There are many programs and algorithms used to plot the Mandelbrot set and other fractals on a computing device. These programs use a variety of methods to determine the color of each individual pixel efficiently. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Wikipedia: Plotting algorithms for the Mandelbrot set
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There are many programs and algorithms used to plot the Mandelbrot set and other fractals, some of which are described in fractal-generating software.
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