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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 first attempt to model the distribution of galaxies with a fractal pattern was made by Luciano Pietronero and his team in 1987, [2] and a more detailed view of the universe's large-scale structure emerged over the following decade, as the number of cataloged galaxies grew larger.
Euclidean human-made space can be altered by integrating the aesthetics of nature. [8] Fractal patterns offer the chance to enhance man-made spaces by introducing visually soothing natural designs. Research indicates a preference for specific fractal complexities that resemble nature's patterns.
The second book of the Mode series by Piers Anthony, Fractal Mode, describes a world that is a perfect 3D model of the set. [48] The Arthur C. Clarke novel The Ghost from the Grand Banks features an artificial lake made to replicate the shape of the Mandelbrot set. [49]
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.
Heighway dragon curve. A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.The dragon curve is probably most commonly thought of as the shape that is generated from repeatedly folding a strip of paper in half, although there are other curves that are called dragon curves that are generated differently.
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 ...
Fractal patterns have been modeled extensively, albeit within a range of scales rather than infinitely, owing to the practical limits of physical time and space. Models may simulate theoretical fractals or natural phenomena with fractal features.