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.
If a parent square has side length 
, the two child squares may be parameterized
by
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
.
The Pythagorean theorem gives 
, so the child areas
sum to the parent area (Trott 2004, pp. 14-15). The
choice 
gives the symmetric tree. At every level, the sum of the areas
of the squares, counted with multiplicity, equals the
initial area. Overlapping squares
mean that this is not generally the area of their union.
