Differential method


Fig. 1: Ordinary Mandelbrot equation. Each frame chooses a different coloring. That is, if the number of iterations n is larger than some distinct value (which is chosen differently in each frame) the color is black.


Fig. 2: To create this picture, the rate of change dz (in addition to z) is calculated during the iterations. The final value of dz determines if the point is colored black.


Apparently no coloring choice in Fig. 1 is able to produce Fig. 2 which shows the structure of the fractal very clearly, independent of the number of iterations (depth) in a certain area of the Mandelbrot Set. This technique is very useful for creating black and white fractals but it can also be used to create nice colored fractals like the ones below.

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