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graphics - Coloring with Hue for a function on a lattice grid


I wish to color a 2-dimensional lattice grid according to the value of a function at each lattice-node. More specifically, if I have 9 angles in a 3x3 array,


angles={{0, π, π}, {0, 0, π/2}, {π/2, 0, 3 π/3}}

then one can plot these angles on a lattice-grid by the following code in Mathematica:



angles = {{0, π, π}, {0, 0, π/2}, {π/2, 0, 3 π/3}};
GraphicsGrid[
 Map[Graphics[{
    LightGray, Circle[{0, 0}, 1], 
    Hue[#/(2 π), .6, .8], Thick, Arrowheads[Medium], Arrow[{{0, 0}, {Cos[#], Sin[#]}}]}] &, 
  angles, {2}]]

Here, the colouring is done using the Hue command according to the value of each angle. However, now I want to compute a function f[i,j]; to be more specific,


f[i_,j_]:=Cos[angles[[i + 1, j]] - angles[[i, j]]] + Cos[angles[[i, j+1]] - angles[[i, j]]];


with


angles[[n+1,i_]]:=angles[[1,i]];
angles[[i_,n+1]]:=angles[[i,1]];

i.e., the boundary conditions.


In the first code, Hue is used with the angles[[i,j]] (through #), which is probably straightforward. But is it possible to use f[i,j] instead, where f[i,j] is defined as above?


P.S. This question is related to: data visualization on a lattice grid


Thanks!


dbm


P.S. The final code, thanks to BoLe's answers:



Clear["Global`*"];
n := 10
angles = Table[RandomReal[{-Pi, Pi}], {i, n}, {j, n}];
f[here_, down_, right_] := Cos[down - here] + Cos[right - here]
g[list_, {i_, j_}] := 
 Module[{m, n}, {m, n} = Dimensions[list]; {list[[i, j]], 
   If[i != m, list[[i + 1, j]], -list[[1, j]]], 
   If[j != n, list[[i, j + 1]], -list[[i, 1]]]}]
GraphicsGrid[
 MapIndexed[

  Graphics[{LightGray, Circle[{0, 0}, 1], 
     Hue[Rescale[f @@ g[angles, #2], {-2, 2}, {0, 1}]], Thin, 
     Arrowheads[Small], Arrow[{{0, 0}, {Cos[#], Sin[#]}}]}] &, 
  angles, {2}]]


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