Abstract
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 circle’s 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 filling 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 half as large, then four times as many will be required; dividing the circle’s diameter by three will cause nine times as many circles to be needed. In both cases the way the number of circles required varies is as the degree to which the circles shrink to the power of the dimension of the figure being covered. We can thus use shrinking circles to measure dimension.
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Ashlock, D., Jamieson, B. (2008). Evolutionary Exploration of Complex Fractals. In: Hingston, P.F., Barone, L.C., Michalewicz, Z. (eds) Design by Evolution. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74111-4_8
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DOI: https://doi.org/10.1007/978-3-540-74111-4_8
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