@acw I'm imagining this having tiles that are anywhere from 10 to 25 cm^2. Put an RGB LED in each of the four corners, with an acetate diffuser on top, and you could do quite a few different effects, including fairly convincing diagonals.
Each tile is self-contained. There are 8-bit TI MSP-430s that run about $0.10 USD in bulk. Make 'em all I2C addressable. Clipping them together routes power and sets up a mesh network. One "special" tile is PSU+master control.
Generalistic and moderated instance.