Popcorn City, an example of fractal architecture on a moon of the hydrojovian gas giant Aexion
Architecture based upon three-dimensional extrusions of various mathematical fractal formulae.
A building or city constructed using fractal architecture incorporates a large number of self-similar structures, but in most cases the smallest structures are large enough to provide usable living or storage space. Some intelligent superobjects incorporate fractal designs and do not have to accomodate biont living spaces, and may incorporate very small fractal structures indeed.
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.
Fractal Dimension - Text by M. Alan Kazlev 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.