Fractal (Latin : fractus - "broken" or "fractured") was defined
by the mathematician Benoit Mandelbrot in 1975
as an irregular self-similar shape (geometrical object),
which however much magnified or reduced,
repeats itself (iterates)
in identical detail ad infinitum.
It cannot be represented by classical (Euclidian) geometry.
A fractal is a graphical image that represents the behaviour of a mathematical
equation.
They are used for illustrating the regular features of complex objects and
patterns,
and allow order to be perceived in disorder.
For example, a river has tributaries, which have tributaries, etc.
A tributary has the same organization as the entire river, but over a smaller
area.
Other examples are : Tree branches and roots, blood vessels,
flowers, snowflakes,
nerves, clouds, lungs, feathers, landscape with peaks and valleys,
aggregates, spider webs, coastline with inlets and peninsulas,
turbulent flow vortices, ferns, populations, movement of economic indices,
the distribution of mass within a galaxy,
the distribution of galaxies in the universe...
Natural objects are random versions of mathematical fractals,
and are statistically self-similar.
Fractal
maths offers models of the processes
that produce natural objects / structures.
Fractals are seen in pre-computer art such as : paisleys,
mandalas, and stupas.
Most
fractal computer art
(1)(2)
starts with a small section of a simple fractal image,
which is repeatedly sectioned and re-magnified.
The process could be repeated indefinitely,
expanding the original image to greater than the size
of the known universe
and beyond.
The mathematics are infinite,
computer precision limits the possibilities. TOP
