Sir Pinski rides again

Maria Ivette Gomes, Dinis Pestana, Pedro Pestana

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Abstract

The iterative procedure of removing “almost everything” from a triangle ultimately leading to the Sierpinski's gasket S is well-known. But what is in fact left when almost everything has been taken out? Using the Sir Pinski's game described by Schroeder [4], we identify two dual sets of invariant points in this exquisite game, and from these we identify points left over in Sierpinski gasket. Our discussion also shows that the chaos game does not generate the Sierpinski gasket. It generates an approximation or, at most, a subset of S.
Original languageEnglish
Title of host publicationCHAOS 2011 - 4th Chaotic Modeling and Simulation International Conference, Proceedings
Publishercmsim.org
Pages137-144
Number of pages8
Publication statusPublished - 2019
Event4th International Conference on Chaotic Modeling and Simulation, CHAOS 2011 - Agios Nikolaos, Crete, Greece
Duration: 31 May 20113 Jun 2011

Conference

Conference4th International Conference on Chaotic Modeling and Simulation, CHAOS 2011
Country/TerritoryGreece
CityAgios Nikolaos, Crete
Period31/05/113/06/11

Keywords

  • Sierpinski gasket
  • Sierpinski points
  • Fractals
  • Sir Pinski game
  • Chaos game
  • Self-similarity
  • Periodicity

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