Escape-time fractals

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(Usually) 2D fractals formed by iterating a function (based on the pixel cooridnates) until the orbit escapes, and colouring the image according the number of iterations required for that to happen. Escape is often towards infinity, in which case the escape condition is something like [math]|Z|\gt R[/math] for some escape radius [math]R[/math]. Sometimes escape towards zero is used, for example when doing periodicity checking (a periodic orbit will never escape to infinity).

Mandelbrot-type fractals add the pixel coordinates each iteration, which often starts from zero. Julia-type fractals add a constant each iteration, while starting from the pixel coordinates.


Original Page by Claude