Fractal canopy
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 and as well, and so on, infinitely.[1][2][3] Canopies are distinguished by the angle between concurrent adjacent segments and ratio between lengths of successive segments.
A fractal canopy must have the following three properties:[4]
- The angle between any two neighboring line segments is the same throughout the fractal.
- The ratio of lengths of any two consecutive line segments is constant.
- Points all the way at the end of the smallest line segments are interconnected. Which is to say the entire figure is a connected graph.
The pulmonary system used by humans to breathe resembles a fractal canopy,[3] as do trees, blood vessels, viscous fingering, electrical breakdown, and crystals with appropriately adjusted growth velocity from seed.[5]
See also
References
- ^ Michael Betty (4 April 1985). "Fractals - Geometry between dimensions". New Scientist, Vol. 105, N. 1450. pp. 31–35.
- ^ Benoît B. Mandelbrot. The fractal geometry of nature. W.H. Freeman, 1983. ISBN 0716711869.
- ^ a b Bello, Ignacio; Kaul, Anton; and Britton, Jack R. (2013). Topics in Contemporary Mathematics, p.511. Cengage Learning. ISBN 9781285528892.
- ^ Thiriet, Marc (2013). Anatomy and Physiology of the Circulatory and Ventilatory Systems, p.110. Springer Science & Business Media. ISBN 9781461494690.
- ^ Lines, M.E. (1994). On the Shoulders of Giants, p.245. CRC Press. ISBN 9780750301039.
External links
- Fractal Canopies at the Wayback Machine (archived 28 January 2007) from a student-generated Oracle Thinkquest website
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