Hairy Julias - no-zoom Mandelbrot

[claude]

http://archive.org/details/hairy_julias_2013-06-18

A Mandelbrot set fractal video with no zooming!

I hope to find time later this week to write a blog post about how I made it.

[cKleinhuis]

it is interesting, if i understand it right, those locations are just found in the mset and assembled together to look like a zoom ?=

[Dinkydau]

interesting idea

[claude]

it is interesting, if i understand it right, those locations are just found in the mset and assembled together to look like a zoom ?=

Yes, something along those lines - I wrote one blog post about it so far, more to come..

http://mathr.co.uk/blog/2013-06-23_patterns_of_periods_in_the_mandelbrot_set.html

Each frame is an embedded Julia set near an island, each section loops around one island, the whole video loops around the (top half of) the whole set.

[cKleinhuis]

wow, the nicest document i have seen talking about these periods! congrats
may i ask how you detected such deeper periods?

[claude]

wow, the nicest document i have seen talking about these periods! congrats
may i ask how you detected such deeper periods?

Thanks

I'm using the Jordan curve method described here (essentially: make a box of C coordinates around the target, iterate them until their Z's surround the origin):

http://mrob.com/pub/muency/period.html "Finding the period of a mu-atom"

I use my explorer[0] to navigate to a region of interest, then hold down control and left-click where I want to label, then it finds the period and adds a text label (which stays in place relative to the set when zooming in/out).

It finds the center with that period using Newton's method to know where precisely to put the label.  And there's a feature to find the size of the atom (by using Newton's method to find the bond with the 1/2 child bulb) and automagically zoom in to a region around the atom.

(0) http://hackage.haskell.org/package/gruff written in Haskell with some heavy dependencies, probably a nightmare to get running if you don't have Haskell experience... am eventually going to rewrite it in C or C++ because it seems the GHC/GMP/MPFR incompatibility issue isn't going to go away any time soon

[Fracturbator]

I really enjoyed your animation - quite a different approach from the usual stuff.