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Unformatted text preview: ﬁned by contractions. However, seeing a good image of
the attractor may burn through a bit of patience if some contraction factor is
close to 1. For example if the starting shape is a 100 × 100 square and one
of the contraction factors is r = s = 0.9, the deterministic algorithm must be
iterated about 43 times for the details of the starting shape to disappear into
a single pixel. While processor speed and memory are not such big issues now,
they were very important in the late 1980s, when many people began writing
and experimenting with IFS software. We needed something faster than the
deterministic IFS algorithm.
For another reason, suppose we want to use IFS to build an image of a
snowﬂake. Easiest would be to build one arm of the snowﬂake, then rotate that
arm by integer multiples of π/3. This can be done in post-processing, after
the snowﬂake arm is grown, but that’s not ideal because the resulting image
would be too symmetrical: each arm of the snowﬂake would be an exact rotated
replica of the original. Better to include the rotation in...
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