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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
Sierpiński Carpet - Infinite perimeter and zero area Mandelbrot set at islands The Mandelbrot set: its boundary is a fractal curve with Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)
A 4K UHD 3D Mandelbulb video A ray-marched image of the 3D Mandelbulb for the iteration v ↦ v 8 + c. 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.
F. Fibonacci word fractal; Filled Julia set; Finite subdivision rule; Force chain; Fractal analysis; Fractal antenna; Fractal art; Fractal canopy; Fractal catalytic model
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.
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]
This Halloween 2024, use these printable pumpkin stencils and free, easy carving patterns for the scariest, silliest, most unique, and cutest jack-o’-lanterns.
This process results in a pattern of growth in which the number of segments at stage n oscillates with a fractal pattern between 0.45n 2 and 0.67n 2. If T ( n ) denotes the number of segments at stage n , then values of n for which T ( n )/ n 2 is near its maximum occur when n is near a power of two, while the values for which it is near its ...