Information

This tool displays chessboard when knight(-like) pieces are placed on an Ulam spiral such that no piece is threatened by a previously placed piece. See the corresponding by Numberphile, the extra video, and A392177 on OEIS for more details.

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A knight with Δx = Δy = 0 is disregarded from the drawing; it will never be placed on the board. Note that exchanging Δx and Δy will not change the knight's behaviour (due to symmetry).

The Size of the drawing is the number of steps the spiral is built off. However, the drawn image will use the next smallest integer such that the spiral makes up a rectangle.

Hold shift and (mouse) scroll on the image to zoom and in about. The size may also be changed using the Size input above. By default, any change will redraw the image; this behaviour can be changed by ticking off the Auto Draw checkbox

Press R to reset all settings to their default values. Press Z to set the zoom to minimum.

Save the drawing by right-clicking and saving!

Click on the ↓ buttons beside every knight to download their corresponding sequence up to the given size in the Size input. The ↓ beside the Empty Cells downloads the sequence of the empty (unoccupied) cells. These sequences are the numbers on the spiral that the knight (or no one if empty) occupies, starting from 0. For example, using the default settings, Knight 1's sequence is A392177; Knight 2's sequence is A392178; and A392179 is the empty's cells.

Note: That two pieces have the same colour does not imply that they do not threaten each other. Instead, it simply means that the piece's cells will be coloured with the given colour; it is the knight's number that indicate which "team" it belongs to.

Warning: Larger sizes take longer to draw. Therefore, it is recommended that you disable Auto Draw when you want to draw larger checkboards to avoid redrawing on every update.