4-shape Tessellation

Rotate the lower left cell of the tile 90 degrees clockwise; mirror, then rotate the lower right cell of the tile 270 degrees counterclockwise. Shape 15 Shape 54 Shape 78 Shape 79

Rotate the lower left cell of the tile 90 degrees clockwise; mirror, then rotate the lower right cell of the tile 180 degrees. Shape 2 Shape 3 Shape 12 Shape 13

Rotate the lower left cell of the tile 90 degrees clockwise; mirror, then rotate the lower right cell of the tile 90 degrees counterclockwise. Shape 54 Shape 73 Shape 76 Shape 77

Rotate the bottom left cell of the tile 90 degrees clockwise; rotate the bottom right cell of the tile 180 degrees. Shape 54 Shape 71 Shape 72 Shape 73

Rotate the bottom left cell of the tile 90 degrees clockwise. Shape 54 Shape 55 Shape 56 Shape 57

Mirror, then rotate the lower right cell of the tile 180 degrees. Shape 54 Shape 55 Shape 64 Shape 65

Mirror, then rotate the lower right cell of the tile 90 degrees counterclockwise. Shape 1 Shape 21 Shape 32 Shape 63

Mirror the lower right cell of the tile. Shape 20 Shape 54 Shape 61 Shape 62

Rotate the lower right cell of the tile 270 degrees clockwise. Shape 7 Shape 54 Shape 59 Shape 60

The twenty-eight patterns you’ve just seen are Regular tessellations — symmetrical, orderly, each one a mirror of itself in some direction. They are, in their way, perfect. But perfection accounts for only twenty-eight of the five hundred and twelve possible patterns this system can generate. What about the other four hundred and eighty-four? They don’t…