![]() In its article entitled "How Mandelbrot's fractals changed the world," the BBC states that fractal geometry has practical applications in diverse areas including diagnosing some diseases, computer file compression systems and the architecture of the networks that make up the Internet. Our world has fractals everywhere exemplified by trees, mountains, blood vessels, mycelium strands, stock market graphs, weather patterns, seismic rhythms, ECG signals and brain waves. As an "IBM fellow," he had access to some of the best computers and technical assistants available for his research at the time.įigure 0.1. The Mandelbrot Set Figure 0.2. Julia Set Figure 0.3. Newton Fractal Benoit Mandelbrot coined the term “fractal” in 1975 and created a branch of mathematics called fractal geometry seven years later. Speaking loosely without using technical terms such as the Hausdorff-Besicovitch dimension, a fractal is an object that is self-similar, i.e., a large part of it contains smaller parts that resemble the large part in some way see Figures 0.1-0.7 shown below. Julia Sets Generalizations The Logistic Equation Newton Fractalsįractal Coloring Algorithms Sekino's Home Page ![]() The Divergence Scheme The Mandelbrot Set The Convergence Scheme Preface Preparations : Dynamical Systems, Orbits and Canvases from MathThematics, Book 3, Houghton Mifflin, 1998, 2008. He now combines art and mathematics to create fractal art. ![]() Digital Artist (Author's Profile): When Junpei Sekino was 10 years old he won first prize for the junior division in a national printmaking contest in Japan. ![]()
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