Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise
Courier Corporation, Mar 13, 2012 - 429 pages
This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author ? hailed by Publishers Weekly as a modern Lewis Carroll ? conveys memorable insights in the form of puns and puzzles. 1992 edition.
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approximation asymptotically bifurcation binary fractions Brownian motion called Cantor dust Cantor set cellular cellular automata chaos bands chaotic Chapter cluster construction continued fraction converge corresponding course curve deﬁned deterministic diffraction digits distribution energy equal equation Euclidean example exponent fact Fibonacci Fibonacci numbers ﬁeld ﬁnd ﬁnite ﬁrst ﬁxed point Fourier fractal dimension frequency ratio function geometric given golden mean Hausdorff dimension inﬁnite initial integer invariant irrational numbers iterated map Iulia set logarithmic spiral Mandelbrot mathematical modulo multifractal noise nonlinear obtained orbit of period parameter values pattern percolation threshold perimeter period length period-doubling physical plane power law power spectrum probability quadratic map quasicrystals rabbit sequence random rational numbers recursion result scaling factor self-similar shows Sierpinski gasket silver means similar simple smaller spin square lattice strange attractors superstable orbit symbolic dynamics symmetry theory trees triangle two-dimensional unit interval variable winding number zero