from numpy import zeros
from random import randint
def cellular(rule, N, initial='Single-cell'):
'''Yields a matrix showing the evolution of a Wolfram's cellular automaton
rule: determines how a cell's value is updated, depending on its neighbors
N: number of iterations
initial: starting condition; can be either single-cell or a random binary row
'''
M=zeros( (N,2*N+2), dtype=int)
if initial=='Single-cell':
M[0,N]=1
else:
M[0]=[randint(0,1) for a in range(0,2*N+2)]
for j in range(1,N):
for k in range(0,2*N):
l = 4*M[j-1,k-1] + 2*M[j-1,k] + M[j-1,k+1]
M[j,k]=rule[ l ]
return M[:,:-1]
def num2rule(number):
if not 0 <= number <= 255:
raise Exception('Invalid rule number')
binary_digits = number.digits(base=2)
return binary_digits + [0]*(8-len(binary_digits))
@interact
def _( initial=selector(['Single-cell', 'Random'], label='Starting condition'), N=input_box(label='Number of iterations',default=100),
rule_number=input_box(label='Rule number',default=110),
size = slider(1, 11, label= 'Size', step_size=1, default=6 ), auto_update=False):
rule = num2rule(rule_number)
M = cellular(rule, N, initial)
plot_M = matrix_plot(M, cmap='binary')
plot_M.show( figsize=[size,size])
