Visualizing multi-state lattice from a data set

Question

Is there any way to make Mathematica visualize a multistate square lattice? That is, I have a data set from a simulation that is x coloumns wide and y rows tall (just a simple .dat file), where each cell has a value *n_i = 0,1,2,3* - and I then want Mathematica to draw a x by y square lattice and color each square in the lattice corresponding to the state in the data set, e.g. 0 = red, 1 = green, 2 = blue, 3 = yellow.

Answer 1

You can use ArrayPlot or MatrixPlot. Note that Mesh setting is optional. It works well if squares are large, but should not be used for small square sizes. MatrixPlot is very intelligent for large arrays of data - it deduces best approximate visual form: "sufficiently large or sparse matrices are downsampled so that their structure is visible in the plot" ~ Documentation.

Make some data and save in .DAT file:

dat = RandomInteger[{0, 3}, {13, 13}];
Export["test.dat", dat];

Now import that file and plot:

imp = Import["test.dat"];
MatrixPlot[imp, ColorRules -> {0 -> Red, 1 -> Green, 2 -> Blue, 3 -> Yellow},Mesh -> True]

Answer 2

ArrayPlot[]/MatrixPlot[] are the most straightforward ways to go about this. Alternatively, one could use Raster[] or Image[] for the purpose:

BlockRandom[SeedRandom[42, Method -> "MersenneTwister"]; (* for reproducibility *)
            arr = RandomInteger[{0, 3}, {15, 20}]];

colorRules = Thread[Range[0, 3] -> List @@@ {Red, Green, Blue, Yellow}];

From here, we could do either of

Image[arr /. colorRules, ImageSize -> 300]

or

Graphics[Raster[Reverse[arr] /. colorRules]]

to give this: