Barthelet says that the contributions of Mathematica come in two primary areas: symmetry and testing. One convenience of using a symbolic computation package is that rules for each replacement need to be implemented only in one orientation. The remaining are easily calculated by taking advantage of symmetry. This "out of one, many" approach saves countless hours and guarantees the accuracy of the resulting rules.
The replacement rules take on the following form.
Text Form of a Rule. Human readable form of the highway rule for capping the end of a diagonal curve.
A nice, readable format, but difficult to visualize. Barthelet relies on Mathematica's graphics capabilities to render each rule, using the actual game graphics; thus, he is able to visually validate them easily. A picture is indeed worth at least a couple of dozen symbols in this case!
Visualization. A visual confirmation of the diagonal highway cap rule.
Converted by Mathematica April 24, 2000