Evolutionary Exploration of Complex Fractals Daniel Ashlock1 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 Collections: Mathematics