Tuesday, May 29, 2018

A couple of revisions to tessellating maze books

When I designed Tantalizing Tessellating Mazes in 2011 and 2012 I not only had enough tessellation patterns to produce 70 mazes for this book, but had enough left over to do another 70 mazes in More Tessellating Mazes. Many of the tessellations were common geometric shapes. At the time I did not see this as a shortcoming because I was more focused on mazes than on tessellations.

In the six years since the publication of these two books I have devoted considerable time to finding new tessellation patterns. Most of what I have found has been used in other maze books, but I early in 2018 I realized that I still had enough unused material to revise and upgrade both Tantalizing Tessellating Mazes and More Tessellating Mazes.

Both books had 70 pages of mazes and 35 pages of solutions, with two solutions per page. The revisions shrink the solutions so that four fit on a page. This change frees up space for an additional fourteen mazes with no change in page count. In addition I dropped patterns that I thought were the least interesting and replaced them with new patterns and mazes. As a result, both books now have a greater percentage of Escher-like mazes, that is, mazes based on shapes that resemble real world objects rather than geometric, abstract shapes. In Tantalizing Tessellating Mazes 35 of the mazes are new and 49 are carried over from the previous edition. The numbers for More Tessellating Mazes are 27 new and 57 holdovers.

The order of mazes has been changed. The new mazes are slightly more difficult than the mazes they replace, but they still seem best described as fairly easy and appropriate for ages 8 and older. Both books have many bird tessellations because I seem prone to find bird shapes as I toy with Tesselmaniac!. (Tantalizing Tessellating Mazes has 29 bird tessellations and More Tessellating Mazes has 21.)

Some of the shapes used in the books have previously appeared on this blog. Here is a bird tessellation illustrated with a small sample maze that I used to keep track of maze typefaces.

The pattern below comes from the quilting world. This maze allows not only horizontal and vertical passages but also passages through the corners. The shape is nothing special but the corner passages make even small mazes a challenge. (This is not a maze from the book but a sample maze to illustrate the pattern.)

Both books are available on Amazon and links to them are in the side margin.

Saturday, May 5, 2018

Tessellating activities

It has been over a year since I last published a book via CreateSpace, and since then CreateSpace has ceased to sell books; all sales are now through Amazon. If you click on any CreateSpace link in a previous post, it will take you to an Amazon page.

I have not spent much time or effort with tessellations (or mazes) since Tessellating Animals Activity Book was published in January 2017. A post at the time tried to indicate what kind of activities were in the book, but the illustrations were of partial puzzles that could not be solved. The sample pages that Amazon shows are even less revealing of what is in the book.

Below are examples of some of the types of puzzles in Tessellating Animals Activity Book. First is a mini-Sudoku. Normal Sudoku puzzles are 9-by-9 grids, but simpler versions can be constructed with 4-by-4 or 6-by-6 grids. The puzzle below uses numbers 1 through 6. All rows and all columns must have each number only once. In addition, there are six boxes indicated by the shading and each of those boxes must also have each of the six numbers only once.

The book contains 14 mini-Sudoku puzzles. (The bird-head shape was in preliminary versions of the book but was dropped before it was published because it is a low-quality design.)

A second type of puzzle is a word search, which also use grids. The grid here is provided by a weird shape that was never in any version of the book but which works well for this type of puzzle. Words can be vertical, horizontal, or diagonal and they may be reversed. Find the following words: reflect, valence, hexagon, rotate, escher, glide, flips, edge. The letters not used in any of these words will spell another word that is related to tessellations.

There are ten word-search puzzles in the book and all are larger than this one.

There are eleven pages of decoder puzzles in the book and most of those pages have more than one puzzle. In the puzzle below the letters have been replaced by their position in the alphabet: A=1, B=2, C=3, etc. 
This shape was a first attempt to find a standing bird that fit Heesch type TGTG. It is not very good and I have found better ways to illustrate the type.

The book contains a number of mazes, some of the traditional variety but others that are coded. They are simpler than the coded mazes in the book Hidden Path Mazes: Decode to Solve.

The various puzzles and activities are supplemented with explanations of basic characteristics of tessellations.