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Chaotic maps and iterated functions often generate fractals. Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal. See also Universality (dynamical systems).
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
Download as PDF; Printable version ... Fractals are self ... Subcategories. This category has the following 6 subcategories, out of 6 total. C. Chaotic maps (1 C ...
Download as PDF; Printable version ... The Fibonacci word fractal is a fractal curve defined on the ... By an iterated construction of 8 square patterns around each ...
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.
Print/export Download as PDF; Printable version; In other projects ... This is a list of fractal topics, by Wikipedia page, See also list ...
The fractal, self-similar nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter [1] and is one of the early examples of modern scientific data visualization. The name reflects the fact that, as Hofstadter wrote, "the large gaps [in the graph] form a very striking pattern somewhat resembling a butterfly." [1]