why1.txt

Why do the tiles in the second tiling run from 121 to 241?
The first 121 tiles (0-120) are the first tiling because each tiling is 11x11 so the second tiling starts with 121 and goes to 241, and so on.

Why is the point (0.1,0.1) in the first tile of the first seven tilings, that is, in tiles 0, 121, 242, 363, 484, 605, 726?
The point is within the boundaries of the tiles, as 0.1 is between 0 and 0.6, as well as between -0.075 and 0.525, -0.15 and 0.45, and so on. Since x and y are equal for both the point therefore the point lies in the first tile for the first seven tilings.

Why is the point (0.1,0.1) in the 13th tile?
The 8th tiling has moved a full tile diagonally down so now its 13th tile is in the exact same spot as the first tile of the first tiling. -0.6/8*(8) = -0.6, which is a the length of a tile.

Why is the 13th tile in the 8th tiling 859?
7*121 + 13 - 1 = 859. The 8th tiling starts at 846 (7*121 - 1) then add 13 for the 13th tile.

Why is the largest possible index 967?
8*121 - 1 = 967. 8 tilings with 121 tiles each, starting at 0.

Why do the second and fourth examples produce very similar sets of indices?
The distance between the two points is very small so the only tiling that notices the difference is the 6th tile.