Pythagoras Tree

The Pythagoras tree is a fractal constructed iteratively from a right triangle with squares erected on each of the sides. Subsequent iterations add additional similar right triangles with erected squares on the outward-facing edges of the squares from the previous iteration. Using an isosceles right triangle gives an attractive symmetric form resembling a tree, while using a general right triangle gives a bent tree somewhat reminiscent of a willow tree. Examples of both forms are illustrated above.

REFERENCES:

Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, pp. 67-77 and 111-113, 1991.

Trott, M. The Mathematica GuideBook for Graphics. New York: Springer-Verlag, pp. 14-15, 2004. http://www.mathematicaguidebooks.org/.