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|
# Generator for Triangular Turmite rules
import golly
import random
import string
from glife.EmulateTriangular import *
from glife.WriteRuleTable import *
prefix = 'TriTurmite'
# http://bytes.com/topic/python/answers/25176-list-subsets
get_subsets = lambda items: [[x for (pos,x) in zip(range(len(items)), items) if (2**pos) & switches] for switches in range(2**len(items))]
# Generate a random rule, while filtering out the dull ones.
# More to try:
# - if turmite can get stuck in period-2 cycles then rule is bad (or might it avoid them?)
# - (extending) if turmite has (c,2 (or 8),s) for state s and color c then will loop on the spot (unlikely to avoid?)
example_spec = '{{{1, 2, 0}, {0, 1, 0}}}'
import random
ns = 2
nc = 3
while True: # (we break out if ok)
example_spec = '{'
for state in range(ns):
if state > 0:
example_spec += ','
example_spec += '{'
for color in range(nc):
if color > 0:
example_spec += ','
new_color = random.randint(0,nc-1)
dir_to_turn = [1,2,4][random.randint(0,2)] # (we don't consider splitting and dying here)
new_state = random.randint(0,ns-1)
example_spec += '{' + str(new_color) + "," + str(dir_to_turn) + "," + str(new_state) + '}'
example_spec += '}'
example_spec += '}'
is_rule_acceptable = True
action_table = eval(string.replace(string.replace(example_spec,'}',']'),'{','['))
# does Turmite change at least one color?
changes_one = False
for state in range(ns):
for color in range(nc):
if not action_table[state][color][0] == color:
changes_one = True
if not changes_one:
is_rule_acceptable = False
# does Turmite write every non-zero color?
colors_written = set([])
for state in range(ns):
for color in range(nc):
colors_written.add(action_table[state][color][0])
if not colors_written==set(range(1,nc)):
is_rule_acceptable = False
# does Turmite ever turn?
turmite_turns = False
for state in range(ns):
for color in range(nc):
if not action_table[state][color][0] in [4]: # u-turn
turmite_turns = True
if not turmite_turns:
is_rule_acceptable = False
# does turmite get stuck in any subset of states?
for subset in get_subsets(range(ns)):
if len(subset)==0 or len(subset)==ns: # (just an optimisation)
continue
leaves_subset = False
for state in subset:
for color in range(nc):
if not action_table[state][color][2] in subset:
leaves_subset = True
if not leaves_subset:
is_rule_acceptable = False
break # (just an optimisation)
# does turmite wobble on the spot? (u-turn that doesn't change color or state)
for state in range(ns):
for color in range(nc):
if action_table[state][color][0]==color and action_table[state][color][1]==4 and action_table[state][color][2]==state:
is_rule_acceptable = False
# so was the rule acceptable, in the end?
if is_rule_acceptable:
break
spec = golly.getstring(
'''This script will create a TriTurmite CA for a given specification.
Enter a specification string: a curly-bracketed table of n_states rows
and n_colors columns, where each entry is a triple of integers.
The elements of each triple are:
a: the new color of the square
b: the direction(s) for the Turmite to turn (1=Left, 2=Right, 4=U-turn)
c: the new internal state of the Turmite
Example:
{{{1, 2, 0}, {0, 1, 0}}}
Has 1 state and 2 colors. The triple {1,2,0} says:
1. set the color of the square to 1
2. turn right (2)
3. adopt state 0 (no change) and move forward one square
This is the equivalent of Langton's Ant.
Enter string:
''', example_spec, 'Enter TriTurmite specification:')
'''Some interesting rule found with this script:
{{{2,4,0},{2,4,0},{1,2,1}},{{1,2,1},{2,1,0},{1,4,1}}} - lightning cloud
{{{1,1,1},{1,2,0},{2,1,1}},{{2,2,1},{2,2,1},{1,4,0}}} - makes a highway (seems to be rarer in tri grids compared to square grids?)
