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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.
The second tree type is made by drawing an open curve between four vertices of each square. The tightness of the curve varies.
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.
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.
Pink Pythagoras tree on tumblr.
The processing-code can be seen at OpenProcessing: Variations on Pythagoras' Tree.