174 pages : 21 cm

Includes bibliographical references and index

Why do fractals matter? -- A smooth world or a rough one? -- The texture of reality -- The origins of fractals -- Classical geometry -- The calculus -- The paradox of infinitesimals -- Effects of Calculus -- The first fractal -- Explaining numbers -- Form foundations and sets -- What are sets? -- Cantor and the continuum -- The Cantor set -- Peano's space-filling curve -- Topological and fractal dimension -- Self-similarity -- The Koch curve -- Similarity dimension -- Similarity and fractal dimension -- Measuring fractal dimension -- Lewis Richardson -- How long is a coastline? -- The Sierpinski Gasket -- The chaos game -- Strange attractor -- Pascal's triangle -- Basins of attraction -- Poincare and non-linearity -- Mathus and population growth -- Negative feedback -- The logistic equation -- Iteration -- Video feedback -- Robert May and the Verhulst Model -- Bifurcation points -- The period-doubling cascade -- The fig tree -- Chaos theory and fractals -- The Feigenbaum constant -- Real numbers, other numbers -- Complex numbers -- The complex plane -- Gaston Julia and Pierre Fatou -- Benoit Mandelbrot -- Uncle Szolem -- A practical education -- The shape of things -- The wiles of Bourbaki -- On the run again -- The more the merrier -- Emerging patterns -- Fractals in practice -- Bad noise -- A general principle emerges -- The simplest possible transformation -- Two types of Julia sets -- A map of Julia sets -- A whole new world -- Simple rules, complex behaviour -- Newton's law and chaos -- Let's admit, it is complicated -- Phase transitions -- Hazy areas of calculation -- The mathematics of wrinkles -- Natural templates -- Forest fires: the fractal boundary -- More phase transitions -- Electro-plated fractals -- Viscous fingering -- Growth by aggregation -- Brownian motion and the quantum world -- Dimensional magic -- The three-quarter power law -- The mysterious brain -- Knowing the mind of God -- Fractals and medical research -- Viruses and bacteria -- AIDS -- Detecting cancer -- Women at risk -- Bubbly bones and breaks -- Fractal beats -- Practical solutions -- Striking oil -- The spring is sprung -- Stress loadings -- Detection -- Fractal ecology -- Orchid fractals and crowds -- Olbers' paradox -- The Great Wall -- The Big bang -- Cosmic connections -- How do we see? -- Fractal image compression-- Affine transformations -- Morphogenesis -- Satellites -- The money markets -- What are the rules? -- Market self-affinity -- Generators -- Beyond portfolio theory -- Multifractals -- Fractals in art: Mandalas -- Decorative patterns: self-similarity -- Scaling and repetition -- Cues in the landscape -- Fractals in music -- Dysfunction in modern architecture -- Organic architecture -- Fractal traditions -- Strength in the details -- Fracology -- Quo vadis? -- Not everyone agrees -- The special talent of mandelbrot -- The order is out there

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