The *Shift* tab allows one to vary the spacing
between tiles. With the default parameters, rectangular tiles
are arranged so that their *Geometric* *bounding boxes*
are touching. The following options are available to add or subtract
space between the tiles:

*Shift X*,*Shift Y*: Adds (or subtracts) to the tile spacing in units of*bounding box*width and height. A random factor can also be added.*Exponent*: Changes the exponent factor*z*so that position of each tile is*x*(or*y*) = (1 + “shift”)^{z}.*Alternate*: The shift alternates between being added and subtracted.*Cumulate*: The previous shift is added to the new shift. For example, if there was a*Shift X*of 10%, normally the space between subsequent tiles would be 10%, 20%, 30%, and so on. With this option, the shifts become 10%, (10+20)% (10+20+30)%, etc. This is useful when one is also scaling the tiles to keep the tile spacing constant. (See the*Scale Tab*section for an example.)*Exclude tile*: The tile width or height is excluded in the calculation of tile spacing. This is useful when using the*Rotation*option to put tiles on a circle. In this case, it is a shortcut for specifying a −100% shift.

Question: What is the symmetry of closely packed hexagons? The answer is P1 as can be seen below. One can use this fact to trivially generate the board for the game Hex invented independently by the mathematicians Piet Hein and John Nash.

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