Mandelbrot Set Zoom

For more information, see http://www.imajeenyus.com/mathematics/20121112_distance_estimates/index.shtml.

Note the Julia sets visible along the way.

Loosely based on Tanner Helland's code at http://www.tannerhelland.com/1494/mandelbrot-vb6/

480x360 pixel frame size, 15fps framerate.

Center at -0.722567163621032, -0.260810355401819
Width at maximum zoom 1E-14 (if the original set stretched from the earth to the sun, the final image would be only 0.25mm wide). Final magnification 300 million million times.

Each frame is 5% smaller than previous.

To calculate widths. Let n= frame number, n goes from 0 to 650.
Width= 5*(0.95^n)

Maximum iterations need to increase at higher magnifications to get a better image. I use maxiter=1000+(1.95E-6*exp(0.03371*n)). This reaches about 10,000 in the last frame.

Colouring scheme. Calculate both the distance estimate (v_dist) and escape time (v_esc). Normalise both to 0...1. Calculate RGB value of pixel using
Red=(1-(v_dist^0.2))*255
Green=v_esc*255
Blue=0

Done in good old Visual Basic 6, render time about 10 hours. Video made with MakeAVI.

Видео Mandelbrot Set Zoom канала Lindsay Wilson