A fractal set from the binary reflected Gray code

Abstract

The permutation associated with the decimal expression of the binary reflected Gray code with $N$ bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is shown to be the attractor of a IFS. For large values of $N$ the set is examined from the point of view of time series analysis

15 pages, 9 figures

References in corpus (3)

• Efficient decomposition of quantum gates
• Systematic Computation of the Least Unstable Periodic Orbits in Chaotic Attractors
• Random walk generated by random permutations of {1,2,3, ..., n+1}