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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
A Jerusalem cube is a fractal object first described by Eric Baird in 2011. It is created by recursively drilling Greek cross-shaped holes into a cube. [15] [16] The construction is similar to the Menger sponge but with two different-sized cubes. The name comes from the face of the cube resembling a Jerusalem cross pattern. [17]
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.)
This Halloween 2024, use these printable pumpkin stencils and free, easy carving patterns for the scariest, silliest, most unique, and cutest jack-o’-lanterns.
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.
This is a list of fractal topics, by Wikipedia page, See also list of dynamical systems and differential equations topics.. 1/f noise; Apollonian gasket; Attractor; Box-counting dimension
The Fibonacci word fractal is a fractal curve ... By an iterated construction of 8 square patterns around each square pattern. ... leaves at the center a free square ...