A Cornucopia of Mazes: Stars, Tilings and Patterns

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Available from Amazon.

From the Introduction:

In January and February of 2012 I designed Tantalizing Tessellating Mazes, a book with 70 mazes. Intended to appeal to children in elementary school, the mazes had to be fairly simple. As I worked on the book, I kept thinking that a similar book, focused on interesting geometric shapes and patterns but designed for an adult audience, would be a fun project. A Cornucopia of Mazes: Stars, Tilings and Patterns is that book, though there is little overlap with the designs used in Tantalizing Tessellating Mazes.

A Cornucopia of Mazes: Stars, Tilings and Patterns has 84 mazes in three sections. The first section features two dozen mazes based on star patterns. Only one of them uses the familiar five-pointed star or pentagram. Stars with three, four, six, and eight points are easier to fit into simple and regular patterns and thus make better building blocks for mazes.

The middle of the book has mazes based on tessellation patterns or tilings. (For mathematicians they are the same thing.) A tessellation is a shape that can fit together with other copies of itself to completely cover the plane. Tantalizing Tessellating Mazes used many tessellations that resembled animals, people, and objects. This book uses mostly tessellation shapes that are purely geometric. A final section has a variety of other patterns, many of them with interlocking or interwoven elements.

The book has 84 mazes because I wanted the book to be exactly 108 pages long. This book is published through Create Space, a division of Amazon, and they charge a fixed amount for any book with a color cover and a black-and-white interior up to 108 pages. Beyond that the price goes up. With a solutions section that has solutions to four mazes on a page plus three pages of introductory material, there was room for exactly 84 pages of mazes. One of the difficult tasks in finishing the book was deciding which mazes had to be cut to keep the book at 108 pages.

The solutions are created by blocking up all dead-end paths, leaving only the correct path through the maze. The reason that I present them this way is that my maze-generating programs produce them in this way. Some of the solutions may require a bit of work on the users part, but this book is intended for people serious about working mazes.

Constructing these mazes involved two elements. The structure of the maze was produced by a maze-generating computer program. I wrote several of these program, each with somewhat different capabilities. The programs generate a maze as a set of numbers and convert those numbers into a text file of what looks like gibberish. To make this gibberish into a maze requires a specialized typeface that I create. Some of these specialized typefaces will make a maze as easy as possible, while others make the same maze very difficult. For more information about my way of producing mazes, visit ingrimayne.com.

I hope you enjoy this book as much as I enjoyed designing it. I apologize in advance for errors that remain in the book.

Robert Schenk March 2012

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