Uniformly Distributed points on a plane are getting clustered in java, why?

Question

I want to generate uniformly distributed circles/points/nodes on a *100 plane. For that I am using the Random() method in java. Specifically I am doing it in in the following manner:

Random r1=new Random();
  for(int i=0;i<100;i++){
  x=100*r1.nextDouble();
  y=100*r1.nextDouble();
} 

But the problem is that as I run the code over and over again, the nodes are not uniformly spaced on the plane, i.e., there are clusters of concentrations and some chunks of un-occupied space.

Any ideas, recommendations would be highly appreciated. The image belows shows a typical output with the clusters and the white spaces. The number of the circles are just the IDs of the circles.

Answer 1

I assume you mean a 100x100 unit plane, with 100 points.

A 10x10 grid overlaid over your plane, with 1 point per grid box means 100 evenly distributed points.

Place points in the center for exact uniformity that's pretty:

for(int i=0;i<100;i++){
    x = 5 + 10*(i/10);
    y = 5 + i % 10;
} 

Or for a little bit of jitter, randomize the location within each grid box:

Random r1=new Random();
for(int i=0;i<100;i++){
    x = 10*r1.nextDouble() + 10*(i/10);
    y = 10*r1.nextDouble() + i % 10;
} 

Answer 2

If you want your random distribution to look more "even", that is you want to cover the space more evenly, you cannot use a completely uniform distribution, since it will contain "gaps", as @Adam pointed out.

You can use instead something called Low-discrepancy sequence: Halton sequence for instance, or Sobol sequence. As you can see in the Wikipedia example pictures, they avoid clusters and gaps you will have with uniform distributions.