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is it possible to find the center of the big black spot(the area which with the set?) I've tried to loop through all points which are in the set, sum their locationד and eventually divided by the num of points which are in the set.

it didn't work as expected because the the set isn't formed, e.g its not a perfect sphere or a square therefore the center always changes. is there another way of finding the center?

thanks!

igal k
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2 Answers2

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Look for centers of mandelbrot set hyperbolic components

enter image description here

http://fraktal.republika.pl/eigensolve.html

Adam
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Adam
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That shape is a perfect cardioid (no other similar shapes in the Mandelbrot set are perfect cardioids, they are somewhat distorted).

Check Wikipedia, you'll find the equation for calculating the cardioid itself: http://en.wikipedia.org/wiki/Cardioid

Note, however that at the borders of the Mandelbrot map (where the black and non-black area meets) deciding whether a point belongs to the map or not, heavily depends on how many times you iterate z = z^2 + c. If you iterate it 50 times, the main cardioid will be smaller than if you iterate it 500 times because with 500 iteration more points at the border will go to infinity.

karatedog
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  • Thanks for your reply! as you said, the mandelbrot's center is defined accordingly to the max_iterations value. after i've managed to store the points which are in the mandelbrot, i simply had to find the edges of the set and calculate their average. – igal k Apr 04 '12 at 12:01