In Geometry, a Fractal is defined as an object with an irregular geometric shape each part of which is statistically similar to the whole. This property, which we call self-similarity, is one of the most curious aspects of Fractals.
Fractals aren't only abstract concept, indeed they exist in the real world if we observe them within a certain scale. The shape of sea cost, constellations, trees and some vegetables are examples of Fractals, just to name a few.
Fractals can be found in places where we don't expect to find them. The mathematician Benôit Mandelbrot, who is the father of Fractal Geometry, demonstrated that we can create a Fractal from a simple equation, the same equation which represents the behavior of a dynamic system.
Mandelbrot adopted the word Fractal from latin Fractus, which means irregular, in 1975, to describe a complete new class of objects with similar properties, such as self-similarity and fractional dimension. All these interesting properties of Fractals are summarized in the book "The Fractal Geometry of Nature", published in 1982.
Mandelbrot revealed a subtle connection between Fractals and the concept of Deterministic Chaos in Physics. Fractals represent indeed an interesting subject which connects Geometry to Mathematics, and Geometry to Physics.
The equation studied by Mandelbrot, toghether with other equations which were studied by mathematicians Gaston Juila and Pierre Fatou, became famous with the diffusion of personal computers capable of advanced computer graphics.
Many people used those equations to create beautiful images, which sometimes we call images of Chaos, because of their relastionship with the chaotic behavior of dynamic systems. Worth mentioning the book "The Beauty of Fractals" by mathematicians Heinz-Otto Peitgen and Peter Richter, which first promoted Fractals with photographs.
NextFractal aims to continue the tradition of many other Fractal generators, making available to everyone simple but powerful tools for exploring the fascinating territory of Mandelbrot, Julia and Fatou Sets, without requiring a deep knowledge of the theory behind.