[takatin]

Because stars in the sky is a high contrast visual. That applies here too, I increased the contrast using Photoshop and the illusion is gone, you can see all 12 dots perfectly fine — http://imgur.com/a/G4xR4 I think they are spot on, outside the fovea, contrast detection capability of our eyes dip drastically thereby blending the dots lying outside the fovea with the surrounding grid. Increase the contrast to the point where even the regions outside the fovea can detect it and the illusion goes away.

[kevinalexbrown]

I don't think that explains it, either: Even in low contrast, the illusion fails w/o the lines, as far as I can tell.

[taeric]

Without the lines... there is much higher contrast.

I'm all for hearing an alternative hypothesis, but right now this article's seems pretty good at covering whta is happening.