
Options for color density are common because some gradients output hugely variable magnitudes resulting in heavy repetitive banding or large areas of the same color. Coloring options often allow colors to be randomised. Limiting the maximum iterations is important when a device's processing power is low. Increasing the iteration count is required if the image is magnified so that fine detail is not lost. One feature of most escape time fractal programs or algebraic-based fractals is a maximum iteration setting. From the early 1980s to about 1995 hundreds of different fractal types were formulated.

Fractals were rendered in computer games as early as 1984 with the release of Rescue on Fractalus!. She followed this up in the March 1984 Acorn User with “Snowflakes and other fractal monsters”. The October 1983 issue of Acorn User magazine carried a BBC BASIC listing for generating fractal shapes by Susan Stepney (now Professor of Computer Science at the University of York. Loren Carpenter created a two-minute color film called Vol Libre for presentation at SIGGRAPH in 1980. This marked the first instance of the generation of fractals by non-linear creations laws or 'escape time fractal'. He and programmers working at IBM generated the first rudimentary fractal printouts.

In 1979, Mandelbrot discovered that one image of the complex plane could be created by iteration.
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The development of the first fractal generating software originated in Benoit Mandelbrot's pursuit of a generalized function for a class of shapes known as Julia sets.
