Fractal patterns (or, in short, "fractals") emerged in the 17th century in mathematics. They are characterized by displaying repeating patterns on every scale.
In the 1960s the mathematician Benoit Mandelbrot published a curious mathematical set, which became widely known as the "Mandelbrot set". This set is defined by a very simple mathmetical formula, but its boundaries display self-similar patterns on every scale. The striking properties and appearance of the Mandelbrot set inspired other mathematicians, who soon discovered more sets with similar characteristics.
The term "Fractal", coined by Mandelbrot soon became a paradigm in many disciplines outside of mathematics. Applications of fractals were found in nature, technology, law, economics, finance, and art.
The gateway to the online community of fractal enthusiasts is the Fractal Forums website. This forum has about 30 boards covering all subjects of interest to the fractals community.
Picture 1: The original Mandelbrot fractal
Picture 2: The Newtonian fractal
Picture 3: The Nova fractal
Picture 4: The quadratic julia set fractal
Fractal Forums: http://www.fractalforums.com/
Online fractal generator: http://usefuljs.net/fractals/