Mapping picture, rotate

Question

I'm trying to do this. it doesn't have to be the same.

Answer 1

Use two functions of your choice:

f1[x_] := -x - Piecewise[{{2 Sin[x ], -2 Pi <= x <= 2 Pi}}]
f2[x_] := x + Piecewise[{{2 Sin[2 x], Abs[ x] <= 3 Pi/2}}]

options = {AspectRatio -> 1, 
   PlotRange -> {{-3 Pi, 3 Pi}, {-3 Pi, 3 Pi}}, Frame -> True, 
   Axes -> False, FrameTicks -> None, ImageSize -> 300};

Plot the functions f1 and f2 with the option Filling:

plota = Plot[{f1[x], f2[x]}, {x, -6 Pi, 6 Pi}, 
  Exclusions -> None, 
  PlotStyle -> ColorData[97]@1, 
  Filling -> {1 -> {2}}, 
  Evaluate @ options]

Use GeometricTransformation + RotationTransform to rotate plota primitives by desired angles and use the option PlotRange to crop resulting graphics:

Multicolumn[
 Table[Legended[
   Show[MapAt[GeometricTransformation[#, RotationTransform[a]] &, plota, {1}], 
     Evaluate @ options], 
   Placed[Style[a, 16], {.5, .9}]], {a, Subdivide[0, 2 Pi, 8]}], 
 3, Appearance -> "Horizontal", Spacings -> {0, 0}]

Animation above is produces using:

frames = Table[Show[MapAt[GeometricTransformation[#, RotationTransform[a]] &, 
     plota, {1}], ImageSize -> 500, Evaluate @ options], 
   {a, Subdivide[0, 2 Pi, 50]}];

Export["rotations.gif", frames, "AnimationRepetitions" -> Infinity]

Answer 2

(b) is problematic because it does not contain the same pixels as (a) and (b).

Look at the following:

ImageRotate[im, #] & /@ {0,-Pi/4,-Pi/2}

It looks like you rotated a larger picture and cut it to size.