3D Printable Golden Sponges

Year: 2017 Authors: Donald Plante

Core claim

By choosing contraction rates with substantial overlap, one can produce 3D-printable fractal approximations that preserve total self-similarity, including Golden Sierpiński tetrahedra, related octahedra, and Menger sponge variants.

Topics

iterated function systems, fractal geometry, 3D printing, self-similarity, overlap in attractors, Sierpiński tetrahedron

Domains

dynamical systems, iterated function systems, fractal geometry, geometry in R^3, self-similar sets, digital fabrication, 3D printing, mathematical visualization

Methods

analytic derivation of contraction-rate conditions, constructing finite approximations Delta_n, computational modeling in OpenSCAD, computational modeling in Maple 2015, 3D printing prototypes

Media

3D printed plastic models, OpenSCAD, Maple 2015, figures of fractal approximations

Source status

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