTET EVERY 32 ]] #C [[ PASTE input 0 -32 ]] .IC\$IOF\$LF!```

PHPBB12345
Posts: 730
Joined: August 5th, 2015, 11:55 pm
Contact:

### Re: Partitioned Cellular Automata

Lattice gas behavior:

Code: Select all

``````#C [[
#C COLOR N 120 120 120
#C COLOR E 120 120 120
#C COLOR NE 160 160 160
#C COLOR S 120 120 120
#C COLOR NS 160 160 160
#C COLOR ES 160 160 160
#C COLOR NES 220 220 220
#C COLOR W 120 120 120
#C COLOR NW 160 160 160
#C COLOR EW 160 160 160
#C COLOR NEW 220 220 220
#C COLOR SW 160 160 160
#C COLOR NSW 220 220 220
#C COLOR ESW 220 220 220
#C COLOR NESW 255 255 255
#C ]]
x = 256, y = 256, rule = 2PCA4,0,4,8,12,1,10,9,13,2,6,5,14,3,7,11,15:T256,256
HD2OIHFAM2OBMEA2DL.HGFMOIFCLKG2IGCBAJDJHGDABKHKDMDOEHNMDOLKAEAIMJFAFK
H2BJCIONFNDKBJHJHJGEBCN2AK2HBOKH2CFBKNJL.CGFE.EC.HK2FEBDLCBJKHNKI2DAG
2BH.I2KCLDBC.LMAIM.KFLCOCMNEME2A.GDAOD.CBJIEL2AINOIMNO2JCGHBIKBLOJCDG
2.FBOFNHFL2BKMEFLO2CKNDH.JI.NDNFENJDJGIEA.KJALJMO\$F.KJGAIEFGNCDHC2AIL
DGH2CDOFEDGBIK.JD2C.GJNOL2AGKHLID2.G.GFCH.OHG2AOHFJBGNFCMFK.DJ3E2KGJO
FDNKDEKANMJOKG2CBEHLMKBAFAO.FNHGA2KM2ACHLFJLMIO2AJBKCIGAJNMD2FKA3BNDF
BNOF2KM2FDOCOJNOKCJBIK2OLEFNIDNAGMEB.G2N.AEIDOABAEM.NI.IM2CODCGBFJLJL
IEAIAHBGLFLAMEHINGFGAKOJNKJO\$MKJCLMFIEI2MDJGOI2OD2J2NIOBAFHNHEGEI2DBM
EGCLH2.FK2IMLAHM.LHOLCD.JBLCINONOKJMFNIHLHCA.KOGMJIKMEGOG2JGNCJKGNOFM
ODCMAEMAJ.H.MKNGLBF.IBJF.AMGCL.HCEJDF2OJDLFAILOEJCLO2EBAEDEAIF2BNEKMB
OGBECMJLEHADLD2CKGO2IK2MJFEINLMALB.2LB2OI.CEOGDCJ.ND2CIHAEG.LIMGFAJ2N
E2KGCBNCH\$O.ODJFMEKANIOFOJNHK3CBKLCGJCA2.F2DLO2AFLHALB.HNGCAJNIDEIHL.
KHADFCMAGMLA.L.JBI2L2DHFKBCH.FE.LNCOMAHLHGOHNINOBA.DKBL2ICBFDGH3FGFDL
MGJMLJEGJEAJ2OD2BF2GBHN.IOIFOEHN.LAGIKJHJINMCNCF2M.OKNADEFCGOA2NOFB2L
GJMBI2GLJMKEDOLF4BI.HOHOAB.MK.FGENBFHIFALBLNHMFO3EKMIB\$MHLGEFAEIGEAGF
NKCNCKE.ODMDHJMNIKANI2FEOK.KIF.LAMNFAEHDLAFDCEOGOLGNBK.BJHBCGOKGIH3CO
NJFHJFH2GILDENHCNOHDJNEK2LBOLAHNJMDLCGCM2JCLFOI2KONOMGEKHBHOEH2JMKLJL
A3JBKELAKBOKE2BFCO.DKMDOM2G3HLJOMJAMGN.AFBAJMJADIGCMGEF.NHJGDMEMHKJ2D
LBGHKCIMKGKHLEDBHLMEL.GBABJLJCOG\$KMCFMGDACGA.MDFMHKGFO2IC.KFKFIMCFBFB
KINGDKNCF2LOBKMHMJCMHJNIKL2B.2MLHGL.GIADCBCGL.IELMJ2OCFIB.BIAJMEC2FIO
2EFNKJNCIMFEAICOHOME.GDHMH.JNGF.M.MNDBEGCHEMHJGLEB2KIJG2KGNLMLDJNANJM
NCDGAN2IMGNGFGJNH.GBC2BCDHN.CNHIEKGKMJKAB3CJGFD.DNOI.2G2AHIJBJDO2GBHF
EOLFBLH.BIFC\$IJFLDCIEIJF.DI2H.IJMFH2AFCEG.KLBIHNI.GABHABNE2LKFMG2MFJ
2ADOE2OJ.BJAM.ECABI.DMBMCADJBFE.ING2.NMIGBNINHFM.MI.2IGMLACLJMIBELCL.
JDEFLOK.KEKHBCLEFK.INKMCKI.I.HCMNEMEIDGJIFOKCIG.NA.IDHLKHNKDHEMODFBFK
.E2CKMBIGOCKCEAFEOBLJHJ2EMADBFCGBKCEAJN.ENHC2MONHFHL2OICNBKEI.N\$KHGAN
D.JOKFIMAFIMBO2KH2I.FDIMNHA2JAFG2IH.HFAODCNJE.NKBCHDLGDO2JAONOIJFB2EM
FIJCHFCJI.NMKOLMHGNJBIJFMFOHMDGCIN.KJA2JFDC.CLJB2OKO.LC.FENOJA2DLKBAD
