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Cellular Automata Entropy

​
P(A)
0.7
rule
110
size
random seed
P(A) 0.7
P(B) 0.3
number of black cells: 214
number of white cells: 206
entropy: -
214P(A)log(P(A))
log(2)
-
206P(B)log(P(B))
log(2)
184.428
The entropy of a list
Q
is defined by
H(Q)=-∑P(q)
log
2
P(q)
, summing over the elements
q
of
Q
.
P(A)
and
P(B)
are the probabilities of black and white cells, respectively. The initial condition is a finite list of random bits.
The entropy can be used to study the amount of information in the evolution of a cellular automaton; it is lower in ordered systems and higher in chaotic (disordered) systems.
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