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block2d_basic_ca_demo.py
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import cellpylib as cpl
import numpy as np
"""
2D Block CA from
https://writings.stephenwolfram.com/2023/02/computational-foundations-for-the-second-law-of-thermodynamics/
"""
initial_conditions = np.array([[
[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, 1],
[1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[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, 1, 1],
]])
def make_block2d_rule():
base_rules = {
((0, 0), (0, 0)): ((0, 0), (0, 0)),
((0, 0), (0, 2)): ((2, 0), (0, 0)),
((2, 0), (0, 0)): ((0, 0), (0, 2)),
((0, 0), (2, 0)): ((0, 2), (0, 0)),
((0, 2), (0, 0)): ((0, 0), (2, 0)),
((0, 0), (2, 2)): ((2, 2), (0, 0)),
((2, 2), (0, 0)): ((0, 0), (2, 2)),
((0, 2), (0, 2)): ((2, 0), (2, 0)),
((2, 0), (2, 0)): ((0, 2), (0, 2)),
((0, 2), (2, 0)): ((2, 0), (0, 2)),
((2, 0), (0, 2)): ((0, 2), (2, 0)),
((0, 2), (2, 2)): ((2, 2), (2, 0)),
((2, 2), (2, 0)): ((0, 2), (2, 2)),
((2, 0), (2, 2)): ((2, 2), (0, 2)),
((2, 2), (0, 2)): ((2, 0), (2, 2)),
((2, 2), (2, 2)): ((2, 2), (2, 2)),
# wall rules
((0, 0), (1, 1)): ((0, 0), (1, 1)),
((0, 1), (1, 1)): ((0, 1), (1, 1)),
((0, 2), (1, 1)): ((2, 0), (1, 1)),
((2, 0), (1, 1)): ((0, 2), (1, 1)),
((2, 1), (1, 1)): ((2, 1), (1, 1)),
((2, 2), (1, 1)): ((2, 2), (1, 1)),
((1, 1), (1, 1)): ((1, 1), (1, 1)),
}
rules = {}
# add rotations
for r, v in base_rules.items():
rules[r] = v
for _ in range(3):
r = ((r[1][0], r[0][0]), (r[1][1], r[0][1]))
v = ((v[1][0], v[0][0]), (v[1][1], v[0][1]))
if r not in rules:
rules[r] = v
def _apply_rule(n, t):
n = tuple(tuple(i) for i in n)
return rules[n]
return _apply_rule
ca = cpl.evolve2d_block(initial_conditions, block_size=(2, 2),
timesteps=40, apply_rule=make_block2d_rule())
cpl.plot2d_animate(ca)