Objective:
Function iterations on line segments and Pythagoras tree motifs are further explored in this lesson. Using programs Prog#3a - Prog#3f, you can step through intricate patterns being evolved at each stage of iteration. First, Prog#3a generates the Koch curves by replacing the middle one-third of a line segment with an equilateral triangle roof. By applying the Koch function to an equilateral triangle landmass, we get a Star of David or the Mitsubishi emblem depending on whether we add or remove three smaller triangular landmasses.

Prog#3b gives Koch island by adding in smaller triangular landmasses, and Prog#3c ends up with Koch archipelago by removing triangular landmasses. Second, Prog#3d generates the so-called dragon curves by folding a long paper strip repeatedly, and the top view of folded paper strip resembling the image of a Chinese dragon. Lastly, we modify the motif of Pythagoras tree of Lesson 2 in two ways as shown;

By the first modified motif, Prog#3e makes a Pythagoras tree that is no longer symmetric about the centerline, and the second modified motif of Prog#3f can generate a much more naturally looking tree.

Scary words: Koch curve, Dragon curve, Pythagoras tree.

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