How to expand/inflate shapes with collision?

Hello!

 I have this grid of dots that I want to expand, so they take up all the white space between them, while not colliding into eachother (which means they won't be circles anymore, but weird hexagon-ish shapes, depending on how many neighbors they have, except the outermost circles that would still be circles on the outside, albeit bigger ones). Kinda similar to what Substance Painter does with unused parts of the texture, so there are no seams around the edges, but in vector.

Basically divide the white space to the objects evenly, while keeping them separate objects, so I can color them differently and make a mosaic.

Does anyone know what this "technique" is called so I can search it better or know a way to achieve it in Illustrator?

Thanks in advance!