Saturday, November 3, 2012

From easiest to hardest

In the past year I have produced nine maze books and I think the ninth will be the last. Some of them were designed to appeal to children and others were designed with adults in mind. Below is a listing of the books sorted by difficulty:

(Blank rows indicate a significant jump in difficulty.)

The two books published by Dover (Fascinating Mazes and Maze Madness) are much shorter than any of these and are about at the level of Amusing Alphabet Mazes.

For more information, see the author's Amazon page or his the maze page on

Thursday, November 1, 2012

Tessellation Byproducts

Over the past year I have invested a lot of time and effort creating tessellation patterns to be used for creating mazes. Five maze books are completely based on these patterns and four others used them in varying degrees. Because there are people who like tessellations but have no interest in mazes, an attempt to re-purpose the results of this effort seemed to me to be a reasonable use of time.

One attempt to reuse the patterns resulted in two coloring books, The Tessellating Alphabet Coloring Book, discussed here, and A Tessellating Coloring Book. Despite what its cover might suggests, the patterns it contains are varied and mostly derived from Tantalizing Tessellating Mazes and More Tessellating Mazes.
So far there is no evidence that this was a worthwhile endeavor.

A second way of utilizing these tessellation patterns is to make typefaces from them. The Tescellations fonts are discussed here. A second set of two fonts, the TessieDingies package, has recently been released on One font is devoted to patterns that are abstract.
 The other contains patterns that are composed of tessellations forms that resemble birds, animals, vehicles, tools, and other objects from the real world.
 The typefaces make creating tessellation patterns very easy. Each pattern is on one key, so one simply makes several lines of the same character, formats in one of the TessieDingies fonts, and makes sure that the line spacing (the leading) is equal to the font size. When you do, you can get patterns like those above.

Saturday, October 27, 2012

Tessellating Alphabet Mazes for Kids

Tessellating Alphabet Mazes for Kids is now available on Amazon.
 Most of the mazes are based on letter tessellation patterns that were used in Puzzling Typography and Puzzling Typography A Sequel, books that were intended for an older audience. The mazes in Tessellating Alphabet Mazes for Kids are much simpler.

However, there are a few new shapes and patterns used in the book, shapes and patterns that were not used in previous books. Here is one of two new letter C shapes.
This way of forming the upper-case D was elementary but had not previously been used.
This new letter G shape is a bit odd but it forms a very nice pattern for a maze.
The three pictures above are of actual pages from the book. The way the mazes are displayed on top of a grayed image of the letter is the same as that used in the Puzzling Typography books. Arrows indicating the exits are included.

The shapes used in Tessellating Alphabet Mazes for Kids were of the upper-case letters. There are no solutions included, so the book contains over 100 pages of mazes, enough to keep a child busy for a long time even though the mazes are not very difficult. Letters that a hard to tessellate, such as K, R, O, and Q, only get one page, while letters that are easier to tessellate get more pages. The letter L is by far the easiest to tessellate in many ways, so it gets more pages than any other letter.

The book is intended to appeal to children in the early primary grades.

Friday, October 26, 2012


A set of typefaces based on the various letter tessellations used in the Puzzling Typography maze books is now available at The complete set contains seven fonts.

Tescellations contains the letter tessellations that best fit together to make a readable font. It contains a regular version plus an italics version. In addition there are regular and italic versions of the font without the counters (interiors).
TescellationsTwo contains additional letter tessellations. It is less readable than Tescellations and it also contains a version without counters.
 Finally, TescellationsPatterns is a one-key way of making patterns of letter tessellations. Simply chose the appropriate key and type, making sure the line spacing (leading) is set tot he same value as the font size.

Saturday, October 6, 2012

A sequel

I could not resist doing a sequel to Puzzling Typography: Mazes with Letter Tessellations. It was not because Puzzling Typography was selling so well. It was not--mazes are a niche market, and I doubt if any maze books sell very well. Rather it was because I had become obsessed with letter tessellations and I kept discovering new ones, either new shapes or new ways of arranging old shapes. I was a little worried that I might not be able to do a book with the same quality as the original, but as time went on, that worry disappeared.

It took a month and and a half, but now Puzzling Typography A Sequel: Mazes with Tessellating Letters is available on Amazon.
The book has the same format as the original. There are 84 pages of mazes and 21 pages showing the solutions. Each letter of the alphabet is represented at least once. More of the pages in the sequel are given to lower-case letters than were devoted to lower-case letters in the the original. Many of the shapes are the same as in the original, but the way they fit together is different, but there are also some new shapes. The R-shape is one case where the shape in the sequel is better than in the original. I was prepared to use a rather strange-looking Z until at the last minute I discovered a way to do a much better Z, one equal to the best in the first book.
The letter L is the letter for which I found the most tessellation patterns, with 21 pages in the two books devoted to them, plus one back cover. After finding many ways to tessellate the letter T in the first book, I struggled to find new ways in the second, but the letter F proved to be more productive than I expected.

I am unaware of any source that gives a larger collection of letter tessellations than what is contained in these two books. Because some mazes have two or three different tessellation patterns in them, there are about 180 different patterns in the two books; no pattern used in the first book is repeated in the second. Even so, I realize that I may have only scratched the surface of what is possible in letter tessellations.

