http://gosper.org/jaggies.png is a 4x blowup of a detail of a Golly (Game of Life) screen, where each pixel is 2^24 x 2^24 cells. The diagonal line marked by arrows is a row of equally spaced gliders, (dx,dy) = (14412108,16685960). The gap at the green arrow is a legitimately missing glider, but every other dot on that line represents one glider. I.e., Golly darkens a pixel iff there's anything in the 2^24 square it represents. Note that dy>dx. Puzzle: How can the nonmonotonicity at the black arrow be anything but a display bug? (Does anybody remember BRMs and DDAs?) --rwg
What about the too-thick line in the upper left? Did that contain two lines of gliders close together? On 9/18/07, R. William Gosper <rwg@osots.com> wrote:
http://gosper.org/jaggies.png is a 4x blowup of a detail of a Golly (Game of Life) screen, where each pixel is 2^24 x 2^24 cells. The diagonal line marked by arrows is a row of equally spaced gliders, (dx,dy) = (14412108,16685960). The gap at the green arrow is a legitimately missing glider, but every other dot on that line represents one glider. I.e., Golly darkens a pixel iff there's anything in the 2^24 square it represents. Note that dy>dx. Puzzle: How can the nonmonotonicity at the black arrow be anything but a display bug? (Does anybody remember BRMs and DDAs?) --rwg
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MikeS>What about the too-thick line in the upper left? Did that contain two >lines of gliders close together? Heck no. It's a complicated pattern about 2000 times denser. The next one down is almost what you describe--close pairs at about the density of the line under discussion. For a false bug, I should have exhibited an enormous perfect diagonal elsewhere in the picture (dx=-dy), which has one "extra, out of place" dot. --rwg
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Mike Stay -
R. William Gosper