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The simplest algorithm for generating a representation of the Mandelbrot set is known as the "escape time" algorithm. A repeating calculation is performed for each x, y point in the plot area and based on the behavior of that calculation, a color is chosen for that pixel.
Mandelbrot used quadratic formulas described by the French mathematician Gaston Julia. [14] The maximum fractal dimension that can be produced varies according to type and is sometimes limited according to the method implemented. There are numerous coloring methods that can be applied. One of earliest was the escape time algorithm. [14]
Here, the most widely used and simplest algorithm will be demonstrated, namely, the naïve "escape time algorithm". In the escape time algorithm, a repeating calculation is performed for each x , y point in the plot area and based on the behavior of that calculation, a color is chosen for that pixel.
The best known example of this kind of fractal is the Mandelbrot set, which is based upon the function z n+1 = z n 2 + c. The most common way of colouring Mandelbrot images is by taking the number of iterations required to reach a certain bailout value and then assigning that value a colour. This is called the escape time algorithm.
There's already sufficient pseudocode in the section Mandelbrot set#Escape time algorithm. ~Amatulić 21:02, 14 May 2016 (UTC) I have a problem with "If the above loop never terminates return true". Even in very abstract pseudocode, I don't think you can get away with a test that cannot be implemented in any language.
Enlarged first quadrant of the multibrot set for the iteration z ↦ z −2 + c rendered with the Escape Time algorithm. Enlarged first quadrant of the multibrot set for the iteration z ↦ z −2 + c rendered using the Lyapunov exponent of the sequence as a stability criterion rather than using the Escape Time algorithm. Periodicity checking ...
The Escape Time Algorithm pseudocode can be the same for Mandelbrot set and Multibrot sets. Provided it is clearly linked from both these articles, I don't think it matters whether it is located in Wikipedia or in the Wikibook on fractals. Cuddlyable3 20:27, 1 October 2008 (UTC)
XaoS is an interactive fractal zoomer program.It allows the user to continuously zoom in or out of a fractal in real-time. XaoS is licensed under GPL.The program is cross-platform, and is available for a variety of operating systems, including Linux, Windows, Mac OS X, BeOS and others.