The Pythagoras tree is named after the Greek mathematician Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to depict the Pythagorean theorem. It is a plane fractal constructed from squares invented by the Dutch mathematics teacher Albert E. Bosman in 1942. In 1957 Bosman published a book on Het wondere onderzoekingsveld der vlakke meetkunde ("the wondrous exploration field of plane geometry") that contained a description of the Pythagorean tree. If the largest square has a size of L L, the entire Pythagoras tree fits snugly inside a box of size 6L 4L. Your task is to write a program PTree.cpp with a recursive function pTree(), and a main() program that calls the recursive function.

Your program shall take two command-line arguments L and N:

L size of the base square (double)

N the depth of the recursion

You should create a PTree class that derives from sf::Drawable.

Then, you can have it just draw itself to your main window.

Review Jon's LineSegment example to see a simple example of how to do this: LineDemo.tar.gz.

Using SFML's ConvexShape class is a good way to draw a square.

Your executable must read two parameters (integers): recursion-depth and window-size. You should create a square SFML window that's exactly as big as the window-size argument, and your triangle should fill it.