Tantalizing Tessellating Mazes

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Available from Amazon.

From the Introduction:

This book contains 83 moderately difficult mazes with solutions. Almost all are displayed using tessellation patterns. A tessellation pattern uses a shape that fits with copies of itself to cover the plane with no gaps or overlaps. Most of the tessellation shapes are Escher-like, that is, they resemble real world objects such as animals or insects.


In the mid 1990s I designed two maze books published by Dover. I produced the mazes with computer programs I wrote and displayed them with special typefaces I created. My method of making mazes led to an interest in tessellations because they provided a way to make mazes both more challenging and more visually interesting. A small maze of North/South and East/West passages displayed with straight walls is instantly solvable by inspection. To make mazes challenging, they can be made larger or some element of visual distraction can be added to make the paths harder to see. This second approach is the one I have taken; using tessellations to frame a maze creates visual distraction.

The advent of on-demand publishing encouraged me to return to maze making after 2011 and I quickly produced a number of additional maze books, some for small children, others for older children, and a few for adults. As I learned more about tessellations, my interest in them increased and eclipsed my interest in mazes.

Since publication of Holiday Mazes in early 2015, I have published an activity book with a tessellation theme, five coloring books focused on tessellations and symmetry, and a book exploring technical aspects of tessellations. In working on these books, I have accumulated more than enough new tessellation patterns to design another maze book. Maze puzzles have a small audience and limited sales, but designing maze books is enjoyable in its own right. Further, my programs that generate mazes date from the 1990s and run on a discontinued operating system and obsolete hardware. (A couple programs run using an emulation program, but three crash it.) So the time may be approaching when my ability to produce mazes is limited.

Almost all of the mazes in this book use tessellation patterns of the type that M. C. Escher made famous. I discovered most of them by toying with an excellent tessellation program called Tessellmaniac!. For some reason I keep stumbling on shapes that resemble birds, which is reflected in the pages that follow. I have attempted to avoid using designs that were used in my previous maze books, but a few may have slipped in. Included are a few non-tessellation mazes that use over/under paths, that is, allow the path to cross over itself. They are included because they make very challenging mazes.

Page 85 gives the Heesch types and isohedral classifications of the tessellation patterns used in the mazes for anyone who is interested in technical details of tessellations. Solutions to all 83 mazes are given starting on page 86.

I hope you enjoy both the mazes and the tessellations. I apologize for any errors that remain in the book.

Robert Schenk
May, 2018

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