Iterating Polyominoes to Create Fractal Reptiles

Year: 2025 Authors: Robert Fathauer

Core claim

Iterating tessellating polyominoes under allowed rotations and scalings yields a wide range of fractal reptiles that tessellate at each stage and become self-replicating in the limit.

Topics

fractal reptiles, polyomino iteration, tessellations, space-filling tiles, 3D sculpture

Domains

geometry, fractal geometry, tiling theory, integer lattice transformations, mathematical art, generative design, tessellation art, sculptural forms

Methods

iterative construction, grid rotation and scaling, translation patches, lattice vector analysis

Media

square-grid polyominoes, figures, 3D cube assemblies

Source status

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