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13.) Where did fractals come from?

The word FRACTAL was first used by Benoit Mandelbrot. These are interesting mathematical figures due to the fact that as you zoom in closer to the middle of the figure, the pattern is just as beautiful as the outside complexity. The first fractals described date back to the 19th century. The most ancient fractal that is known is Cantor's dust. Peano published, in 1890, his famous curve, followed by a similar curve, yet less well-known, published by Hilbert in 1891.

Peano's curve

Hilbert's curve

Sierpinski also produced a well known fractal: Sierpinski's Triangle. This was produced in 1915.

Natural objects, such as Britain's coast, were prominent in Mandelbrot's explanation of fractals. Britain's coast, when examined closer, seems to get smaller and smaller in size. Therefore, Mandelbrot stated that the coast of Britain is infinite, a statement that is not considered literal, but had clearly been stated by Perrin without mathematical justification.

Mathematical functions also contributed to Mandelbrot's explanations. Fundamental works were also explained by Besicovitch and Hausdorff. This dimension, later, played an important role in Mandelbrot's explanation.

By compiling all of his knowledge and the discoveries of other mathematicians. At first, these were just scattered elments with no significant meaning. However, Mandelbrot compiled them into many explanations about fractals and what the mathematical explanations are behind their looks. The word fractal was invented and has been used prominently since 1975.

This information was found at

http://fractals.iut.u-bordeaux1.fr/jpl/history.html