The following are examples of variations in rulesets and the inputs that created them.

The above is an example of a perfect permutable, 3-space, ternary, midwise ruleset. To the left of the images shows inputs to the rules and what the rule will output in the next timestep.

The program above is nearly identical to the first program, accept for it's nwise. n = -1 so we would say it is leftwise.

Here is where things get interesting,

I have been talking about perfect permutable ECA. This implies the existence of imperfect permutable ECA. Any investigation into the science of complex dynamics necessitates a comfortability, and even appreciation of imperfection. This exploration has taught me just how beautiful imperfection can be.

Before we dive in to imperfect permutables, let's examine the outputs of a perfect permutable 2-space binary midwise ECA.

Below is a perfect permutable 2-space binary midwise ECA.

Images below show different outputs based on ruleset inputs 00, 01, 10, 11.

Amazingly, even perfect permutable 2-space binary ECA are capable of some interesting behavior. Unfortunately, the most complex behavior we can see is in the two cases where a Sierpinski triangle is generated. It is possible that we have hit a lower bound in the rules needed for behavioral complexity (maybe/maybe not). At least for perfect permutable 2-space binary rulesets, it seems nothing more complex than the Sierpinski triangle is generated. That doesn't mean there isn't a workaround... There are some incredible surprises waiting for us in the next section.

Let's keep exploring.

I think it's time I introduce 'imperfect' or partial permutable ECA.

Section 3