I implemented the attached with
mndynamics.com/papers/bedlewo1 3a multiplier map for hyperbolic components (page 15)

Later I will try to figure out 3b so I can also highlight the filaments that are owned by the mu-units.

Later still I'll try to use wakes to select one specific mu-unit, probably will try to highlight limbs first.

see also: mrob.com/pub/muency/muunit.htm (but I replicated the method behind this one (afaict, something to do with mapping the multiplier to the period 1 cardioid even outside the interior of the mu-unit's owning hyperbolic component) and the distortion of features is too great - there are halos around discs where the supposed mu-unit does not align with the true set shape).

mndynamics.com/indexp.html Mandel by Wolf Jung can do proper renormalization

will dig into its source code (GPL) soon

Follow

oh, if you download the zip, make a new directory and unzip it there, as otherwise it will spam your filesystem with its contents (it isn't packaged nicely in its own tidy directory)

mathr.co.uk/mandelbrot/mu-unit got mu-unit renormalization working, the idea (reverse engineered from the code) I used from Mandel was to use 2 divided by the derivative w.r.t. z of the superstable periodic cycle (excluding the critical point z_crit = 0) as an escape radius for |f^p(z)-z_crit|.

The implementation of Mandel is a bit messy with loads of magic values (eg code does something completely different if one parameter is 65001u vs 65003u). Not many comments either.

I'm not entirely happy with my scaling of the distance estimates relative to the mu-unit and relative to the enclosing entire Mandelbrot set. Need to experiment a bit more.

Sign in to participate in the conversation
lurk.org

Welcome to post.lurk.org, an instance for discussions around cultural freedom, experimental, new media art, net and computational culture, and things like that. This is part of a family of services that include mailing lists, group chat, and XMPP.