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We can use this answer on math.SE to determine on which side of a line a point lies. Based on this formula, we have that the new gray level is given by

f[{{x1_, y1_}, {x2_, y2_}}][gl_, {x_, y_}] := gl + 0.1 Sign[(x - x1) (y2 - y1) - (y - y1) (x2 - x1)]

We can apply this to all pixels recursively in the following manner:

iterate[img_] := Module[{dimx, dimy, pts},
  {dimx, dimy} = ImageDimensions[img];
  pts = Transpose[{RandomInteger[dimx, 2], RandomInteger[dimy, 2]}];
  ImageApplyIndexed[f[pts], img]
  ]

img = ConstantImage[0.5, {300, 300}];
Nest[iterate, img, 50]

Below is another test run with more iterations, and I also changed the constant 0.1 in front of Sign to 0.02. This constant determines how much each side is raised or lowered, and it has a big influence on the visual effect.

Nest[iterate, img, 100]

I'm not sure how to prove correctness for this algorithm, so if anyone spots an error please tell me.

We can use this answer on math.SE to determine on which side of a line a point lies. Based on this formula, we have that the new gray level is given by

f[{{x1_, y1_}, {x2_, y2_}}][gl_, {x_, y_}] := gl + 0.1 Sign[(x - x1) (y2 - y1) - (y - y1) (x2 - x1)]

We can apply this to all pixels recursively in the following manner:

iterate[img_] := Module[{dimx, dimy, pts},
  {dimx, dimy} = ImageDimensions[img];
  pts = Transpose[{RandomInteger[dimx, 2], RandomInteger[dimy, 2]}];
  ImageApplyIndexed[f[pts], img]
  ]

img = ConstantImage[0.5, {300, 300}];
Nest[iterate, img, 50]

Below is another test run with more iterations, and I also changed the constant 0.1 in front of Sign to 0.02. This constant determines how much each side is raised or lowered, and it has a big influence on the visual effect.

Nest[iterate, img, 100]

I'm not sure how to prove correctness for this algorithm, so if anyone spots an error please tell me.

We can use this answer on math.SE to determine on which side of a line a point lies. Based on this formula, we have that the new gray level is given by

f[{{x1_, y1_}, {x2_, y2_}}][gl_, {x_, y_}] := gl + 0.1 Sign[(x - x1) (y2 - y1) - (y - y1) (x2 - x1)]

We can apply this to all pixels recursively in the following manner:

iterate[img_] := Module[{dimx, dimy, pts},
  {dimx, dimy} = ImageDimensions[img];
  pts = {RandomInteger[dimx, 2], RandomInteger[dimy, 2]};
  ImageApplyIndexed[f[pts], img]
  ]

img = ConstantImage[0.5, {300, 300}];
Nest[iterate, img, 50]

Below is another test run with more iterations, and I also changed the constant 0.1 in front of Sign to 0.02. This constant determines how much each side is raised or lowered, and it has a big influence on the visual effect.

Nest[iterate, img, 100]

I'm not sure how to prove correctness for this algorithm, so if anyone spots an error please tell me.

We can use this answer on math.SE to determine on which side of a line a point lies. Based on this formula, we have that the new gray level is given by

f[{{x1_, y1_}, {x2_, y2_}}][gl_, {x_, y_}] := gl + 0.1 Sign[(x - x1) (y2 - y1) - (y - y1) (x2 - x1)]

We can apply this to all pixels recursively in the following manner:

iterate[img_] := Module[{dimx, dimy, pts},
  {dimx, dimy} = ImageDimensions[img];
  pts = Transpose[{RandomInteger[dimx, 2], RandomInteger[dimy, 2]}];
  ImageApplyIndexed[f[pts], img]
  ]

img = ConstantImage[0.5, {300, 300}];
Nest[iterate, img, 50]

Below is another test run with more iterations, and I also changed the constant 0.1 in front of Sign to 0.02. This constant determines how much each side is raised or lowered, and it has a big influence on the visual effect.

Nest[iterate, img, 100]

I'm not sure how to prove correctness for this algorithm, so if anyone spots an error please tell me.

We can use this answer on math.SE to determine on which side of a line a point lies. Based on this formula, we have that the new gray level is given by

f[{{x1_, y1_}, {x2_, y2_}}][gl_, {x_, y_}] := gl + 0.1 Sign[(x - x1) (y2 - y1) - (y - y1) (x2 - x1)]

We can apply this to all pixels recursively in the following manner:

iterate[img_] := Module[{dimx, dimy, pts},
  {dimx, dimy} = ImageDimensions[img];
  pts = {RandomInteger[dimx, 2], RandomInteger[dimy, 2]};
  ImageApplyIndexed[f[pts], img]
  ]

img = ConstantImage[0.5, {300, 300}];
Nest[iterate, img, 50]

Below is another test run with more iterations, and I also changed the constant 0.1 in front of Sign to 0.02. This constant has a big influence on the visual effect.

Nest[iterate, img, 100]

I'm not sure how to prove correctness for this algorithm, so if anyone spots an error please tell me.

We can use this answer on math.SE to determine on which side of a line a point lies. Based on this formula, we have that the new gray level is given by

f[{{x1_, y1_}, {x2_, y2_}}][gl_, {x_, y_}] := gl + 0.1 Sign[(x - x1) (y2 - y1) - (y - y1) (x2 - x1)]

We can apply this to all pixels recursively in the following manner:

iterate[img_] := Module[{dimx, dimy, pts},
  {dimx, dimy} = ImageDimensions[img];
  pts = {RandomInteger[dimx, 2], RandomInteger[dimy, 2]};
  ImageApplyIndexed[f[pts], img]
  ]

img = ConstantImage[0.5, {300, 300}];
Nest[iterate, img, 50]

Below is another test run with more iterations, and I also changed the constant 0.1 in front of Sign to 0.02. This constant determines how much each side is raised or lowered, and it has a big influence on the visual effect.

Nest[iterate, img, 100]

I'm not sure how to prove correctness for this algorithm, so if anyone spots an error please tell me.