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Playing the chaos game in (Previous Section)

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One of the basic properties of fractal images is the notion of
self-similarity. This idea is easy to explain using the Sierpinski
triangle. Note that **S** may be decomposed into 3 congruent figures,
each of which is exactly 1/2 the size of **S**! See Figure 7. That is to
say, if we magnify any of the 3 pieces of **S** shown in Figure 7 by a
factor of 2, we obtain an exact replica of **S**. That is, **S** consists
of 3 * self-similar* copies of itself, each with * magnification
factor* 2.

We can look deeper into **S** and see further copies of **S**. For the
Sierpinski triangle also consists of 9 self-similar copies of itself,
each with magnification factor 4. Or we can chop **S** into 27
self-similar pieces, each with magnification factor 8.
In general, we may divide **S** into 3^n self-similar pieces, each
of which
is congruent, and each of which may be maginified by a factor of 2^n to
yield the entire figure.
This type of self-similarity at all scales
is a hallmark of the images known as fractals.

Chaos in the Classroom (Cover Page)

Playing the chaos game in (Previous Section)

BU Math Home Page

Sun Apr 2 14:31:18 EDT 1995