The ideas of fractals were developed by Mathematicians such as Cantor, Hausdorff, Julia, Koch, Peano, Poincare, Richardson, Sierpinski and Weierstrass. They all had ideas which were largely ignored until Mandelbrot presence who took these ideas to a new level.
Fractals are a part of fractal geometry, which is a branch of mathematics concerned with irregular patterns made of parts that are in some way similar to the whole (e.g.: twigs and tree branches). Fractal geometry should not be confused with conventional geometry. Conventional geometry concerns mostly with regular shapes and whole number dimensions, such as lines which are one-dimensional or cones, which are three-dimensional. Fractal geometry on the other hand deals with shapes found in nature that have non-integer, or fractal, dimensions -- like rivers with a fractal dimension of about 1.2 and cone-like mountains with a fractal dimension between 2 and 3.
A fractal is a design of infinite details. It is created using a mathematical formula. No matter how closely you look at a fractal, it never loses it detail. It is infinitely detailed, yet it can be contained in a finite space. Fractals are generally self-similar and independent of scale.
The theory of fractals was developed from Benoit Mandelbrot's study of complexity and chaos. According to Mandelbrot, who invented the word: "I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means "to break:" to create irregular fragments. It is therefore sensible - and how appropriate for our needs! - that, in addition to "fragmented" (as in fraction or refraction), fractus should also mean "irregular," both meanings being preserved in fragment." (The Fractal Geometry of Nature, page 4.)
Fractals today are important as they have been applied in diverse fields such as stock market, chemical industry, meteorology and computer graphics.
What is the length of the British Columbian coastline?