Bond percolation on a Non-PCF sierpinski gasket, iterated barycentric subdivision of a triangle, and hexacarpet Articles uri icon

authors

  • LOUGEE, DEREK MICHAEL
  • STEINHURST, B.

publication date

  • June 2016

issue

  • 2

volume

  • 24

International Standard Serial Number (ISSN)

  • 0218-348X

Electronic International Standard Serial Number (EISSN)

  • 1793-6543

abstract

  • We investigate bond percolation on the iterated barycentric subdivision of a triangle, the hexacarpet, and the non-p.c.f. Sierpinski gasket. With the use of known results on the diamond fractal, we are able to bound the critical probability of bond percolation on the non-p.c.f. gasket and the iterated barycentric subdivision of a triangle from above by 0.282. We then show how both the gasket and hexacarpet fractals are related via the iterated barycentric subdivisions of a triangle: the two spaces exhibit duality properties although they are not themselves dual graphs. Finally, we show the existence of a non-trivial phase transition on all three graphs.

keywords

  • percolation; barycentric subdivision; fractals; phase-transition; carpet lattices