Types Of Fractals

As we said earlier, Fractals are generated using some kind of mathematical relationship(Algorithm). There are three common types of systems which are used to genetate fractals.

Escape-time fractals — These are defined by a recurrence relation at each point in a space (such as the complex plane). Examples of this type are the

Mandelbrot set



Julia set


Burning Ship fractal

*pics in courtesy of www.wikipedia.org


Iterated function systems — These have a fixed geometric replacement rule. Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Heighway dragon curve, T-Square, Menger sponge, are some examples of such fractals.


Sierpinski carpet



Sierpinski gasket



More interesting examples...

2-D tree generated using IFS



3-D trees generated using IFS









For more details on Iterated Function Systems,visit:
http://iteratedfunctions.blogspot.com/


Random fractals — Generated by stochastic rather than deterministic processes, for example, trajectories of the Brownian motion, Lévy flight, fractal landscapes and the Brownian tree. The latter yields so-called mass- or dendritic fractals, for example, diffusion-limited aggregation or reaction-limited aggregation clusters.


await for more details!!!!