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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.
The branching, self-similar patterns observed in Lichtenberg figures exhibit fractal properties. Lichtenberg figures often develop during the dielectric breakdown of solids, liquids, and even gases. Their appearance and growth appear to be related to a process called diffusion-limited aggregation (DLA).
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.
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 ...
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior.Maps may be parameterized by a discrete-time or a continuous-time parameter.
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.
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. [50]
Patricia Sokol's detailed analysis of the novels, short stories and audio books in the Space: 1999 series published by Powys Media. It contains a detailed synopsis of each of the works, a timeline and an encyclopedic section of all the persons, places and things in the expanded Space: 1999 universe, meaning the original series and the ...