A fractal as a geometric object generally has the following features:
- fine structure at arbitrarily small scales
- is too irregular to be easily described in traditional Euclidean geometric language.
- is self-similar (at least approximatively or stochastically)
- has a Hausdorff dimension that is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve)
- has a simple and recursive definition.
For example:
Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, mountains, river networks, cauliflower or broccoli, and systems of blood vessels.
Trees and ferns are fractal in nature and can be modeled on a computer by using a recursive algorithm. This recursive nature is obvious in these examples — a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature.
Following are some Fractal programs - have fun!
