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 video by Numberphile as well as the extra video 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 the is number of pixels in every column of the image.

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 (size = 50), and Shift+Z to set it to maximum (size = 1500).

You can save the drawing by right-clicking and saving!

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. In fact, that is why the size has an upper limit.