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The Beauty of Fractals is a 1986 book by Heinz-Otto Peitgen and Peter Richter which publicises the fields of complex dynamics, chaos theory and the concept of fractals. It is lavishly illustrated and as a mathematics book became an unusual success. The book includes a total of 184 illustrations, including 88 full-colour pictures of Julia sets.
Pietronero argues that the universe shows a definite fractal aspect over a fairly wide range of scale, with a fractal dimension of about 2. [3] The fractal dimension of a homogeneous 3D object would be 3, and 2 for a homogeneous surface, whilst the fractal dimension for a fractal surface is between 2 and 3.
Pickover fractal map [44] continuous: real: 3: Pomeau-Manneville maps for intermittent chaos : discrete: real: 1 or 2: Normal-form maps for intermittency (Types I, II and III) Polynom Type-A fractal map [45] continuous: real: 3: 3: Polynom Type-B fractal map [46] continuous: real: 3: 6: Polynom Type-C fractal map [47] continuous: real: 3: 18 ...
The second book of the Mode series by Piers Anthony, Fractal Mode, describes a world that is a perfect 3D model of the set. [ 49 ] The Arthur C. Clarke novel The Ghost from the Grand Banks features an artificial lake made to replicate the shape of the Mandelbrot set.
Indra's Pearls: The Vision of Felix Klein is a geometry book written by David Mumford, Caroline Series and David Wright, and published by Cambridge University Press in 2002 and 2015. The book explores the patterns created by iterating conformal maps of the complex plane called Möbius transformations , and their connections with symmetry and ...
Escape-time fractals – use a formula or recurrence relation at each point in a space (such as the complex plane); usually quasi-self-similar; also known as "orbit" fractals; e.g., the Mandelbrot set, Julia set, Burning Ship fractal, Nova fractal and Lyapunov fractal. The 2d vector fields that are generated by one or two iterations of escape ...
Fractal fern in four states of construction. Highlighted triangles show how the half of one leaflet is transformed to half of one whole leaf or frond.. Though Barnsley's fern could in theory be plotted by hand with a pen and graph paper, the number of iterations necessary runs into the tens of thousands, which makes use of a computer practically mandatory.
A detail from a non-integer Multibrot set. There are many different kinds of fractal images. They can be subdivided into several groups. Fractals derived from standard geometry by using iterative transformations on an initial common figure like a straight line (the Cantor dust or the von Koch curve), a triangle (the Sierpinski triangle), or a cube (the Menger sponge).