Introducing Fractal Geometry
Fractal geometry is the geometry of the natural world. It mirrors the uneven but real shapes of nature, the world as we actually experience it, unlike the idealized forms of Euclidean geometry. We see fractals everywhere. Indeed, we are fractal! Using computers, fractal geometry can make precise models of physical structures - from ferns, arteries and brains to galaxies. Fractal geometry is a new language. Once you are able to speak it, you can describe the shape of a cloud as precisely as an architect can describe a house. new discipline from Zeno to calculus, set theory and the first maverick mathematicians who set the stage for the genius of fractal geometry, Benoit Mandelbrot. Text and graphics combine to offer the most accessible account of fractal geometry that any reader is likely to find. To quote J.A. Wheeler, protege of Niels Bohr and friend of Albert Einstein: No one will be considered scientifically literate tomorrow, who is not familiar with fractals. This book is the ideal guide to that literacy.
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affine transformation attractor axis behaviour BenoTt Mandelbrot bifurcations Big Bang boundary Bourbaki brains calculus called Cantor set cells chaos theory circulatory system complex numbers complex plane cycle of period describe discovered discovery draw another dot dynamics equations esarqus esclrc explored feedback Feigenbaum fractal complexity fractal dimension fractal geometry fractal nature fractal structure graphic Hausdorff idea images imaginary numbers infinite infinity iteration Julia sets Karl Weierstrass Koch curve lan Stewart llll look lt's M-set Mandelbrot set mapping mathematicians mathematics Michael Barnsley Newton's one-third-sized copies Pascal's Triangle patterns phase transitions physical Pierre Fatou Poincare population problem random rate of change real numbers real world repeat revealed Roger Penrose scales scientists screens self-affinity Self-Similarity Sierpinski gasket Sierpinski triangle smaller and smaller square starting point straight line strange television documentary topological tree Uncle Szolem universe Verhulst visual word fractal wrinkly