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Fractals and Fractal geometry were discovered and developed by Benoit Mandlebrot. Mandlebrot was born in Poland in 1924 and emigrated with his family to France in 1936 where his uncle took responsibility for his education. The polish born French man became a mathematical physicist after attending the Lyce Rolin in Paris and the California Institute of Technology in the United States. It was in 1918 that Mandlebrot's uncle showed him a paper, written by Julia, one of the forefathers of modern dynamical systems theory, which faced Mandlebrot with a set of interesting problems. However Mandlebrot did not like it and decided to take a different career path, which in the end brought him back to Julia's paper. Mandlebrot went on to work for the company IBM, where he was able to spend time working with the aid of computer graphics. He was able to show that Julia's work is a source of some of the most beautiful fractals known today. Mandlebrot is considered to be the father of fractals. The word Fractal came from the Latin Fractus meaning broken or irregular, which was introduced by Mandlebrot in 1975. Mandlebrot produced fractals using computers; he generated one of the most famous and puzzling fractals ever seen - Mandlebrot's set. Mandlebrot was convinced that the phenomenon he had discovered was universal and produced many papers on it. It was not until he published his book 'The fractal Geometry of Nature' that he began to be taken seriously, and fractals were really appreciated.
It was Mandlebrot who coined the phrase 'fractal dimension', which is used to describe fractals as they have non integer dimensions and fractals have been shown to have no actual real characteristic scale.
Originally posted by Amorymeltzer
Eh? Math doesn't exist, it's just a creation by mankind to allow us to understand the universe - just another language. Fractals are amazing, but in the end, they're just mathematical functions repeated and changed. If you've ever programmed you can see how easy they are to create. (I prefer Java)
It's not a universal "truth."
Originally posted by Sri Oracle
check out aros fractals... it is pretty easy to use and creates great images. I have been into fractals for a while.
The math comes down to a pretty simple equation that revolves around an "irrational number"; the square root of negative one times some number. The equation creates the graph of the base fractal by using the real vs irrational parts as x and y locations. those two coordinates act as a seed to the equation which then responds that the location is either limiting at zero or limiting at infinity. Then if infinity, it will tell you how many iterations of computation it took to resolve the equation at infinity. The number of iterations is then colored in spectrum. The contrast that you see between the black (zero's) and the spectrum (infinites) is the fractaline image. As you zoom into the image you are in a way adding increasingly "accurate" descriptions of exactly what is occuring (infinity vs. zero limit) to smaller fractions of x,y (rational vs irrational) seeds.