Friday, October 5, 2012

The Tessellating Alphabet

For several months I have been exploring letter tessellations in the an effort to design maze books. The first result was Puzzling Typography: Mazes with Letter Tessellations. Now a second result, a byproduct of the maze books, is also available on Amazon, The Tessellating Alphabet Coloring Book.
The Tessellating Alphabet Coloring Book features many of the letter tessellations that were used in Puzzling Typography but also includes many new shapes and patterns, such a the S shape above and the pattern below for the letter R, one of the most difficult letters to tessellate.
Some people who find letter tessellations interesting may not like them in the form of mazes. This books is one attempt to appeal to these people by presenting the tessellations in a different way. With 106 different tessellation patterns, it is one of the largest collections of letter tessellations available.

The Tessellating Alphabet Coloring Book is 105 pages long and has at least one page devoted to each letter. For some letters there are many pages. (More means more than six.) Letters F and L are especially well represented.

There are other projects in the pipeline and two of them are almost completed. Stay tuned.

Tuesday, August 28, 2012

Puzzling Typography

Early this year I published two books of mazes that used letters as their themes, Easy Alphabet Mazes and Amusing Alphabet Mazes. In the process of designing mazes for the latter book, I used some tessellation patterns in which a letter form could interlock in a way to fill the plane. In the months following I spent a lot of time working on non-letter tessellation patterns, and the questions gradually arose of whether I could do a complete book of mazes using letter tessellations. It took a while for me to answer that question in the form of Puzzling Typography: Mazes with Letter Tessellations.

 The lettering on the cover is composed of letter shapes that tessellate and they are all used in mazes within the book.

The easiest letter to tessellate is probably the sans-serif letter I, which seemed so simple that I did not include it in this book. The letter that has the most possibilities is probably the letter L. There are ten pages devoted to various ways of tessellating this letter and there are many more ways that I did not use, though eventually they become so complex that they will not fit well with the way I create mazes.

The most difficult letters to tessellate are the letters O, K and R. Below is a picture of one of the ways I found to tessellate a shape that is recognizable as the letter K.
The picture above shows how all pages are formatted. Behind the maze is the gray letter form on which the maze is constructed. The maze is on top of it. There are arrows marking the beginning and end of the correct path and a bit of text on the bottom. The mazes are difficult enough so that they will only frustrate small children; the recommended ages are 12 to adult (and the mazes may frustrate some in that age range as well).

Most of the pages are devoted to tessellations of upper-case letters, and every letter has at least one maze devoted to it. Sometimes I also included some lower-case letters when they made for interesting patterns and mazes. Below is a picture of the maze for a decorative lower-case letter f.
There are 84 mazes in the book with 86 different patterns. Solutions are shown in the back of the book. The book has 108 pages and uses 8 inch by 11.5 inch pages.

When I started I was unsure if the book was even possible, but by the time I was finished I had found so many different ways of tessellating letters that I now am wondering if a sequel would be a fun adventure.

Update: I made some changes to the book and the letter f tessellation was removed from the book, though it will soon appear in an new book. It had a worthy replacement.

Saturday, June 9, 2012

More Tessellating Mazes

More Tessellating Mazes, a sequel to Tantalizing Tessellating Mazes, is now available on

It has the same format as Tantalizing Tessellating Mazes, with a selection of 70 mazes all built using tessellations, with solutions at the end. The tessellations include a variety of shapes that resemble real-world objects such as geese,
 stylized birds
 and many more living things. There are also mazes built on patterns of inanimate objects such as planes
 and clothespins.
 I could not resist the temptation to include a few mazes built on tessellations that that are non-representational but are visually intriguing.
The mazes in both More Tessellating Mazes and Tantalizing Tessellating Mazes are fairly easy and intended for pre-teenage children. (The samples shown above are not mazes from the book--they merely illustrate a few of the tessellations patterns used in the book.)

Sunday, April 1, 2012

A book of train mazes

Casey Loves Trains (And Likes Mazes)
 is now available at

This book is the result of a request from my daughter, who has a son who loves trains, to do a maze book about trains. My initial reaction was that I could not do such a book. Trains are one dimensional while mazes are two dimensional. After a bit of thought, I figured out how to manage the project.

There are some mazes that are clearly train related. In the maze below, you have to stay on cars with hearts.
 Rails can be used to form mazes in several ways.

 Obey the semaphores in this maze.
 There are several ways to make mazes of tracks, and also of ties and spikes.
 But if you want a book that is more than a few pages long, and Casey Loves Trains is over 100 pages, you have to find ways to bring other sorts of things into the story line. Like elephants.
 Or horses.
 Or cows.
(I like tessellations.)

 And dinosaurs.
How did all these things get into a book about trains? The mazes illustrate the story of a trip that a young boy takes on a train. While he is on the train, he sees and does many things.

It is a book designed to appeal to young people who love trains (as well as dinosaurs) and who like mazes.

Friday, March 30, 2012

Maze Cornucopia

A Cornucopia of Mazes: Stars, Tilings and Patterns was published earlier this month.
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.
It is available from Amazon for $6.95.