Mandelbrot phase angle GIF loop

billtavis

Safarist

Posts: 96

Mandelbrot phase angle GIF loop

« on: February 18, 2015, 09:58:28 PM »

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


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Adam Majewski

Fractal Lover

Posts: 221

Re: Mandelbrot phase angle GIF loop

« Reply #1 on: February 18, 2015, 11:18:35 PM »

Great. Can you post the code and describe algorithm ?


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billtavis

Safarist

Posts: 96

Re: Mandelbrot phase angle GIF loop

« Reply #2 on: February 19, 2015, 04:58:42 PM »

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.


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billtavis

Safarist

Posts: 96

Re: Mandelbrot phase angle GIF loop

« Reply #3 on: February 20, 2015, 06:41:31 PM »

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.


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Chris Thomasson

Conqueror

Posts: 137

Re: Mandelbrot phase angle GIF loop

« Reply #4 on: February 24, 2015, 06:29:58 AM »

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

:^D


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