Doppler effect

In the context of Life and other cellular automata, Doppler effect refers to several^[which?] 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).

Another example is gliders being reflected by a 2-engine Cordership; in the viewer below, the glider stream period is 64 toward the Cordership and 128 away from the Cordership.

x = 153, y = 121, rule = B3/S23 18bo$18bo$18bo8bo$25bobo$19b3obbo3bo$20bob5o$26bo$21boo15boo$38boo5$4b 3o$bb7o6bo$b9o4bo31boo$o7b3obboo31boo$b3o6bo3bobbo$bboo11b3o$5bo10bo 23bo$6bo31bo4bo$7bo29bo5bo$43bo10b3o$38bobbo12bo$39b3o13bo$33bo$31b4o$ 30b3oboobo$30boobbo$24bo5bo4bobbo$20bo4bo5bo3boobo$11boboo5bo3boo5bo$ 5boo4bo$5boo6bo5bo6boo$18b3ob7o$18booboo5bo$25boo$28bo$25bobbo41b3o$ 26bo43bo$13boo56bo$13boo13$86b3o$86bo$87bo14$102b3o$102bo$103bo14$118b 3o$118bo$119bo14$134b3o$134bo$135bo14$150b3o$150bo$151bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 16 THUMBSIZE 2 ]]

(click above to open LifeViewer)

External links

• Doppler effect at Wikipedia (name origin)