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In geometry, a fractal canopy, a type of fractal tree, is one of the easiest-to-create types of fractals. Each canopy is created by splitting a line segment into two smaller segments at the end ( symmetric binary tree ), and then splitting the two smaller segments as well, and so on, infinitely.
14 steps of the Fractal Canopy tree, animated. The H tree is an example of a fractal canopy , in which the angle between neighboring line segments is always 180 degrees. In its property of coming arbitrarily close to every point of its bounding rectangle, it also resembles a space-filling curve , although it is not itself a curve.
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Drawing fractal canopy diagrams had me wondering for a given SVG file size, I could add more branches or more depth. Below are two examples: 2 branches, depth 12:
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.
The usage of the word "gasket" to refer to the Sierpiński triangle refers to gaskets such as are found in motors, and which sometimes feature a series of holes of decreasing size, similar to the fractal; this usage was coined by Benoit Mandelbrot, who thought the fractal looked similar to "the part that prevents leaks in motors". [23]
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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.)