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There are many ways to make mazes. The most flexible way is to draw them by hand, though to do this well requires time and special talent. Several of the people who drew mazes for the Dover series of maze books showed great creativity in inventing many different types of mazes.
Many of the mazes available today have been produced by computer programs. Although this approach to maze making also requires time and talent, once the program is completed, producing another maze is almost effortless. This approach is less flexible because the programmer must specify how the maze is to be constructed and only mazes of the types allowed by the software are possible. Different programmers have approached the task in different ways and, as a result, each program produces somewhat different mazes.
My first computer program that constructed mazes was done as part of a game for an early home computer, the Texas Instrument 99/4A, in the early 1980s. It constructed a maze by starting with a grid of squares and then breaking down the walls so that in the end every point in the maze connected to every other point by one and only one path. When I again took up mazes a decade later, this time writing a program that would produce mazes for printing, I used the same method of constructing a maze. The resulting maze would look like the small maze below.
If a maze of based on a grid of squares is possible, a maze based on a grid of triangles is fairly easy to do. The difference is that certain connections are not possible for the triangular grid that are possible for the grid of squares.
There are three regular polygons (polygons with equal sides and angles) that cover the plane: the triangle, square, and hexagon. Extending the program to make mazes based on a grid of hexagons is not a big stretch. (Notice that all of these mazes are five rows and five columns.
What else can a maze program do? One of the first extensions I wanted to do was to allow paths to cross over and under each other. This creates mazes that are more interesting and in some cases harder to solve.
Hexagonal mazes can also use underpasses.
Other things possible are multiple exits and different shapes.
Though octagons do not cover the plane, they can be used as the basis of a maze. The restriction is that the program should not have two paths crossing the same corner. Eventually I developed a program that did this type of maze.
In the late 1990s I stopped developing maze software when it appeared that there was no easy way to get any more maze books published. Since then operating systems have changed and my old software no longer runs on any currently-produced computer. Programming skills evaporate when not used, so I have no easy way to alter these old programs. However, I had another avenue left open because of the way in which my programs outputted the mazes. Like other programs, my programs constructed mazes based on numbers. They differed from most other programs because they saved a maze as a collection of letters, that is, as a text file. This meant that the maze could not be displayed without a special typeface. However, typeface design was a topic that interested me much more than computer programming. I have designed hundreds of different typefaces.
One way to make a mazes more difficult is to make them bigger. Another way is to add visual distraction with the way it is displayed. For example, the simple maze of blocks that was illustrated at the beginning can be made simpler if it is displayed in the more usual way.
Below is the same maze with a typeface that makes it more difficult.
In my second Dover book of mazes, I explored odd ways to display mazes. One way was to display a maze as blocks of letters with only certain letters forming the path. Below is the same maze as above with the path made of vowels--you cannot move to a block of with a consonant.
Displaying the maze in this way makes it far more difficult than it was in its traditional form. (It also does not seem to be a way that appeals to people because it is not visually attractive or interesting.)
What distinguishes the mazes in my maze books from other mazes? It is not the computer programs that generate mazes--others have developed programs as good or better than mine. Rather it is the wide variety of different specialized maze typefaces that I can use that makes my mazes different from others.
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