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I want to create uniformly distributed disks(dots) in a specific rectangular area.

Suppose:

  1. the disk radii should be uniformly between $a$ and $b$ ($0<a<b$); there is no interaction between any two disks;
  2. the cover ratio $r$ is defined as the ratio of total area of all dots to the area of the rectangle.
  3. $a$ and $b$ decreases(increases?) accordingly with the increase of $r$

How to establish a mathematical model and obtain the desired graphs?

There is basically no criterion except for the visual effects of the example figures below; I have thought of using VoronoiMesh function but the visual effects may be different.

So constructive proposals or codes which generates similar visual effects will be accepted.

Here are example figures:

enter image description here

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  • 2
    $\begingroup$ Have you seen this? Probably a dupe. $\endgroup$ – Öskå Dec 23 '14 at 10:11
  • $\begingroup$ thank you! It seems how to calculate the radii of disks are also critical $\endgroup$ – LCFactorization Dec 23 '14 at 10:23

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