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Hi Hobold,
How did you chose where to seed the rays? Do you have a way to calculate the distance between points on the iso-contour boundary?

If you look at the picture I attached earlier, you can see the Mandelbrot set surrounded by a warped checker board pattern. The algorithm scans along the edges of those curvy rectangles and locks on to their corners.

I start from one of the outer (almost-)circles, with a few hand initialized vertices. Then I can refine an existing polyline from there repeatedly. First I move the vertices inward by scanning along the respective bin border. Then one new point is inserted halfway between any two existing points, and its location refined with bisection. I can make use of the theoretical property that equipotential lines are always orthogonal to field lines to get good initial guesses of scanning direction.

It's not a particularly sophisticated method. But todays hardware has so much brute force ...

EDIT: Wait! You want to know where that checker board pattern is coming from? The equipotential lines are just the usual coloring according to number of iterations. The rays emerge when you look at the sign bit of the imaginary component of the final iteration. I.e. you check if the escaped value is above or below the real axis, and then brighten or darken the pixel accordingly.

If I get enough complaints about the program's uselessness, I might even go and shoehorn my homebrew multiprecision arithmetic into it. Then it can waste even more cycles and RAM.

But jokes aside, If anyone wants to play with the algorithm, trying to make it more practically useful, I'll gladly explain whatever the hell I was thinking when I wrote some unintelligible piece of the program. Ask away! There are no stupid questions, only stupid answers.

Glad you liked it!

As always, my ideas and code fragments come with a "give credit where credit is due" license, and otherwise I do not care if you get rich or famous with them. I would love to be rewarded with ever more beautiful fractal imagery, and I would hate if you took over the world with a logic bomb that I helped build. But there is no obligation to do the former or to not do the latter.

a julia animation