{{{2,2,1},{1,2,0},{1,1,1}},{{1,2,0},{2,1,0},{1,4,1}}} - data pyramid
{{{2,1,0},{1,4,1},{1,1,0}},{{2,4,0},{2,2,1},{1,1,1}}} - a filled version of the tri-grid Langton's ant
{{{1,1,0},{2,2,1},{1,1,0}},{{1,4,0},{2,2,0},{2,2,0}}} - hypnodisc
'''
# convert the specification string into action_table[state][color]
# (convert Mathematica code to Python and run eval)
action_table = eval(string.replace(string.replace(spec,'}',']'),'{','['))
n_states = len(action_table)
n_colors = len(action_table[0])
# (N.B. The terminology 'state' here refers to the internal state of the finite
# state machine that each Turmite is using, not the contents of each Golly
# cell. We use the term 'color' to denote the symbol on the 2D 'tape'. The
# actual 'Golly state' in this emulation of Turmites is given by the
# "encoding" section below.)
n_dirs = 3
# TODO: check table is full and valid
total_states = n_colors+n_colors*n_states*3
# problem if we try to export more than 255 states
if total_states > 128: # max allowed using checkerboard emulation (see EmulateTriangular)
golly.warn("Number of states required exceeds Golly's limit of 255.")
golly.exit()
# encoding:
# (0-n_colors: empty square)
def encode(c,s,d):
# turmite on color c in state s facing away from direction d
return n_colors + 3*(n_states*c+s) + d
# http://rightfootin.blogspot.com/2006/09/more-on-python-flatten.html
def flatten(l, ltypes=(list, tuple)):
ltype = type(l)
l = list(l)
i = 0
while i < len(l):
while isinstance(l[i], ltypes):
if not l[i]:
l.pop(i)
i -= 1
break
else:
l[i:i + 1] = l[i]
i += 1
return ltype(l)
# convert the string to a form we can embed in a filename
spec_string = ''.join(map(str,map(lambda x:hex(x)[2:],flatten(action_table))))
# (ambiguous but we have to try something)
# what direction would a turmite have been facing to end up here from direction
# d if it turned t: would_have_been_facing[t][d]
would_have_been_facing={
1:[2,0,1], # left
2:[1,2,0], # right
4:[0,1,2], # u-turn
}
not_arriving_from_here = [range(n_colors) for i in range(n_dirs)] # (we're going to modify them)
for color in range(n_colors):
for state in range(n_states):
turnset = action_table[state][color][1]
for turn in [1,2,4]:
if not turn&turnset: # didn't turn this way
for dir in range(n_dirs):
facing = would_have_been_facing[turn][dir]
not_arriving_from_here[dir] += [encode(color,state,facing)]
# What states leave output_color behind?
leaving_color_behind = {}
for output_color in range(n_colors):
leaving_color_behind[output_color] = [output_color] # (no turmite present)
for state in range(n_states):
for color in range(n_colors):
if action_table[state][color][0]==output_color:
leaving_color_behind[output_color] += [encode(color,state,d) for d in range(n_dirs)] # any direction
# we can't build the rule tree directly so we collect the transitions ready for emulation
transitions = []
# A single turmite is entering this square:
for s in range(n_states):
for dir in range(n_dirs):
# collect all the possibilities for a turmite to arrive in state s from direction dir
inputs = []
for state in range(n_states):
for color in range(n_colors):
if action_table[state][color][2]==s:
turnset = action_table[state][color][1] # sum of all turns
inputs += [encode(color,state,would_have_been_facing[turn][dir]) \
for turn in [1,2,4] if turn&turnset]
if len(inputs)>0:
for central_color in range(n_colors):
