Variations on Pythagoras' Tree
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JavaScript is needed!
Click on the animated tree to toggle the variation of curve tightness, on or off.
When constructing a Pythagoras' tree, you start with a right-angled triangle and three squares. For a detailed explanation see Pythagoras & Thales. Then you build a tree recursively. By using Thales' theorem, you can vary the triangle by moving the vertex at the right angle along a circle. This is how you make an animated Pythagoras' tree.
The tree types
The first (leftmost) tree type is a regular animated Pythagoras' tree.
![tree type 1a](images/tree1a.png)
![tree type 1b](images/tree1b.png)
The second tree type is made by drawing an open curve between four vertices of each square. The tightness of the curve varies.
![tree type 2a](images/tree2a.png)
![tree type 2b](images/tree2b.png)
![tree type 2c](images/tree2c.png)
The third tree type is made by drawing one open curve along the left and right branch of the tree. The vertices at the right angle of each right-angled triangle are shown as dots.
![tree type 3a](images/tree3a.png)
![tree type 3b](images/tree3b.png)
![tree type 3c](images/tree3c.png)
The fourth tree type is made by drawing one open curve along the left and right branch of the tree. Then one such branch is drawn for each sub-tree.
![tree type 4a](images/tree4a.png)
![tree type 4b](images/tree4b.png)
![tree type 4c](images/tree4c.png)
Animated gifs
Pink Pythagoras tree on tumblr.
The code
The processing-code can be seen at OpenProcessing: Variations on Pythagoras' Tree.