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A Property of Area and Perimeter

  • Douglas DunhamEmail author
  • John Shier
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)

Abstract

We describe an algorithm that creates a fractal pattern within a planar region R by ranplacing within it progressively smaller copies of a subpattern or fill-shape. After placing i copies of the fill-shape, we use the term gasket to describe the unfilled part of R. The size of the next fill-shape is determined by a constant \(\gamma \) times the remaining area of the gasket divided by the total perimeter of the gasket. Experimental evidence is presented indicating that the areas of the fill-shapes obey an inverse power law for large i.

Keywords

Algorithm Area Perimeter Fractal Power law Space filling 

References

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    Newman, M.: Power law distribution. Significance 14:4 (August 2017). https://doi.org/10.1111/j.1740-9713.2017.01050.xCrossRefGoogle Scholar
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    Shier, J., Bourke, P.: An algorithm for random fractal filling of space. Comput. Graphics Forum 32(8), 89–97 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of Minnesota DuluthDuluthUSA
  2. 2.6935 133rd CourtApple ValleyUSA

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