Delightful Designs: A Coloring Book of Magical Patterns

Coloring books for adults are a new fad. As I write this, nine of the top twenty best selling books on Amazon are coloring books. That is not nine of the top twenty craft books or design books. That is nine of the top twenty books of any kind.

I have released a few coloring books as offshoots of the maze books I have designed, and this fall these offshoots are selling better than the maze books by a considerable margin. (For me a book that sells five copies in a month is a spectacular hit. Only rarely does one of my books crack the top 100,000 list on Amazon.) So when I finished up the FabFours typefaces, I decided to add another book to my coloring book offerings. It is titled Delightful Designs: A Coloring Book of Magical Patterns. Below is the cover.

Here are examples of what is inside. I have kept the lines thin to aid coloring.

 Each of the designs in made from a family of four tiles that share the same identically shaped edge.

 Some of the adult coloring books have incredibly intricate designs. The designs in my coloring books are fairly simple, but they have interesting geometric properties that the intricate designs often lack.

The book features a result I discovered while studying tessellations. There are sets of four shapes that can be tiled in a checkerboard-like pattern of tiles and voids, and the voids must take the same four shapes that the set of tiles has. The result is two-, three- and four-tile tessellations, that is, patterns that tessellate with two shapes, or three shapes, or four shapes. The tiling above, for example, has two distinct shapes in it, while the first two have three distinct shapes in them. When I discovered the patterns that these sets of shapes could make, it seemed magical, and hence the name of the book.

Delightful Designs is available on CreateSpace and Amazon.

The FabFours family of typefaces

While working on Exploring Tessellations: A Journey through Heesch Types And Beyond, I discovered that if a square template is shaped with identical center-point rotation edges, there are exactly four distinct shapes possible. Two of those shapes can be in two orientations, one in four orientations, and the last in eight orientations, for a total of 16 orientations.

If the shapes are connected not edge to edge but vertex to vertex, they form a checkboard-like pattern of tiles and voids. The voids have four edges that are formed by the four adjacent tiles and thus they too must have the same four shapes in 16 orientations that the tiles have. By arranging the tiles in different ways, a huge number of different patterns become possible. I tried to find some place on the web that explored these patterns, but could not. However, it is unclear what the best search terms would be.

I have taken this insight and made a series of eleven typefaces that are now available on MyFonts.com. A person using these typefaces can, by simply typing in letters from A to P or a to p, explore possible patterns that these four shapes can generate. Each typeface has two different designs on it. Below are a couple examples.

I was able to use these patterns to illustrate 11 of the 17 wallpaper groups of symmetry.

They are available at www.myfonts.com/fonts/ingrimayne/fab-fours/.

More Tessellations: A Coloring Book

Before I continue with posts about Exploring Tessellations: A Journey through Heesch Types and Beyond, I would like to mention a spinoff of that effort. For some of the isohedral classes that have shapeable sides, I had no examples in the collection of designs I used for mazes. For others I had only weak examples. I needed to develop examples that would clearly illustrate each class and show contrasts with other classes. As I finished the book (if in fact I have finished it —I expect I will be making revisions as I discover mistakes and as I learn more—there is so much more to know), I decided to reuse material in the format of a coloring book. The creation of More Tessellations: A Coloring Book was quick and easy compared to the time I have spent on Exploring Tessellations.

The book has the same format as an earlier coloring book of tessellations, A Tessellating Coloring Book. The cover is more attractive and an added feature is that the last page of the book identifies the Heesch type, isohedral class, and symmetry group of the designs used on each page. Three years ago I did not know enough about tessellations and symmetry to do a similar page.

The pages have many pictures of standing birds, though not those previously used in A Tessellating Coloring Book. (For some reason I find birds the easiest motif to tessellate.)

 I was very pleased with finding a bird design for Heesch type CC3C3C6C6.

These birds form a C3C3C3C3C3C3 type tessellation.

I like the abstract appearance of this pattern that on closer inspection is composed of mites (though they do not have enough legs).

IH90 is type CCC with all edges identically formed. It makes a visually appealing pattern

 IH14 is special case of type TTG1G2TG2G1 in which the TT edges are unshapeable straight lines and the four G sides are shaped identically. The right side of the tile is a mirror image of the left side. The illustration shows two ways it can be formed with the same sides. It has cm symmetry.

In a previous post I showed an illustration of class IH9. So far I have not converted it in Fontographer. The coloring book has a different illustration of IH9, shown below.

Some pages have more than one tessellation pattern. In the picture below are
examples of IH71 and IH61. Both patterns have all edges identically shaped, but the way the edges are arranged differs from one pattern to the other.

Here is the finished version of IH18, illustrated earlier while still in Tesselmaniac. It has p31m symmetry.

There is a very limited audience for all the books I have designed. I hope that the few people who eventually buy this one will enjoy it. It is available from CreateSpace and Amazon.

Exploring Symmetry Coloring Book

I recently published a new book and it is not the one that I have been working on for the past five months. Rather it is an offshoot from that book.

In the process of working on the still uncompleted book, I realized I needed to get much more comfortable with symmetry. Mathematicians have shown that there are only 17 groups of two-dimensional symmetry in patterns that periodically repeat in more than one direction. My way of getting familiar with these 17 groups was to review the patterns that I have used to make mazes and classify them by group. Making a book ("writing a book" is not an accurate description of the process) organized my exploration of the topic and the coloring book format was quick and easy. As I worked on sorting patterns into groups, I developed additional patterns and some of these are included in the book. The title is Exploring Symmetry Coloring Book and the book is available from Amazon and CreateSpace with a list price of $5.99.

The book starts with six pages that give a short explanation of each of the 17 symmetry groups with feet used to illustrate the patterns. This is how feet illustrates the p31m group:

 p31m is one of the more difficult groups to identify because there is another group with very similar symmetry called p3m1.  Both groups repeat themselves if rotated 120 degrees around their centers of rotation and both have mirror reflection.

Below feet illustrate a group called p4g. It needs to be distinguished from a group called p4m.

 After the short introduction explaining how one can identify groups of symmetry, the book has almost 100 pages of patterns that can be colored or decorated. The pages may also inspire or help readers to create new designs and patterns.

I designed a maze book with a railroad theme and used the pattern of rails shown below for a maze. It has reflection symmetry around both vertical and horizontal lines. It can reproduce itself it rotated 180 degrees. Finally, it has a staggered pattern that is caused by what is called glide reflection.The group that has these attributes is called cmm.

In designing a book of pirate mazes, I used a pattern with swords. In working on this book I found several other ways to use swords in patterns, such as this one which is p3. A benefit of working out thoughts in a book form is that it led to new patterns.

I tried to limit the number of designs that are fairly well known though I have used quite a number of them in mazes. The one below I found years ago in Tilings and Patterns by Branko Grunbaum and Geoffrey Shepard, It is another example of p4g.

There are other coloring books of geometrical and symmetrical designs that feature more complex and intricate designs and are probably better choices for those who want only a coloring book. Exploring Symmetry Coloring Book is not only a coloring book, it is also an introduction to the topic of symmetry. It is an educational coloring book.

Although young children can color the pages, only older people will appreciate the explanation of the symmetry groups. Supplementing the introduction, there is a page of notes at the end that identifies the groups used on each page.

Available from Amazon and Create Space.