ABSTRACT
Recent advances in nonlinear dynamics have led to the concepts of fractals and fractal dimension. In 1919, Hausdorff and Besicovitch extended the definition of dimension to fraction and created the fundamental mathematical principles of fractional dimension in their study of pathological structure in geometry. In 1975, Mandelbrot studied some special geometric structures and related physical phenomena that could not be explained with Euclidean geometry based on the fractional dimension, and created the fractal geometry theory.
