Pythagoras tree

This application shows a Pythagoras tree to interact with.
Pythagoras tree on wikipedia:
The Pythagoras tree is a plane fractal constructed from squares.
Invented by the Dutch mathematics teacher
Albert E. Bosman in 1942, 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.
The finer details of the tree resemble the Lévy C curve.

Next to watching the Pythagorean theorem and recursion in action,
this application can also be used as a benchmark for
comparing the different ways of drawing in GameMaker.
Provides are the following modes:
– Using d3d and primitives with textures.
– Using d3d and primitives with color gradients.
– Drawing (colored) lines.
– Drawing sprites scaled and rotated.

For playing around with the tree you can change the number of recursions,
the top angle of all triangles as well as the edge lenghts of all rectangles.

Controlls & Shortcuts

 Buttons Effect
F1 / M Show / hide explanation.
1
Change language (English, German).
C
Change tree color.
R
Change display mode of the tree.
T
Show / hide triangles.
Enter / W
Activate / deactivate wind.
Backspace
Reset tree settings.
Arrow-Key Up / Mouse Wheel Up
Increase number of recursions.
Arrow-Key Down / Mouse Wheel Down
Decrease number of recursions.
Left Mouse Button (hold)
Change triangles (angles).
Right Mouse Button (hold)
Change size of the rectangles.
ESC
Close info / quit program.

Start the HTML5 version online

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Downloads

Download Pythagoras
13.1MB
(Windows Version)
Download Pythagoras
16.4MB
(Android Version)
Download Pythagoras
11.6MB
(HTML5 Version)