G2KML2GO2JBNHENHI2GKAI2.BABF2NLAJFMOJF.DHLNDOICMCKBKEFDFDLNK2BJO2CMGA
LNLAFEG.FLGJHEOKGJFLEFHFHJOD.GIEBKB2GB2IDM.B\$ABGAKDLIE2BHL2DGB.GJO2CD
BNHINMELMDC2AIHBMIM2E.C.BLJEJG.LBLINLHDNJEIJHEKGANEMLNEJDKGJG2MKIN.HC
AOHMKMHKGHONOAODAEHNHNOJ.MCMAGFIKJBA3IEDHJGHALD.OIOMIKDMICLNFH2AJMGMG
LOE2BF2BCLGD.LOMCFHKNLKNOMAJBICGO.HBHI.JEOHEKANG.NIODHMJM2NECDCFB2N2F
HDJELFG.OJCHJMFI.A.2BOGK\$N.JDMNONOJMDAMANOMCDECANMDABFACLCNEF2B.KAOJE
KINK.OGKJAEG2NHOGCJADGCIMLN.HGOJEN2HGBGIBA3GDJLOKBNKGI2NMBJEFJFHBOL.G
FEC2ACEGIMGBC.FDHGC.EMOKNOMADGNKCJCD.NHEMEFEHJLALFK.2EBCKHJLKDIHGBH3A
KHMKAHMLHMJM2.BICFLGEGIB2ACICDE2L2HCO.BIMDCBLEMELIF2.KG2MKFJEMOJ.FHB.
JHA\$DOAFHJLAMNHIOEB2GCGBOAFNCDBOGEDJNBIOJMDKNCLJBIEJDEJLOHACHMD.DEND.
OLAIC.KMAGIGKBKMHJGABKMIJINEDN2FDCBHDKANAFNMIJEBA.NAOBGEADOFN2.ELDGJK
EDLFD3.DMHOMBHGFGACDKDGBLF2LH.JMFI.DHJEG.NBO.OFHIJNCLHCGK2IG2IFI.2KE.
DBMDFAKFMIMCDNCKJN.FDCH2DJMEBA2OG2BFK2C2FGNCHJC2AGDO\$EFN.L2CNBGFA2HGL
MLD2OHBA2FLHCBLB.KBEM2ENGOH.KJKGBIDAI2HJEA.LDHBAOGHL.G.BAHMFEAEMIHCNF
JMGAIMGFDCIBLO2NEFLKLH.FOIOEONGEDCHNFLEIJ.N.JNEL.HIBCFIOEBEADJNC.MFG.
NC2NKLH2IL.MLNLBOMNML.M2GFMOCALGBMBK2INCOMNE2HDIEJ.BCIBGABNCL2CLN.A.A
BLKFDGFHNMEFNBFICL2NFN2DOKHDIG.NO\$CABLKCGN.OIEMNBHABLEFAIOHDBILBKLKCA
BKBENL2NOJFB2KFGDLIKFDENLIEH2C2I2C.CNGCDJ.JBHMKDHDCM2.KJBDGEBNJMKOKEF
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2GICI.HGIDLAOICFOBAJ2AOFCOLNELFDELGFGABMFKGFC2IADEKAE.ECJCBFDLDHOJF.K
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FK.BCHGNLMBMHIJGEINAN3IG3OAHFJNOFDFDGLJF2H.D.JBKEODKOHB.JLAFDI.N.OEMK
O.AMALIBE.CIJIJGHKODIFNHBKNOCFNKB.MALDHICGBNMJ2MEDAF.KEHFMKEHA2LCIBGF
DKGN2KGMNJI2KNLAOMFI2CJBGJHLHICDAIJ2.ILH2.OGMBCGKBLNFJFG.FIMJAMD2GLFG
JHDCLJGENMCL2.GAHDLIL.BJNOM\$2EMKB.H.NHCHNHMOHLAI2KCKGCIJAGDMCOLK.CIAC
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.DHDGJM.I.JBGJO.IAIKBEKFN2MJE.KIBFLNAOJLBIOFBNCDCABGEDNHFONBA.ML2ILBO
DMBJKHJNAN.MJEOHICM2GNOLNMKAIJAJG2.MAHILECO2IHAKLMBJLOCIJ.LBICBHEMEBO
MHOGJOB\$F.CNOBI.KOIHA.FJ.BLBJGBIKEIGFNAIJOFAHME4GNAKC.MNK2ABLGDFGIM.G
LIAFDFMJOJNML2DNCFLIMAHJL.GFGFDFLJAIJIGBGDH2FEAGKGKIOCGEAIGIEKE2GNEAC
BCFALBG.KONIBGICLBHGBF2HBODBJ.HCKNCKOK.OLMGFAKBC2.BFDMICBFJIJACLBJIJB
ILFOAICBLGICNE.MCKL.OIBA2DAOLKMNCOMFBLKLKFADJBOCLJIMGAL\$GCDGLOLHD3IEO
J.JHEHEJ.FCGH.KMIMN.JA.ADMLKC.JKCMANHJCHG.N.FGK2FEJO2EOHLADBCIFJFEIEK
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MNKIO2GBE.DGK.2ONOM2GD2LAH2LIBGKMNGF\$LFD.K.BAMACDKAK3JOE2N2MODIMCMOBA
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IOFIB2DJOEGBAOMB2NLJODLAGN.CM.OEF2E2H.H.D.JAJGN3HDGFMCNDMICEI.N.N2IFL
FMJMDN2HBJ2ABDENEAMBLDBNIDAF2MAEJMOGKG2EDJBEL2BEO3IFJKGMDA2DBEHBAC.N
2FBMAGCAJANJIBI!
``````
Last edited by PHPBB12345 on January 18th, 2020, 11:11 pm, edited 1 time in total.

