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Summary: 1
Evolutionary Exploration of Complex Fractals
Daniel Ashlock1
and Brooke Jamieson2
1
University of Guelph, Department of Mathematics and Statistics, 50 Stone Road
East, Guelph, Ontario, Canada, N1G 2W1 dashlock@uoguelph.ca
2
University of Guelph, Department of Mathematics and Statistics, 50 Stone Road
East, Guelph, Ontario, Canada, N1G 2W1 bjamieso@uoguelph.ca
1.1 Introduction
A fractal is an object with a dimension that is not a whole number. Imagine
that you must cover a line segment by placing centers of circles, all the same
size, on the line segment so that the circles just cover the segment. If you
make the circles smaller then the number of additional circles you require
will vary as the first power of the degree the circles were shrunk by. If the
circles diameter is reduced by half then twice as many circles are needed; if
the circles are one-third as large then three times as many are needed. Do the
same thing with a square and the number of circles will vary as the second
power of the amount the individual circles were shrunk by. If the circles are
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