Three-Dimensional Diagonal Cross-Sections of Four-Dimensional Menger Sponges
Rob Hocking

Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture
Pages 291–298
Regular Papers

Abstract

When the 3D Menger sponge is sliced with a suitably chosen diagonal plane, a novel 2D fractal is obtained. In this work, I generalize this result by exploring the 3D fractal structures obtained by slicing two distinct 4D generalized Menger sponges with suitable hyperplanes. The resulting fractals are either etched in glass or 3D printed in precious metals and used to create fractal art. Analytical results are derived presenting the mathematics behind the art, including symmetries of the 3D cross-sections.

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