# output the required transition
### AKT: this code causes syntax error in Python 2.3:
### transition = [leaving_color_behind[central_color]] + \
### [ inputs if i==dir else not_arriving_from_here[i] for i in range(n_dirs) ] + \
### [ [encode(central_color,s,dir)] ]
transition = [leaving_color_behind[central_color]]
for i in range(n_dirs):
if i==dir:
transition.append(inputs)
else:
transition.append(not_arriving_from_here[i])
transition += [ [encode(central_color,s,dir)] ]
transitions += [transition]
# default: square is left with no turmite present
for output_color,inputs in leaving_color_behind.items():
transition = [inputs]+[range(total_states)]*n_dirs+[[output_color]]
transitions += [transition]
rule_name = prefix+'_'+spec_string
# To see the intermediate output as a rule table (can use RuleTableToTree.py to load it):
#WriteRuleTable("triangularVonNeumann",total_states,transitions,golly.getdir('rules')+rule_name+'_asTable.table')
# -- make some icons --
palette=[[0,0,0],[0,155,67],[127,0,255],[128,128,128],[185,184,96],[0,100,255],[196,255,254],
[254,96,255],[126,125,21],[21,126,125],[255,116,116],[116,255,116],[116,116,255],
[228,227,0],[28,255,27],[255,27,28],[0,228,227],[227,0,228],[27,28,255],[59,59,59],
[234,195,176],[175,196,255],[171,194,68],[194,68,171],[68,171,194],[72,184,71],[184,71,72],
[71,72,184],[169,255,188],[252,179,63],[63,252,179],[179,63,252],[80,9,0],[0,80,9],[9,0,80],
[255,175,250],[199,134,213],[115,100,95],[188,163,0],[0,188,163],[163,0,188],[203,73,0],
[0,203,73],[73,0,203],[94,189,0],[189,0,94]]
if total_states<=16:
TriangularTransitionsToRuleTree_SplittingMethod("triangularVonNeumann",total_states,transitions,rule_name)
width = 15*(total_states*total_states-1) + 15 # we set the background color
height = 22
pixels = [[(0,0,0) for x in range(width)] for y in range(height)]
# turmite icons: 0=black, 1=background color, 2=turmite color
turmite_big = [[[0,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1],
[1,1,0,1,1,1,1,1,1,2,2,2,2,1,1],
[1,1,1,0,1,1,1,1,1,1,1,2,2,1,1],
[1,1,1,1,0,1,1,1,1,1,2,1,2,1,1],
[1,1,1,1,1,0,1,1,1,2,1,1,2,1,1],
[1,1,1,1,1,1,0,1,2,1,1,1,1,1,1],
[1,1,1,1,1,1,1,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,2,1,0,1,1,1,1,1,1],
[1,1,2,1,1,2,1,1,1,0,1,1,1,1,1],
[1,1,2,1,2,1,1,1,1,1,0,1,1,1,1],
[1,1,2,2,1,1,1,1,1,1,1,0,1,1,1],
[1,1,2,2,2,2,1,1,1,1,1,1,0,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,0]],
[[0,1,1,1,1,1,1,1,2,1,1,1,1,1,1],
[1,0,1,1,1,1,1,1,2,1,1,1,1,1,1],
[1,1,0,1,1,1,1,1,1,2,1,1,1,1,1],
[1,1,1,0,1,1,1,1,1,2,1,1,1,1,1],
[1,1,1,1,0,1,1,1,1,1,2,1,1,1,1],
[1,1,2,1,1,0,1,1,1,1,2,1,2,1,1],
[1,1,2,2,1,1,0,1,1,1,1,2,2,1,1],
[1,1,2,2,2,1,1,0,1,1,2,2,2,1,1],
[1,1,2,2,1,1,1,1,0,1,1,2,2,1,1],
[1,1,2,1,2,1,1,1,1,0,1,1,2,1,1],
[1,1,1,1,2,1,1,1,1,1,0,1,1,1,1],
[1,1,1,1,1,2,1,1,1,1,1,0,1,1,1],
[1,1,1,1,1,2,1,1,1,1,1,1,0,1,1],
[1,1,1,1,1,1,2,1,1,1,1,1,1,0,1],
[1,1,1,1,1,1,2,1,1,1,1,1,1,1,0]],
[[0,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
[1,0,1,1,1,1,1,1,1,1,1,1,1,1,1],
[1,1,0,1,1,2,2,2,2,2,1,1,1,1,1],
[1,1,1,0,1,1,2,2,2,1,1,1,1,1,1],
[1,1,1,1,0,1,1,2,1,2,2,1,1,1,1],
[1,1,1,1,1,0,1,1,1,1,1,2,2,1,1],
[1,1,1,1,1,1,0,1,1,1,1,1,1,2,2],
[1,1,1,1,1,1,1,0,1,1,1,1,1,1,1],
[2,2,1,1,1,1,1,1,0,1,1,1,1,1,1],
[1,1,2,2,1,1,1,1,1,0,1,1,1,1,1],
[1,1,1,1,2,2,1,2,1,1,0,1,1,1,1],
[1,1,1,1,1,1,2,2,2,1,1,0,1,1,1],
[1,1,1,1,1,2,2,2,2,2,1,1,0,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,0]]]
turmite_small = [[[0,1,1,1,1,1,1],
[1,0,1,2,2,2,1],
[1,1,0,1,1,2,1],
[1,2,1,0,1,2,1],
[1,2,1,1,0,1,1],
[1,2,2,2,1,0,1],
