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.
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.