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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.
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Fractal generating software creates mathematical beauty through visualization. Modern computers may take seconds or minutes to complete a single high resolution fractal image. Images are generated for both simulation (modeling) and random fractals for art. Fractal generation used for modeling is part of realism in computer graphics. [2]
The Koch snowflake (also known as the Koch curve, Koch star, or Koch island [1] [2]) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" [3] by the Swedish mathematician Helge von Koch.
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.
Because it is space-filling, its Hausdorff dimension is 2 (precisely, its image is the unit square, whose dimension is 2 in any definition of dimension; its graph is a compact set homeomorphic to the closed unit interval, with Hausdorff dimension 1). The Hilbert curve is constructed as a limit of piecewise linear curves.
This technique is used to good effect in the B&W images of Mandelbrot sets in the books "The Beauty of Fractals [9]" and "The Science of Fractal Images". [10] Here is a sample B&W image rendered using Distance Estimates: This is a B&W image of a portion of the Mandelbrot set rendered using Distance Estimates (DE)
F. Fibonacci word fractal; Filled Julia set; Finite subdivision rule; Force chain; Fractal analysis; Fractal antenna; Fractal art; Fractal canopy; Fractal catalytic model