[1,1,1,1,1,1,0]],
[[0,1,1,1,1,1,1],
[1,0,1,1,1,2,1],
[1,1,0,1,2,2,1],
[1,2,1,0,1,2,1],
[1,2,2,1,0,1,1],
[1,2,1,1,1,0,1],
[1,1,1,1,1,1,0]],
[[0,1,1,1,1,1,1],
[1,0,1,2,2,2,1],
[1,1,0,1,2,1,1],
[1,1,1,0,1,1,1],
[1,1,2,1,0,1,1],
[1,2,2,2,1,0,1],
[1,1,1,1,1,1,0]]]
# TODO: do something about this horrible code
for lc in range(n_colors):
for uc in range(n_colors):
'''draw the cells with no turmites'''
golly_state = uc * total_states + lc
for row in range(15):
for column in range(15):
if column>row:
# upper
pixels[row][(golly_state-1)*15+column] = palette[uc]
elif column<row:
# lower
pixels[row][(golly_state-1)*15+column] = palette[lc]
for row in range(7):
for column in range(7):
if column>row:
# upper
pixels[15+row][(golly_state-1)*15+column] = palette[uc]
elif column<row:
# lower
pixels[15+row][(golly_state-1)*15+column] = palette[lc]
'''draw the cells with a turmite in the upper half'''
for us in range(n_states):
for ud in range(n_dirs):
upper = encode(uc,us,ud)
golly_state = upper * total_states + lc
for row in range(15):
for column in range(15):
if column>row:
# upper
bg_col = palette[uc]
fg_col = palette[n_colors+us]
pixels[row][(golly_state-1)*15+column] = [palette[0],bg_col,fg_col][turmite_big[ud][row][column]]
elif column<row:
# lower
pixels[row][(golly_state-1)*15+column] = palette[lc]
for row in range(7):
for column in range(7):
if column>row:
# upper
bg_col = palette[uc]
fg_col = palette[n_colors+us]
pixels[15+row][(golly_state-1)*15+column] = [palette[0],bg_col,fg_col][turmite_small[ud][row][column]]
elif column<row:
# lower
pixels[15+row][(golly_state-1)*15+column] = palette[lc]
for ls in range(n_states):
for ld in range(n_dirs):
lower = encode(lc,ls,ld)
for uc in range(n_colors):
'''draw the cells with a turmite in the lower half'''
golly_state = uc * total_states + lower
for row in range(15):
for column in range(15):
if row>column:
# lower
bg_col = palette[lc]
fg_col = palette[n_colors+ls]
pixels[row][(golly_state-1)*15+column] = [palette[0],bg_col,fg_col][turmite_big[ld][row][column]]
elif column>row:
# upper
pixels[row][(golly_state-1)*15+column] = palette[uc]
for row in range(7):
for column in range(7):
if row>column:
# lower
bg_col = palette[lc]
fg_col = palette[n_colors+ls]
pixels[15+row][(golly_state-1)*15+column] = [palette[0],bg_col,fg_col][turmite_small[ld][row][column]]
elif column>row:
# upper
pixels[15+row][(golly_state-1)*15+column] = palette[uc]
'''draw the cells with a turmite in both halves'''
for us in range(n_states):
for ud in range(n_dirs):
upper = encode(uc,us,ud)
golly_state = upper * total_states + lower
for row in range(15):
for column in range(15):
if row>column:
# lower
bg_col = palette[lc]
fg_col = palette[n_colors+ls]
pixels[row][(golly_state-1)*15+column] = [palette[0],bg_col,fg_col][turmite_big[ld][row][column]]
elif column>row:
# upper
bg_col = palette[uc]
fg_col = palette[n_colors+us]
pixels[row][(golly_state-1)*15+column] = [palette[0],bg_col,fg_col][turmite_big[ud][row][column]]
for row in range(7):
for column in range(7):
if row>column:
# lower
bg_col = palette[lc]
fg_col = palette[n_colors+ls]
pixels[15+row][(golly_state-1)*15+column] = [palette[0],bg_col,fg_col][turmite_small[ld][row][column]]
elif column>row:
# upper
bg_col = palette[uc]
fg_col = palette[n_colors+us]
pixels[15+row][(golly_state-1)*15+column] = [palette[0],bg_col,fg_col][turmite_small[ud][row][column]]
ConvertTreeToRule(rule_name, total_states, pixels)
elif total_states<=128:
