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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 ...
The Mandelbrot set is widely considered the most popular fractal, [47] [48] and has been referenced several times in popular culture. The Jonathan Coulton song "Mandelbrot Set" is a tribute to both the fractal itself and to the man it is named after, Benoit Mandelbrot. [49]
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.
L-Systems branching pattern having 4 new pieces scaled by 1/3. Generating the pattern using statistical instead of exact self-similarity yields the same fractal dimension. Calculated: 1.2683: Julia set z 2 − 1: Julia set of f(z) = z 2 − 1. [9] 1.3057: Apollonian gasket
The Mandelbulb is a three-dimensional fractal, constructed for the first time in 1997 by Jules Ruis and further developed in 2009 by Daniel White and Paul Nylander using spherical coordinates. A canonical 3-dimensional Mandelbrot set does not exist, since there is no 3-dimensional analogue of the 2-dimensional space of complex numbers.
Patterns that mimic motifs in nature can also help calm the space. “This can include fractal patterns found in textiles, the symmetry of natural shapes like leaves or shells, or biomorphic ...
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.
About properties and symmetries of the Burning Ship fractal, featured by Theory.org; Burning Ship Fractal, Description and C source code. Burning Ship with its Mset of higher powers and Julia Sets; Burningship, Video, Fractal webpage includes the first representations and the original paper cited above on the Burning Ship fractal.