Video (3min 30sec) of An extremely deep dive into the mandelbrot zoom (fractal). If the final frame were the size of your screen, the full set would be larger than the known universe. "
A fractal as a geometric object generally has the following
features: It has a fine structure at arbitrarily small scales. It is too irregular to be easily described in traditional
Euclidean geometric language. It is self-similar (at least
approximately or stochastically). It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as
the Hilbert curve). It has a simple and recursive definition.
Because they appear similar at all levels of magnification,
fractals
are often considered to be infinitely complex (in informal terms).
Natural objects that approximate fractals to a degree include clouds,
mountain ranges, lightning bolts, coastlines, and snow flakes. However,
not all self-similar objects are fractals—for example, the real
line (a straight Euclidean
line) is formally self-similar but fails to have other fractal
characteristics.
