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2003•The Mathematica JournalRequires access

Polyominoes and Related Families

Jaime Rangel-Mondragón

Open publisher page 5 citations

Abstract

Polyominoes are generalizations of dominoes constructed by joining congruent squares side by side. By describing a polyomino as a list of Gaussian integers, we generate all different polyominoes of a given size. This method is extended to the generation of the families of polyiamonds, polyhexes, and polykites. We also give a method to tile rectangles using polyominoes and explore the fractal family of rep-tiles.

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What this paper is about

Polyominoes are generalizations of dominoes constructed by joining congruent squares side by side. By describing a polyomino as a list of Gaussian integers, we generate all different polyominoes of a given size. This method is extended to the generation of the families of polyiamonds, polyhexes, and polykites. We also give a method to tile rectangles using polyominoes and explore the fractal family of rep-tiles.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Polyominoes are generalizations of dominoes constructed by joining congruent squares side by side. By describing a polyomino as a list of Gaussian integers, we generate all different polyominoes of a given size. This method is extended to the generation of the families of polyiamonds, polyhexes, and polykites. We also give a method to tile rectangles using polyominoes and explore the fractal family of rep-tiles.

Key concepts: Polyomino, Mathematics, Combinatorics, Gaussian, Fractal, Discrete mathematics, Geometry, Mathematical analysis

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