The Sierpinski-cheese iterated function system extended to a 3-simplex system

• Autores: Stephen Leon Lipscomb
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 1, 2007, págs. 169-207
• Idioma: inglés
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• Resumen

  • The n-web fractal -the attractor of the IFS of (n+1) contractions by 1/2 toward the vertices of an n-simplex - emerges from a manifold (n-simplex). The classical example is Sierpinski's gasket (2-web) which emerges from a 2-simplex. It is therefore natural (inverse of moving from manifolds to fractals) to seek, for each n greater than 1, an extension of the n-web system to an n-simplex system. For n = 2, the author recently provided such a (minimal) extension. Here, we extend the 3-web system to one whose attractor is the 3-simplex. For n greater than 3, the extension problem remains open.