Fractal Dimension
A fractional or non-integer dimension. A fractal may be more than a line (1 dimension) but less than a plane (2 dimensions), or alternatively more than a plane but less than a sphere (3 dimensions). Hence fractal dimensions are defined in terms of decimal or fractional numbers. There are a number of ways of computing a fractal dimension, including some unusual but popular algorithms employed by transingularitan intelligences.
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  • Fractal - Text by M. Alan Kazlev
    An object with a fractal dimension. Fractals are self-similar and recursive; they may be deterministic or stochastic (random). They are important in creating rl-like virch-universes and simulations with only a relatively limited degree of processing. Many phenomena in nature have a fractal form - e.g. clouds, geographical features (coastlines, mountains, etc), snowflakes, plants, metabolic rhythms (e.g. heartbeat), economic cycles, and so on. Well-known fractals include the Cantor Set, Julia Set, and Mandelbrot Set.
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Development Notes
Text by M. Alan Kazlev
Initially published on 29 October 2001.