EDIT: Exploring, I see the island I live on -- Manhattan -- has the four main dot colors well represented, though mainly in blocks. The main mixing is between whites and Asians and between blacks and Hispanics. Notably parts of the Upper West Side, East Village/Lower East Side, and Midtown west show significantly more mixing, at least by eye -- it would be interesting to quantify the data.
Some parts of Queens and Brooklyn show mixing of all four dot colors within the same city block.
Still, on the whole most dot colors remain in blocks with less mixing on the edges. Some dot colors rarely mix with other dot colors.
EDIT TWO: How they made the map is here -- http://www.coopercenter.org/demographics/Racial-Dot-Map -- which describes the data sources and links to the code on Github.