Application of Fractal Mathematics In Economics

Abstract

The notion of fractals was developed by Benoit Mandelbrot in the 1960's. He found that nature exhibits not simply a higher degree but an altogether different level of complexity. Nature shows fractal (self-similar) properties everywhere. For example, a branch has a shape similar to the whole tree. The self-similar property that lies in nature was ignored by scientists for a long time. From the early days of Euclidean geometry to the present century, mathematicians and scientists measured the natural world by straight lines, circles and other regular shapes. But clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, etc(Peitgen & Richter 1). The fractal idea gives another visual prospective from which to measure nature. It has been used in many branches of science and has helped to explore new territory. Economics is complex because it is affected by both nature and human behavior. To measure an economic systems by traditional mathematical tools has not given satisfactory solutions for many problems. Fractal mathematics helps economists find new truth in a complex world. Through this thesis, the reader will see its application in solving selected problems in economics.