Mandelbrot phase angle GIF loop

[billtavis]

animating lines along the phase angle of the normalized iteration count, shows period doubling

[Adam Majewski]

Great. Can you post the code and describe algorithm ?

[billtavis]

Thanks! For every exterior pixel, I used the formula on this page: http://linas.org/art-gallery/escape/ray.html to find the gradient of the potential. In practical terms, this gave me a gx and gy describing the change in smoothed iteration. Then, I just used the value of atan2(gx,gy) to actually draw the image (giving the phase angle of the gradient). I used a different program to run contour lines along this image. I'll post some code for the gradient part when I get to my computer later.

[billtavis]

I posted a function here: http://www.fractalforums.com/programming/smooth-external-angle-of-mandelbrot-set/msg80726/#msg80726 which gives the gradient of a c-value, stored in the variables gzx and gzy. To make this gif, I just plotted the values of

Code:

std::atan2(gzx,gzy);

which gave a grayscale picture of the phase angle of the gradient:



Then I used another program to run contour lines along this grayscale.

[Chris Thomasson]

Simple mesmerizing work. Thank you for posting this excellent piece.

:^D