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I was bored one day, staring at a window, and I started imagining a continuous series of diagonals, going across the panes of the window. It reminded me of the path a pool ball would make, if you shot it from one corner at a 45° angle.
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I always start the path in the upper left corner, and travel at a 45° diagonal across the grid.
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If the path hits an edge of the outer rectangle, it bounces off at a 45° angle and continues its travel.
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The path continues in this way until it hits a corner of the outer rectangle (where a corner pocket would be on a pool table).
Here are the paths generated by some of the windows in my house:
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the 2x3 window

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the 3x4 window

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the 4x6 window

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the 6x8 window

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