One
of the easiest fractals to define is a tree. I drew these four trees using
Geometer's Sketchpad and then edited the
picture with Paint Shop Pro (to crop it and
make the background transparent). Return to my Mathematics pages
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© Copyright 2002, Jim Loy
One
of the easiest fractals to define is a tree. I drew these four trees using
Geometer's Sketchpad and then edited the
picture with Paint Shop Pro (to crop it and
make the background transparent).
First I drew the leftmost asymmetric tree. That tree embodies all of the rules for drawing the second tree. In the second tree, every branch is a copy of the original tree. In the third tree, after two more iterations (repetitions), every sub-branch becomes a copy of the second tree. And the fourth tree shows a few more iterations, and drawn larger to show more detail. This amounts to defining a kind of self-similarity (See Fractals and Self-Similarity), and then repeating it exactly, over and over. Notice that the initial asymmetry is repeated everywhere in the final tree.