How do you achieve this optical illusion of a picture?

Question

In MSE by a similar problem about the optical illusion, but I feel that the solution ideas of other problems can not be applied to the following diagram, I would like to ask you how to draw this kind of diagram? I don't have any ideas.

Answer 1

The image in blue and pink has been overlayed with small boxes in black and white. At the cordners of each box protrudes a line with same color as the corner half way to the next box. Every second box in x and y direction is rotated by 180° and in addition in the pink area by another 90°.

im = Image[ImagePad[Binarize[
    Import["https://image.spreadshirtmedia.net/image-server/v1/products/T1459A839PA4459PT28D16690413W9915H10000/views/1,width=120,height=120,appearanceId=839,backgroundColor=F2F2F2/cat-icon-sticker.jpg"]
], 50, 1], ImageResolution -> 72];

ClearAll[box]
box[x_, y_, d_:1, s_:0.17] := Translate[{
    Black,
    Polygon[(Plus[d])*{{0, s}, {s, 0}, {s, -s}/2, {-s, s}/2}], 
    Line[d*{{0, s}, {0, 0.5}}],
    Line[d*{{s, 0}, {0.5, 0}}],
    White,
    Polygon[(-d)*{{0, s}, {s, 0}, {s, -s}/2, {-s, s}/2}],
    Line[(-d)*{{0, s}, {0, 0.5}}],
    Line[(-d)*{{s, 0}, {0.5, 0}}]
}, {x, y}]

dat = Transpose[Reverse[ImageData[im]]]; 
{px, py} = Dimensions[dat]
n = 20; 

boxes = Table[Module[{
        x = (i - 1) / (n - 1) * px,
        y = (j - 1) / (n - 1) * py
    },
    phi = Pi/2 + 
          Pi * Mod[i + j, 2] + 
          Pi / 2 *dat[[Round[i * px / n],Round[j * py / n]]];
    Rotate[box[x, y, px / (n - 1)], phi]
], {i, n}, {j, n}];

Graphics[{
    ColorReplace[im, {
        0 -> RGBColor[1, 0.6, 0.8],
        1 -> RGBColor[0.4, 0.8, 1]
    }],
    boxes
}, ImageSize -> 800]

Answer 2

I'll post the code tomorrow, it's a bit of a mess at the moment.

Here is the code with abusing of GriGraph for a little piece of art.

n = 11;
r = {{-(1/2), 0}, {1/2, 0}, {1/2, 1/2}, {-(1/2), 1/2}};
{c1, c2} = {RGBColor[0.4, 0.8, 1], RGBColor[1, 0.6, 0.8]};
vs[fi_, r_] := 
  Graphics[{Black, Polygon[RotationMatrix[fi] . # & /@ (-r)], White, 
    Polygon[RotationMatrix[fi] . # & /@ r]}];

g = GridGraph[{2 n + 1, 2 n + 1}, EdgeStyle -> Black, 
   VertexShape -> {Alternatives @@ Range[1, (2 n + 1)^2, 2] -> 
      vs[-π/4, r], 
     Alternatives @@ Range[2, (2 n + 1)^2, 2] -> vs[3 π/4, r]}, 
   VertexSize -> 0.4, Background -> c1, ImageSize -> 720];
AnnotationValue[g, 
   EdgeStyle] = {Alternatives @@ Select[EdgeList[g], OddQ[#[[1]]] &] ->
     White};

h = GridGraph[{2 n + 1, 2 n + 1}, EdgeStyle -> Black, 
   VertexShape -> {Alternatives @@ Range[1, (2 n + 1)^2, 2] -> 
      vs[π/4, r], 
     Alternatives @@ Range[2, (2 n + 1)^2, 2] -> vs[-3 π/4, r]}, 
   VertexSize -> 0.4, Background -> c2, ImageSize -> 720];
AnnotationValue[h, 
   VertexCoordinates] = {2 n + 
      2 - #[[1]], #[[2]]} & /@ (AnnotationValue[{h, #}, 
       VertexCoordinates] & /@ Range[(2 n + 1)^2]);
AnnotationValue[h, 
   EdgeStyle] = {Alternatives @@ Select[EdgeList[g], OddQ[#[[1]]] &] ->
     White};

im = ColorNegate@
   Graphics[{Disk[], White, Disk[{-0.32, 0.54}, 1/5], 
     Disk[{0.32, 0.54}, 1/5], 
     Disk[{0, -0.15}, 3/5, {π, 2 π}]}, PlotRange -> 1.25, 
    ImageSize -> 720];

ImageCompose[Image@g, SetAlphaChannel[Image@h, im]]

Answer 3

Just an alternative relying on image operations and using some emojis as input for testing purpose:

emoji = "🐬"(*"🐎"*)(*"🐖"*)(*"🐘"*);
imgSize = {800, 800};
colors = <|"back" -> RGBColor[0.4, 0.8, 1], "front" -> RGBColor[1, 0.6, 0.8]|>;
image = Image[ Rasterize@Magnify[emoji, 40] // Binarize // RemoveBackground // 
    ColorReplace[#, Black -> colors["front"]] &];
mask = Image[Graphics[{{
      Inset[Graphics[image // ColorReplace[#, colors["front"] -> Black] &, 
        ImageSize -> imgSize], Center]}}, ImageSize -> imgSize], ImageResolution -> 500];

transform[image_, direction_ : "<" | ">", background_ : colors["back"], steps_ : 20] := 
   Module[{size = 7}, 
    colLineColor[x_, y_] := If[EvenQ[x + y], Black, White];
    rowLineColor[x_, y_] := 
     If[If[direction == "<", EvenQ, OddQ][x + y], Black, White];
    theta = If[direction == "<", 45 °, 135 °];
    Image[Graphics[{
     {Inset[Graphics[image, ImageSize -> imgSize], Center]}
     , Table[{
         colLineColor[x, y]
       , Line[{{x + 1,  y}, {x + 1 , Min[y + size, steps size]}}]
       , rowLineColor[x, y] 
       , Line[{{x, y + 1}, {Min[x + size, steps size] , y + 1}}]
       , Rotate[#[x, y], If[EvenQ[x + y], theta, theta + 180 °]] }
    , {x, 0, steps size, size}, {y, 0, steps size, size}] &[
      {x, y} |-> {White, Rectangle[{x, y}, {x + 1, y + 2}]
                , Black, Rectangle[{x + 1, y}, {x + 2, y + 2}]}]}
   , Background -> background, ImageSize -> imgSize], ImageResolution -> 500]]

backgroundImage = ImageAdd[ImageMultiply[transform[image, "<"], mask],ColorNegate@mask] ;
frontImage = ColorNegate@ImageMultiply[transform[image, ">", White], ColorNegate@mask] // 
   ColorReplace[#, {ColorNegate@colors["front"] -> colors["front"]}] &;
Grid[{{backgroundImage, frontImage}}]
(* Output *)

(* Putting them together *)
ImageDifference[ColorNegate@backgroundImage, frontImage]