So, if I understand this correctly, there is no simulation, but you ‘draw’ the tiles and want the patterns and colors to be set automatically.
If you’re not too fixed on using GN, here’s what you could do for the Power/Color:

Just Duplicate the tile and move it and calculate the Manhatten Distance to get the Strength (numbers can be tweaked to set the Strength of the first tile).
The patterns for the connections are a bit more difficult and might not be do-able with just Shader Nodes…