[ls65536]

For some reason this also made me think of the boundary of the Mandelbrot set...that place where all the interesting structure reveals itself.

[taneq]

Yep, you're getting it. That same universal principle where the interesting things all happen in that boundary between boring and random (ie. trivially-predictable, and not-predictable-under-any-conditions).

If you haven't already, I heartily recommend James Gleick's book "Chaos" (https://en.wikipedia.org/wiki/Chaos:_Making_a_New_Science) which is, to me, the introduction to both self similarity and sensitive dependence on initial conditions.

[Jerrrrrrry]

https://en.wikipedia.org/wiki/Rule_30

[taneq]

Wow, that's really different to rule 34. :P