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

PHPBB12345 wrote:
October 14th, 2019, 12:30 am
Lattice gas behavior

Code: Select all

``` x = 8, y = 8, rule = 2PCA4,0,4,8,12,1,10,9,13,2,6,5,14,3,7,11,15:T100 8O\$8O\$8O\$8O\$8O\$8O\$8O\$8O! ```
Brian Prentice

PHPBB12345
Posts: 730
Joined: August 5th, 2015, 11:55 pm
Contact:

### Re: Partitioned Cellular Automata

bprentice
Posts: 638
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Partitioned Cellular Automata

Run forward and backward.

Code: Select all

``` x = 1, y = 1, rule = 2PCA4,0,4,2,11,9,1,6,13,10,12,7,8,3,14,5,15 J! ```
Brian Prentice

muzik
Posts: 3774
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Partitioned Cellular Automata

Is there such thing as a hexagonal PCA, given that k{6,3} = {3,6}?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Gustone
Posts: 606
Joined: March 6th, 2019, 2:26 am

### Re: Partitioned Cellular Automata

bprentice wrote:
October 15th, 2019, 9:52 pm
Run forward and backward.

Code: Select all

``` x = 1, y = 1, rule = 2PCA4,0,4,2,11,9,1,6,13,10,12,7,8,3,14,5,15 J! ```
Brian Prentice
colo
My favourite oscillator of all time

Code: Select all

``````x = 15, y = 13, rule = B3/S23
7bo2\$3b2o5b2o\$b2o4bo4b2o\$5b2ob2o\$bobo7bobo\$bo2bobobobo2bo\$5obobob5o\$o
4bo3bo4bo\$b3obobobob3o\$3bob2obo2bo\$8bobo\$8b2o!
``````

AforAmpere
Posts: 1080
Joined: July 1st, 2016, 3:58 pm

### Re: Partitioned Cellular Automata

Gustone wrote:
October 20th, 2019, 9:15 am
colo
Can you please not do one word replies to posts, especially when said word isn't even spelled properly?
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)