How to effectively distribute points on plane I have a plane (screen) with its width and height (monitor resolution, not square). And I'd like to distribute points on that plane with the (approximately) same distance from each other.
For example:


*

*1 point will be in the middle,

*2 points will be in the middle of y axis, and x axis will be divided by 3

*3 points may be like triangle, but if sceen is wide enough, thay can be alighned in same y

*4 like second part of above, or as rectangle..

*etc to 8 points max


Is there any algorithm for this?
Thank you for your time!
EDIT: same distance from each other and from plane border
EDIT2: I compute centers of mass for groups of objects on which behavior I simulate on plane. 
 A: The question is a bit vague, but the first idea that came to my mind would be to use a low-discrepancy sequence such as a Halton sequence or a Sobol sequence.  Here are examples of 256 points distributed on the plane using each of them, with a random distribution for comparison:



From left to right: Halton sequence, Sobol sequence, random sequence.  Images by Jheald / Wikimedia Commons, licensed under the CC-By-SA 3.0 license.
At least, you could use these sequences as starting configurations for a local optimization algorithm, which might e.g. repeatedly move each point a small distance away from its nearest neighbor until the configuration stabilizes.
A: First of all, thanks to everybody for suggestions which helped me to define my problem better and to find best solution to my problem.
Now I am using Centroidal Voronoi tessellation which according to Wikipedia: "In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation or Voronoi diagrams. A Voronoi tessellation is called centroidal when the generating point of each Voronoi cell is also its mean (center of mass). It can be viewed as an optimal partition corresponding to an optimal distribution of generators."
Its very fast and there is implementation in D3js library for javascript which I am using.
