Fat Roads

A short post today, following up on the last post.

We determined that forty-seven tiles are necessary in order to produce any shape between road and grass. However, how many tiles might we need if we wanted to produce any thick shape? That is, if we wanted to produce roads that were at least two squares thick, but never only a single square thick?

No brain teaser today the answer is sixteen again. These fifteen, plus the 'blank' tile (all green):

In most applications, you would choose to make the tiles for a one-square-thick application (common examples are roads and rivers) or for a two-or-more-square-thick application (common examples are lakes or gardens). The sixteen other tiles, which I call 'connectors', are of limited use. In the days of yore, when memory was expensive, nobody would have produced them without good cause.

Next week, however, we will look at a way to construct a small set of sub-tiles which can be used to produce all forty-seven of our shapes.