Modifications of Pythagoras tree

The house motif for Pythagoras tree introduced in Lesson 2 consists of a square building with an isosceles triangle roof. First, the Pythagoras tree of such a motif grows symmetrically about the centerline, and the first modification we propose here involves asymmetric roof slants. Second, the Pythagoras tree is perhaps too stout to be naturally looking, because the tree branches are very short between branching, and this will be addressed in the second modification. Further modifications for random growth patterns will be considered in Lesson 7.

Modification #1: The house motif still has a square building, but the roof is now a right-angle triangle of (, 90 °, 90 °-) as shown in figure 6. For =45°, it becomes the isosceles triangle roof. First, Prog#3e demonstrates asymmetric branching over the 60°-90°-30° triangle roof. It is interesting to note that the main tree trunk has turned around almost 270° clockwise after the 8th generation branching. Also, the main trunk does not follow a circular arc, but winds around inwardly. This is an example of the logarithmic spiral to be explained in Lesson 4. You may experiment with Prog#3e the following roof angles

= 45°, 50°, 55°, 60°, 65°, 70°, 75°, 80°.

Can you explain the shape of Pythagoras trees as roof angle is incremented by 5°? Note that it looks more like a tree for =45° and turns into a bamboo at =80°.

Figure 6. Motif for Pythagoras tree (modification #1)

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