SPHERES + CUBES = x^n+y^n+z^n = 0

William F. Duffy
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 609–612

Abstract

One of the topologies that I am currently exploring is Triply Periodic Minimal Surfaces TPMS or Infinite IPMS, this term has been coined by Alan Schoen at NASA in the 1960s. These surfaces can be observed in nature, exhibiting the behavior and properties of bubbles that make up foam structures. In foams, when bubbles join in mass and in random polydispersion, as observed in nature, they collectively behave unpredictably. The dynamics of these independent regions comprising foam masses, which transfers energy from one polyhedral node to the next articulated by their intersecting plateau borders is intrinsic to my creative thinking.

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