Page "Fractal" Paragraph 9

The history of fractals traces a path from chiefly theoretical studies to modern applications in computer graphics, with several notable people contributing canonical fractal forms along the way.

According to Pickover, the mathematics behind fractals began to take shape in the 17th century when the mathematician and philosopher Gottfried Leibniz pondered recursive self-similarity ( although he made the mistake of thinking that only the straight line was self-similar in this sense ).

In his writings, Leibniz used the term " fractional exponents ", but lamented that " Geometry " did not yet know of them.

Indeed, according to various historical accounts, after that point few mathematicians tackled the issues and the work of those who did remained obscured largely because of resistance to such unfamiliar emerging concepts, which were sometimes referred to as mathematical " monsters ".

Thus, it was not until two centuries had passed that in 1872 Karl Weierstrass presented the first definition of a function with a graph that would today be considered fractal, having the non-intuitive property of being everywhere continuous but nowhere differentiable.

Not long after that, in 1883, Georg Cantor, who attended lectures by Weierstrass, published examples of subsets of the real line known as Cantor sets, which had unusual properties and are now recognized as fractals.

Also in the last part of that century, Felix Klein and Henri Poincaré introduced a category of fractal that has come to be called " self-inverse " fractals.