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)


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.


Algorithm Area Perimeter Fractal Power law Space filling 


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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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