Gray codes have several applications:
The fourth algorithm to produce Gray codes will actually produce an m-ary (not just binary) Gray code of length n. It is compact and relatively fast. Though discovered independently, this appears to be the same as the first algorithm of M. C. Er [E].
The gray package contains routines to
For example, the coordinate (x,2y+1) of the plot below signifies that the y-th peg should be moved at the x-th step of the Brain puzzle:
There is a example worksheet which may be downloaded as well.
[CSW] J. Conway, N. Sloane, and A. Wilks, "Gray codes and reflection groups", Graphs and combinatorics 5(1989)315-325
[E] M. C. Er, "On generating the N-ary reflected Gray codes", IEEE transactions on computers, 33(1984)739-741
[G] M. Gardner, "The binary Gray code", in Knotted donuts and other mathematical entertainments, F. H. Freeman and Co., NY, 1986
[Gi] W. Gilbert, "A cube-filling Hilbert curve", Math Intell 6 (1984)78
[Gil] E. Gilbert, "Gray codes and paths on the n-cube", Bell System Technical Journal 37 (1958)815-826
[R] F. Ruskey, "A Survey of Venn Diagrams", Elec. J. of Comb.(1997), and updated versions
[S] Web page of T. Sillke
[W] A. White, "Ringing the cosets", Amer. Math. Monthly 94(1987)721-746