Hue function for negative arguments

Question

I want to use Hue function for different colours with the argument being a function, i.e.,

Hue[f[i,j]]

Now, f[i,j] in my case can take negative values. The range of my function is [-2,2] (which can be rescaled to [-1,1] if necessary, by dividing the function by 2). The problem is that Hue automatically rescales its argument to put it into the range of [0,1). This is a problem for me as it will then show the same colour when my function is either -1 or 0 or 1, for example. The actual figure I want to work on can be generated by the following code:

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}, {-1, 1}]], Thin, 
      Arrowheads[Small], Arrow[{{0, 0}, {Cos[#], Sin[#]}}]}] &, angles, {2}]]

Answer 1

Hue does not rescale its argument, but it is a periodic function, equivalent to Hue[Mod[x, 1]]. What you need is rescaling: Rescale[f[...], {-2,2}].