ABSTRACT
Benoit Mandelbrot first used the word fractals to describe a set of models that accurately depict natural geometry. He put forward the geometry of fractals that contained infinite details that can accurately model objects such as trees, mountains, and clouds. By 1980 Mandelbrot accomplished his goal while working at Harvard University, and started working on fractal images and exploring the self-similarity characteristic of all fractals. He also worked closely with IBM in its fractal project and added to an incredible visual field of mathematics. Fractals describe objects that are too irregular to fit into traditional geometrical settings. The wavelet transform takes advantage of multifractal self-similarities to compute the distribution of their singularities. Signals that are singular at almost every point are multi-fractals and they appear in the maintenance of economic records, physiological data including heart records, electromagnetic fluctuations in galactic radiation noise, textures in images of natural terrain and variations of traffic flow.
