I wrote an excel VBA program that shows how a dye diffuses through water by taking one spreadhsheet cell and getting the average dye concentration for this cell and 8 of its immediate neighbours and repeating the procedure in a loop. Seems to work well. I am now doing this for weather prediction. How large are the errors likely to be in this procedure? It has the advantage that it only takes a couple of minutes to run the program. The photos below are symmetrical (have symmetrical values) as expected from putting dye in 4 corners in one and in the middle of the spreadsheet in the other.