[MSE] Shape of orbit of iterations with base b on Shell-Thron-region

[Gottfried]

I think \( \Psi^{-1}(z) \) is the ideal tool to understand the behavior, but perhaps Yoccoz's work isn't quite as directly applicable as the general work on https://en.wikipedia.org/wiki/Siegel_disc

Hi Sheldon -

in the meantime I've aggregated more data for plots based on c=silver constant, and I've to recompute accordingly data for the other types of c - just to apply the new insights to the small paper that I'd linked to, and hopefully extend that small paper towards becoming a better "catalogue".            

However, I need a break for a couple of days and surely cannot be much productive in this matter. A question which is coming up at the moment is how to characterize the interior of the \( z_0=1 \) fractal shape, say the set of curves produced by \( 0.5 < z_0 < 0.99 \), somehow like a gradient-field, displaying little arrows instead of dots, perhaps including directions of fractional iteration-height (as far as this might be meaningfully applicable). That's just the desire to embed the observation into known phenomena in other areas, hopefully of the physical world.           

Moreover, I think I've to meditate first a bit about that Yoccoz-work and Siegel-discs which you have directed me to and what this shall give me for the understanding of the whole phenomen.

Cordially -  
Gottfried