Doppler effect

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Revision as of 13:40, 15 October 2023 by HotdogPi (talk | contribs) (partial revert — the first sentence is generic (not solely CA), and there's still a Doppler effect if they're moving away from each other (and even in a CA context, this can occur with rakes))
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The Doppler effect refers to several phenomena regarding the relative motion of two objects, moving with different velocities.

In Conway's Game of Life

An example of how the Doppler effect applies to Life is in this viewer below, where a crabstretcher moves forward at c/4, while the fuse behind burns at c/3.

x = 21, y = 17, rule = B3/S23 11b2o$12b2o$11bo$8b2o$10bo2$8bo2bo$6bobo2b2o5b2o$5bobo5bo5b2o$4bobo4bo bo4bo$3bobo6bo2b2o$2bobo10b2o$2b2o$bo$bo$o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 8 THUMBSIZE 2 ZOOM 14 ]]
(click above to open LifeViewer)

The net contraction is 1/3 - 1/4 = 1/12, i.e., 1/3 the rate of the crab and 1/4 the rate of the fuse. The crab and fuse will get one cell closer every 12 generations. As the crab is period 4 and the fuse is period 3, they'll both match phase every 12 generations. Because both numbers are 12, this means that what happens when the fuse hits the crab is independent of timing, and it will always be the same (in this case, the crab survives while the fuse becomes an E-heptomino relative).

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