Title: Mandelbrot phase angle GIF loop Post by: billtavis on February 18, 2015, 09:58:28 PM animating lines along the phase angle of the normalized iteration count, shows period doubling
(http://38.media.tumblr.com/73d8f63e5cff5339c8cda3e46378e24c/tumblr_njtnrcK6Fc1tre1zbo1_500.gif) Title: Re: Mandelbrot phase angle GIF loop Post by: Adam Majewski on February 18, 2015, 11:18:35 PM Great. Can you post the code and describe algorithm ?
Title: Re: Mandelbrot phase angle GIF loop Post by: billtavis 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.
Title: Re: Mandelbrot phase angle GIF loop Post by: billtavis 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); (http://i288.photobucket.com/albums/ll174/BillTavis/MandelbrotAngleOfGradient_zpsin5ldxqv.png) Then I used another program to run contour lines along this grayscale. Title: Re: Mandelbrot phase angle GIF loop Post by: Chris Thomasson on February 24, 2015, 06:29:58 AM Simple mesmerizing work. Thank you for posting this excellent piece. :^D |