Investigating Transformational Complexity: Counting Functions a Region Induces on Another in Elementary Cellular Automata

Figure 10

Comparison to known classifications of ECA rules. For each classification, we compare each of our four classes (rows A–D downward) with each of the classes in Martinez [10], by taking the ratio of the number of rules in intersection of the classes to the number of rules in the union of the classes. This gives a number between 0 and 1 which is represented by gray scale here where black is equal to one. A ratio of one indicates that two classes contain exactly the same rules and thus the other classification identifies exactly the same set of rules as a single class. A value of zero means that no rule is in both classes. Note that rules 11, 12, and 16 contain classes that coincide with our class of exceptional rules.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)