As @twic and the OP discussed, the equal distribution of numbers within a defined range is naturally achieved through low discrepancy sequences (eg recurrence,Halton, Sobol, etc..) Furthermore, in ultra high-speed / low-level computing situations the additive recurrence methods are often preferred due to the incredibly fast and simple method of calculating the each successive term simply by adding (modulo) a constant value to the previous term.
For the one-dimensional case, it is well known, and relatively easily proven that the the additive recurrence method based on the golden ratio offers the optimal 'evenness' [low discrepancy] in distribution [1].
For higher dimensions, it is still an open research question as to how to create provably optimal methods. However, one of my recent blog posts [2] explores the idea that a generalization of the golden ratio, produces results that are possibly optimal, and better than existing contemporary low discrepancy sequences.
In the one dimensional case, the critical additive constant is of course, the golden ratio. In the two dimensional case, the additive constant is based on integral powers of the plastic number. The generalization to even higher dimensions follows other Pisot numbers.
For the one-dimensional case, it is well known, and relatively easily proven that the the additive recurrence method based on the golden ratio offers the optimal 'evenness' [low discrepancy] in distribution [1]. For higher dimensions, it is still an open research question as to how to create provably optimal methods. However, one of my recent blog posts [2] explores the idea that a generalization of the golden ratio, produces results that are possibly optimal, and better than existing contemporary low discrepancy sequences. In the one dimensional case, the critical additive constant is of course, the golden ratio. In the two dimensional case, the additive constant is based on integral powers of the plastic number. The generalization to even higher dimensions follows other Pisot numbers.
[1] https://en.wikipedia.org/wiki/Low-discrepancy_sequence#Addit...
[2] http://www.extremelearning.com.au/unreasonable-effectiveness...