  In a recent arXiv-manuscript Fox studies infinite subtraction games with a
finite (ternary) and aperiodic Sprague-Grundy function. Here we provide an
elementary example of a game with the given properties, namely the game given
by the subtraction set $\{F_{2n+1}-1\}$, where $F_i$ is the $i$th Fibonacci
number, and where $n$ ranges over the positive integers. Our definition of
nim-dimension reflects the precise number of power-of-two-components generated
by the games; the group of nim-values is of order four so the dimension is two
(in the classical definition this dimension would have been one). Thanks to
Carlos Santos for an enlightening discussion on this matter.
