Fractal Geometry Essay Example | Topics and Well Written Essays - 500 words

Fractal Geometry - Essay Example In colloquial speech fractal is a shape which is self-similar or recursively constructed. It means that such shape is similar at all levels of magnification and therefore it is sometimes called "infinitely complex". In the sphere of mathematic the word "fractal" means geometric object "that satisfies a specific technical condition, namely having a Hausdoff dimension greater than its topological dimension". (26) The simplest fractal is known to be Cantor Bar Set which was called after German famous mathematician. It is necessary to admit that fractals refer not only to the realm of geometry and mathematics. They can be found everywhere in natural world. Self-similarity (recursive nature) means that fractals are constructed by iteration and they are made up of the smaller parts (copies) of themselves. The examples of self-similarity are Sierpinski Gasket, the Mandelbrot Set, Self-affine fractals, etc. it must be admitted that fractals are not all self-similar objects. Scientists found out three main types of self-similarity: Exact self-similarity means that fractals are completely identical at all levels of magnification. It is the strongest type of self-similarity, because fractals bear exact and complete self-similarity. Quasi-self similarity is a loose form of self-similarity. It means that fractals are approximately identical, but not completely.