I can confirm your finding. complexity raises really fast this way

I have to say that I already did this, but more intuitivley than in the analytic way you did it. Fascinating what happens when you really repeat this very often.

I'm still trying to find out how and why this works.

Unsure if I use the mathematical correct words to desribe this:

I guess it's simple periodic doubling (but of an already complex shape).

Íf you doulbe an already very complex part of the julia set (instead of e.g. a simple spiral at the beginning) you double that complexity. its like 128² compared to 2².

and if you repeat this process all over the complexity must rise much faster than if you take the long route.

though of course you will reach 128 too when starting with 2². but at much deeper zoom depth.

it might not "speed up" the distance to the next minibrot, but the minibrot is much more complex than without.

the only "downside" to this is that you will only repeat the simple patterns you used in the very beginning, the shapestacking phase.

with the long route you can still change details in your zoom path at any time.

details that of course show up later. but those will be subtle details in complex deep julia-sets like your example from yesterday. so it doesn'T really matter in that context.

I guess you could call it level-2-shapestacking. shapestacking of julia-sets.

very interesting. nice share.