Julia Set Animation by boundary walking Mandelbrot

[asimes]

I found an old post about walking through the Julia Set. Because the post was pretty old I figured I'd start a new one but the old one is here: http://www.fractalforums.com/general-discussion-b77/how-would-you-define-a-path-along-mandelbrot-border/msg43113/

Here was my method:

- Find all points that are part of the Mandelbrot Set
- Find all points that touch the Mandelbrot Set that are not inside of it (I'll call this Boundary Set)
- Organize the Boundary Set by theta and store the associated real and imaginary points in that order
- Run the Julia Set in a loop through the organized points

It doesn't quite work as well as I would like. It is pretty close but it looks glitchy because organization by theta is not quite accurate enough. Here's the result so far: http://alexsimes.com/Julia_Test/index.html

[asimes]

I can't seem to get stable looking results with high iterations of the Mandelbrot Set. If I set the max iterations to something small then the resulting Julia Set animation is very smooth but also boring because it misses the complicated Julia Sets.

Any thoughts on how to index the points on the boundary of the Mandelbrot Set? I have the points, the problem with theta sorting seems to be that the Mandelbrot spikes / branches that go perpendicular cause incorrect sorting.

[eiffie]

Actually the path finding method described early in the other post worked well but I still had the problem of "flashing" julias as you describe. It doesn't matter how accurately you define the border as it is fractal and "rough" at all scales. When you combine the julias with an image of the mandelbrot showing the start position on the border you see interesting relationships between the two. It was an education. Good luck!