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| As another example of word function, we consider a tree whose branches split into two new branches at each spurt of growth. The schematic function of figure 10 describes such a binary branching, whereby the input piece is stretched and bent at the |
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Figure 10. Binary
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midpoint to form a “V” shaped branch. Specifically, let us begin with a main trunk of, say, 1 meter in figure 11. By the binary branching function (figure 10), we first stretch the main trunk by a factor of You may use the computer program Prog #1 to step through binary branching up to the tenth level.
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Figure 11. A
binary tree |
and bend it at the midpoint by 
angle. Hence, each branch of the first branching is 
meter long. We now arrange the first generation branch symmetrically about the main trunk, so that the branches fan out by the equal angle 
to right and left of the main trunk. Next, we apply the binary branching function to each of the two first generation branches. There are now 4 branches, each of 
meter long, lying symmetrically about the main trunk. Although not shown in figure 11, after the third branching there will be 8 branches, each of 
meter long. By continuing iterations, we find the number of branches doubling at each spurt of branching by 2, 4, 8, 16, 32, ..., which are doubling numbers (2). 