Hello Jakub,
Here is a suggestion
pointAverage[function_, i_, j_] :=Integrate[function[x, y], {x, i, i + 1}, {y, j, j + 1}]
which takes a function defined wth two arguments and a grid point i,j. For example:
cfunc[x_, y_] := x Sin[Pi x] + y Cos[Pi y] I
pointAverage[cfunc, 1, 2]
pixels = Table[pointAverage[cfunc, i, j], {i, 1, 10}, {j, -10, 10}];
pixels[[1;;3]]
Image[Im[pixels], ImageSize -> 200] // Colorize
Image[Re[pixels], ImageSize -> 200] // Colorize
Image[Arg[pixels], ImageSize -> 200] // Colorize
(*or another example*)
cfuncOther[x_, y_] := Exp[x + I y] (x + I y)
pointAverage[cfuncOther, 2, 2]
pixels = Table[pointAverage[cfuncOther, i, j], {i, 1, 10}, {j, -10, 10}] (*may take a while*)
Image[Arg[pixels], ImageSize -> 200] // Colorize
Image[Im[pixels], ImageSize -> 200] // Colorize