TriangularTransitionsToRuleTree_CheckerboardMethod("triangularVonNeumann",total_states,transitions,rule_name)
width = 15*(total_states*2-2) + 15 # we set the background color
height = 22
pixels = [[(0,0,0) for x in range(width)] for y in range(height)]
# turmite icons: 0=black, 1=background color, 2=turmite color
lower = [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],
[0,0,0,0,0,1,1,1,1,1,0,0,0,0,0],
[0,0,0,0,1,1,1,1,1,1,2,0,0,0,0],
[0,0,0,1,1,1,1,1,2,2,1,1,0,0,0],
[0,0,1,1,2,1,2,2,1,1,1,1,1,0,0],
[0,1,1,2,2,2,1,1,1,1,1,1,1,1,0],
[1,1,2,2,2,2,2,1,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],
[0,0,0,0,0,1,1,1,1,1,0,0,0,0,0],
[0,0,0,0,1,1,1,2,1,1,1,0,0,0,0],
[0,0,0,1,1,1,2,2,2,1,1,1,0,0,0],
[0,0,1,1,1,2,2,2,2,2,1,1,1,0,0],
[0,1,1,1,1,1,1,2,1,1,1,1,1,1,0],
[1,1,1,1,1,1,1,2,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,2,1,1,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],
[0,0,0,0,0,1,1,1,1,1,0,0,0,0,0],
[0,0,0,0,2,1,1,1,1,1,1,0,0,0,0],
[0,0,0,1,1,2,2,1,1,1,1,1,0,0,0],
[0,0,1,1,1,1,1,2,2,1,2,1,1,0,0],
[0,1,1,1,1,1,1,1,1,2,2,2,1,1,0],
[1,1,1,1,1,1,1,1,2,2,2,2,2,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]]
lower7x7 = [[[0,0,0,0,0,0,0],
[0,0,0,0,0,0,0],
[0,0,0,1,0,0,0],
[0,0,1,1,1,0,0],
[0,1,2,2,1,1,0],
[1,1,1,1,1,1,1],
[0,0,0,0,0,0,0]],
[[0,0,0,0,0,0,0],
[0,0,0,0,0,0,0],
[0,0,0,1,0,0,0],
[0,0,1,2,1,0,0],
[0,1,2,1,2,1,0],
[1,1,1,1,1,1,1],
[0,0,0,0,0,0,0]],
[[0,0,0,0,0,0,0],
[0,0,0,0,0,0,0],
[0,0,0,1,0,0,0],
[0,0,1,1,1,0,0],
[0,1,1,2,2,1,0],
[1,1,1,1,1,1,1],
[0,0,0,0,0,0,0]]]
# (we invert the lower triangle to get the upper triangle)
for color in range(n_colors):
bg_color = palette[color]
# draw the 15x15 icon
for row in range(15):
for column in range(15):
# lower triangle
pixels[row][(color-1)*15+column] = \
[palette[0],bg_color,bg_color][lower[0][row][column]]
# upper triangle
pixels[row][(color+total_states-2)*15+column] = \
[palette[0],bg_color,bg_color][lower[0][13-row][column]]
# draw the 7x7 icon
for row in range(7):
for column in range(7):
# lower triangle
pixels[15+row][(color-1)*15+column] = \
[palette[0],bg_color,bg_color][lower7x7[0][row][column]]
# upper triangle
pixels[15+row][(color+total_states-2)*15+column] = \
[palette[0],bg_color,bg_color][lower7x7[0][6-row][column]]
for state in range(n_states):
fg_color = palette[n_colors+state]
for dir in range(n_dirs):
# draw the 15x15 icon
for row in range(15):
for column in range(15):
# lower triangle
pixels[row][(encode(color,state,dir)-1)*15+column] = \
[palette[0],bg_color,fg_color][lower[dir][row][column]]
# upper triangle
pixels[row][(encode(color,state,dir)+total_states-2)*15+column] = \
[palette[0],bg_color,fg_color][lower[2-dir][13-row][column]]
# draw the 7x7 icon
for row in range(7):
for column in range(7):
# lower triangle
pixels[15+row][(encode(color,state,dir)-1)*15+column] = \
[palette[0],bg_color,fg_color][lower7x7[dir][row][column]]
# upper triangle
pixels[15+row][(encode(color,state,dir)+total_states-2)*15+column] = \
[palette[0],bg_color,fg_color][lower7x7[2-dir][6-row][column]]
ConvertTreeToRule(rule_name, total_states, pixels)
else:
golly.warn('Too many states!')
golly.exit()
# -- select the rule --
golly.new(rule_name+'-demo.rle')
golly.setalgo('RuleLoader')
golly.setrule(rule_name)
golly.setcell(0,0,encode(0,0,0)) # start with a single turmite
golly.show('Created '+rule_name+'.rule and selected that rule.')
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