I am looking for online algorithms to generate points that are reasonably uniformly distributed in the unit square.
The number of points is not known in advance. For every n, the distribution of the first n points generated must be reasonably uniformly distributed.
The coordinates are real (floating-point) numbers (between 0 and 1); so, not on a grid.
The points need (must) not be random; in fact, I want a deterministic algorithm, with provable properties (not based on statistics).
Generating such points in the unit interval can be done by using the golden ratio Phi:
- Take as point i the number (i * Phi) mod 1.
How to do that in 2D?
If the number of points is known in advance to be N, then ((Phi * i) mod 1, i/N) works nicely. But that is not online.
For some c, the points ((Phi * i) mod 1, (c * i) mod 1) could work, but it is not clear which c is best. Especially, for larger numbers of points, all c that I tried had clear deficiencies.