If I was to recreate this in Processing then I would treat each dot as a seperate entity with a predetermined end position (x/y), when all the dots are in the end position then the image is visible
The starting point for each dot could be random or the end point of the explosion from the previous image. The animation would move all the dots to their end position wait a while then explode them outwards.

The actual dot end positions and sizes could be calculated from the brightness values from an actual bitmap.

There are other ways to program this effect - these are just my initial thoughts.

HTH

That's what I was thinking. What would I look for when creating the the dot end positions by brightness.. is there a specific term for it?

There are two principal colour maps used to specify a colour, RGB (red / green / blue) and HSB (hue / saturation / brightness). In Processsing you can swap between the two with colorMode(), once in HSB mode you can use brightness() to determine how 'light' a pixel is.