A fractal is “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,” a property called self-similarity. Roots of mathematical interest in fractals can be traced back to the late 19th Century; however, the term “fractal” was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning “broken” or “fractured.” A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.

definition from Wikipedia

Fibonacci Sequence when nature meets numbers

Fractals in nature:

Web resources and tutorials:

For those who want to experience with fractals :

A real time freeware fractal generator for MS Windows – ChaosPro

Flash tutorial – Fractals in ActionScript 3

Paul Nylander’s site – Fractals Math and Physics simulations