ABSTRACT
The concept of fractals was initially proposed by B.B. Mandelbort in 1975, after he had spent a long period of time on several scientific areas that have been historically remote and had hardly anyone considered. Like other concepts in history, the groundwork for such a concept had been laid for quite some time. For example, in the early nineteenth century, French mathematician Poincare employed some innovative geometric methods in his studies of the three-body problem. However, due to its level of theoretical difficulty, hardly anyone noticed these methods. In 1875, German mathematician Weierstrass constructed a surprisingly continuous function that is not differentiable everywhere. After that, Cantor, the founder of set theory, constructed his well-known trichotomic Cantor set with a great many strange properties. In 1890, Italian mathematician Guiseppe Peano discovered an incredible curve that can theoretically fill a space. In 1904, Swedish mathematician Cohen designed a curve that looks like a snow flake and the edge of an island. Ten years later, Polish mathematician Sierpinski successfully drew such geometric figures that look like a carpet and sponge. However, due to their peculiarity, all these discoveries suffered from the same fate: they were laid aside without being investigated further. However, it is the commonalities of these peculiar discoveries that some rich mathematical thoughts were germinated. In the 1920s, German mathematician Hausdorff introduced the concept of fractal dimension in order to study the properties of peculiar sets. After that, several mathematicians employed the concept of fractal dimensions to resolve their individual research problems. However, these exotic and innovative mathematical thoughts and concepts were initially introduced to overthrow an accepted conclusion. It was not until 1975 that these incomprehensible small pieces of knowledge were assembled together to form a new field of scientific activities.
