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The Pythagoras tree is a plane fractal constructed from squares. Invented by the Dutch mathematics teacher Albert E. Bosman in 1942, [ 1 ] it is named after the ancient Greek mathematician Pythagoras because each triple of touching squares encloses a right triangle , in a configuration traditionally used to depict the Pythagorean theorem .
The H tree is a self-similar fractal; its Hausdorff dimension is equal to 2. [2]The points of the H tree come arbitrarily close to every point in a rectangle (the same as the starting rectangle in the constructing by centroids of subdivided rectangles).
A simple fractal tree A fractal "tree" to eleven iterations. The word "fractal" often has different connotations for mathematicians and the general public, where the public is more likely to be familiar with fractal art than the mathematical concept. The mathematical concept is difficult to define formally, even for mathematicians, but key ...
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.
Fractal art developed from the mid-1980s onwards. [2] It is a genre of computer art and digital art which are part of new media art. The mathematical beauty of fractals lies at the intersection of generative art and computer art. They combine to produce a type of abstract art. Fractal art (especially in the western world) is rarely drawn or ...
3-branches tree: Each branch carries 3 branches (here 90° and 60°). The fractal dimension of the entire tree is the fractal dimension of the terminal branches. NB: the 2-branches tree has a fractal dimension of only 1. 1.5850: Sierpinski triangle: Also the limiting shape of Pascal's triangle modulo 2.
Fractals are mathematical patterns that are scale invariant. This means that the shape of the pattern does not depend on how closely you look at it. Self-similarity is found in fractals. Examples of natural fractals are coast lines and tree shapes, which repeat their shape regardless of what magnification you view at.
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.