Coevolving Complements

rule for positive

118

rule for negative

673

mask

rule

step

random

run random

automata

reset

pause

run

combination

difference

sum

observe

mask

positive

negative

mix

seed random

The initial image

g

is the overlay of two complementary masks

b

and

d

. This overlay evolves according to two rules

p

and

q

. The result

u

of evolving

g

by the first rule

p

is masked by multiplication with bitmap mask

b

. The result

v

of evolving

g

by the second rule

q

is masked by multiplication with the inverted bitmask

d

which is taken to be

1-b

. The sum of the results

b×u

and

d×v

gives the next image

g'

.

The rule numbers

p

and

q

specify two of the 1024 totalistic 9-neighbor two-color cellular automaton rules.

In this Demonstration mask

b

and its negative

d

can display (1) the selected rule numbers, (2) a number which gives the number of the current step, (3) static random patterns, or (4) a new random pattern for each step.

Note that the sums of the masked automaton results are always positive. Differences of those intermediary masked results can give negative values. However, taking the absolute value makes negative results of differences acceptable for the next step of evolution by the binary automaton rules

p

and

q

.