вторник, 19 февруари 2013 г.
Pythagoras tree (fractal)
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The Pythagoras tree.
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. If the largest square has a size of L × L, the entire Pythagoras tree fits snugly inside a box of size 6L × 4L.[2][3] The finer details of the tree resemble the Lévy C curve.
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[edit]Construction
The construction of the Pythagoras tree begins with a square. Upon this square are constructed two squares, each scaled down by a linear factor of ½√2, such that the corners of the squares coincide pairwise. The same procedure is then applied recursively to the two smaller squares, ad infinitum. The illustration below shows the first few iterations in the construction process.[4][3]
[caption id="" align="alignright" width="128"]  Construction of the Pythagoras tree, order 1 (Photo credit: Wikipedia)[/caption] | [caption id="" align="alignright" width="128"]  Order 2 (Photo credit: Wikipedia)[/caption] | [caption id="" align="alignright" width="128"]  Order 3 (Photo credit: Wikipedia)[/caption] |
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