FractionalGeometry-Chap2

What happens if the ti are selected in a non random

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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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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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