The Mathematica Journal: Volume 9, Issue 3: Polyominoes and Related Families

Polyominoes and Related Families

Jaime Rangel-Mondragón

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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Tiling Rectangles with Polyominoes

Rep-Tiles

Acknowledgments

References

About the Author

Jaime Rangel-Mondragón earned M.Sc. and Ph.D. degrees in applied mathematics and computation from the University College of North Wales in Bangor, Great Britain. He has held research positions in the School of Computer Science at UCNW, the College of Mexico, the Center of Research and Advanced Studies, the Monterrey Institute of Technology, and the University of Queretaro in Mexico, where he is presently a member of the Computer Science faculty. As a prolific contributor to MathSource, his current research interests include recreational mathematics, combinatorics, the theory of computing, computational geometry, and functional languages.

Jaime Rangel-Mondragón
Facultad de Informática
Universidad Autónoma de Querétaro
Mexico
jrangel@uaq.mx