Evolutionary exploration of Complex Fractals - Versionsgeschichte

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== Referenz ==
[[Daniel Ashlock | Ashlock, Daniel]]; [[Brooke Jamieson | Jamieson, Brooke]]: Evolutionary exploration of Complex Fractals. In: [[Literatur_zur_Evolution%C3%A4ren_Kunst#Design_by_Evolution | Hingston & Barone & Michalewicz: Design by Evolution, Springer, Berlin, 2008]]. S. 121-144.

== DOI ==
http://link.springer.com/10.1007/978-3-540-74111-4_8

== 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.

== Extended Abstract ==

== Bibtex ==

== Links ==
=== Full Text ===
[extern file]

[[intern file]]

=== Sonstige Links ===

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	== Bibtex ==		== Bibtex ==
		+	@incollection{
		+	year={2008},
		+	isbn={978-3-540-74109-1},
		+	booktitle={Design by Evolution},
		+	series={Natural Computing Series},
		+	editor={Hingston, PhilipF. and Barone, LuigiC. and Michalewicz, Zbigniew},
		+	doi={10.1007/978-3-540-74111-4_8},
		+	title={Evolutionary Exploration of Complex Fractals},
		+	url={http://dx.doi.org/10.1007/978-3-540-74111-4_8 http://de.evo-art.org/index.php?title=Evolutionary_exploration_of_Complex_Fractals },
		+	publisher={Springer Berlin Heidelberg},
		+	author={Ashlock, Daniel and Jamieson, Brooke},
		+	pages={121-143},
		+	language={English}
		+	}

	== Used References ==		== Used References ==

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	== Bibtex ==		== Bibtex ==
		+
		+	== Used References ==
		+	Ashlock, D.: Evolutionary exploration of the Mandelbrot set. In: Proceedings of the 2006 Congress on Evolutionary Computation, pp. 7432–7439 (2006)
		+
		+	Ashlock, D., Bryden, K., Gent, S.: Creating spatially constrained virtual plants using L-systems. In: Smart Engineering System Design: Neural Networks, Evolutionary Programming, and Artificial Life, pp. 185–192. ASME Press (2005)
		+
		+	Ashlock, D., Jamieson, B.: Evolutionary exploration of generalized Julia sets. In: Proceedings of the 2007 IEEE Symposium on Computational Intelligence in Signal Processing, pp. 163–170. IEEE Press, Piscataway NJ (2007)
		+
		+	Barrallo, J., Sanchez, S.: Fractals and multi-layer coloring algorithm. In: Bridges Proceedings 2001, pp. 89–94 (2001)
		+
		+	Castro, M., Pérez-Luque, M.: Fractal geometry describes the beauty of infinity in nature. In: Bridges Proceedings 2003, pp. 407–414 (2003)
		+
		+	Fathaner, R.: Fractal patterns and pseudo-tilings based on spirals. In: Bridges Proceedings 2004, pp. 203–210 (2004)
		+
		+	Fathaner, R.: Fractal tilings based on dissections of polyhexes. In: Bridges Proceedings 2005, pp. 427–434 (2005)
		+
		+	Ibrahim, M., Krawczyk, R.: Exploring the effect of direction on vector-based fractals. In: Bridges Proceedings 2002, pp. 213–219 (2002)
		+
		+	Mandelbrot, B.: The Fractal Geometry of Nature W. H. Freeman and Company, New York (1983)
		+
		+	Mitchell, L.: Fractal tessellations from proofs of the Pythagorean theorem. In: Bridges Proceedings 2004, pp. 335–336 (2004)
		+
		+	Musgrave, F., Mandelbrot, B.: The art of fractal landscapes. IBM J. Res. Dev. 35(4), 535–540 (1991)
		+
		+	Parke, J.: Layering fractal elements to create works of art. In: Bridges Proceedings 2002, pp. 99–108 (2002)
		+
		+	Parke, J.: Fractal art — a comparison of styles. In: Bridges Proceedings 2004, pp. 19–26 (2004)
		+
		+	Rooke, S.: Eons of genetically evolved algorithmic images. In: P. Bentley, D. Corne (eds) Creative Evolutionary Systems, pp. 339–365. Academic Press, London, UK (2002)
		+
		+	Syswerda, G.: A study of reproduction in generational and steady state genetic algorithms. In: Foundations of Genetic Algorithms, pp. 94–101. Morgan Kaufmann (1991)
		+
		+	Ventrella, J.: Creatures in the complex plane. IRIS Universe (1988)
		+
		+	Ventrella, J.: Self portraits in fractal space. In: La 17 Exposicion de Audiovisuales. Bilbao, Spain (2004)
		+
		+

	== Links ==		== Links ==

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	=== Sonstige Links ===		=== Sonstige Links ===
		+
		+	[http://www.fractal.org/Bewustzijns-Besturings-Model/Generalized-Julia-Sets.pdf Evolutionary Exploration of Generalized Julia Sets]