Cellular Automata

Brainstorming

Let's try it myself!

In [2]:
rule = 54
In [3]:
# format to binary
"{0:08b}".format(rule)
Out[3]:
'00110110'
In [4]:
# get the correct bit in rule
pattern = '101'
int(pattern, 2)
Out[4]:
5
In [5]:
# correct result
def get_result(pattern, rule):
    return "{0:08b}".format(rule)[7-int(pattern, 2)]

get_result(pattern, rule)
Out[5]:
'1'
In [6]:
# should look ok!
for ptn in ['111', '110', '101', '100', '011', '010', '001', '000']:
    print(get_result(ptn, 54))
0
0
1
1
0
1
1
0

Does it work?

In [7]:
size = 11 # preferably odd number
cells = '0'*(size//2) + '1' + '0'*(size//2)

print(cells)
00000100000
In [8]:
def get_partition(string, idx):
    if idx == 0:
        return '0' + string[idx:idx+2]
    elif idx == len(string) - 1:
        return string[idx-1:idx+1] + '0'
    return string[idx-1:idx+2]
In [9]:
# looks ok!
get_partition(cells, 6)
Out[9]:
'100'
In [10]:
rule = 54
''.join([get_result(get_partition(cells, i), rule) for i in range(size)])
Out[10]:
'00001110000'
In [11]:
def evolve(cells, rule):
    return ''.join([get_result(get_partition(cells, i), rule) for i in range(len(cells))])
In [12]:
# matches wolfram!
print(cells)
for _ in range(20):
    cells = evolve(cells, 54)
    print(cells)
00000100000
00001110000
00010001000
00111011100
01000100010
11101110111
00010001000
00111011100
01000100010
11101110111
00010001000
00111011100
01000100010
11101110111
00010001000
00111011100
01000100010
11101110111
00010001000
00111011100
01000100010

Putting it together

Here, I'll restate all the code that I just wrote.

In [13]:
def initialize_cells(n):
    return '0'*n + '1' + '0'*n

def evolve(cells, rule):
    return ''.join([get_result(get_partition(cells, i), rule) for i in range(len(cells))])

def get_partition(string, idx):
    if idx == 0:
        return '0' + string[idx:idx+2]
    elif idx == len(string) - 1:
        return string[idx-1:idx+1] + '0'
    return string[idx-1:idx+2]

def get_result(pattern, rule):
    return "{0:08b}".format(rule)[7-int(pattern, 2)]

def automata(rule, n, gens):
    cells = initialize_cells(n)
    print(cells)
    for _ in range(gens):
        cells = evolve(cells, rule)
        print(cells)

Examples

In [14]:
automata(220, 45, 80)
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In [15]:
automata(222, 45, 80)
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In [16]:
automata(250, 45, 80)
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In [17]:
automata(182, 45, 80)
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In [18]:
automata(188, 45, 80)
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In [19]:
automata(161, 45, 80)
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In [25]:
automata(105, 45, 80)
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In [26]:
automata(1, 45, 80)
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Rule-adjusting

What if the rule changes each generation?

In [28]:
def automata_ruleplus(rule, n, gens, ruleplus):
    cells = initialize_cells(n)
    print(cells)
    for _ in range(gens):
        cells = evolve(cells, rule)
        print(cells)
        rule += ruleplus
In [29]:
automata_ruleplus(112, 45, 80, 1)
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In [30]:
automata_ruleplus(10, 45, 80, 2)
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In [31]:
automata_ruleplus(48, 45, 80, 5)
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In [32]:
import random
def automata_random(n, gens):
    cells = initialize_cells(n)
    print(cells)
    for _ in range(gens):
        cells = evolve(cells, random.randint(0, 255))
        print(cells)
In [33]:
automata_random(45, 40)
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In [34]:
automata_random(45, 40)
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In [35]:
automata_random(45, 40)
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In [36]:
automata_random(45, 40)
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Future ideas

  1. what about different starting seeds than just the middle of the board?
  2. can we make a moving picture, instead of new lines of text? Then you can see the things moving (i.e. conway's game of life)
  3. starting seeds, then randomized?
  4. list of rules to repeat?
  5. 2-d automata?
  6. don't use 1s and 0s, use * and - or something?
In [37]:
automata(62, 45, 40)
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In [ ]: