On Fri, Aug 29, 2008 at 8:27 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
On 8/30/08, Mike Stay <metaweta@gmail.com> wrote:
On Fri, Aug 29, 2008 at 11:09 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
but I think one essential property of any generalisation must be that the resulting walk is Hamiltonian --- each step altering just one coordinate by (+/-)1 --- which this construction fails to enforce.
It inherits it from the fact that the original walk is a Gray code, which has that property.
I think not. Quoting from your example, lines 4-5
01 00 01 10 (first bit is 01, second bit goes 10,11,01,00)
the second vector component increments by +2 !
It changes by one bit, and when you use the level n-1 code as the length along the axis, that means you change by one unit---i.e. you have to change it back from the Gray code for the offset to the standard binary code for the offset to see actual differences in position. Look at the diagram I drew: going from 00 to 10 doesn't jump by two cells. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com