|The stupid question is the question not asked|
This is one time I'd advocate not re-inventing the wheel. (Depends on how you are using your results.)
Graphics packages are contain very optimised fast circle drawing algorithms coded in C. So, define your "array" as a 2-color (BW) image and then have it draw the circles.
GD for example, can draw thousands of circles per second.
With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority". The enemy of (IT) success is complexity.
In the absence of evidence, opinion is indistinguishable from prejudice. Suck that fhit