Figure eight (or less frequently, big beacon^{[1]} or lemniscate) is a period-8oscillator found by Simon Norton in 1970.^{[2]} With 12 cells in its smallest phase, it is the smallest known period 8 oscillator, ahead of blocker at 15 cells. It is known that no period 8 oscillators exist with 10 or fewer cells.^{[3]}
Producing a dominospark, it is useful for constructing larger oscillators with period that is a multiple of eight. For example, it appears in tumbling T-tetson (period 8), sailboat (period 16), caterer on figure eight (the smallest period-24 oscillator), and a p64 pi-heptomino hassler; the latter two are shown below in Gallery. It is also the key component in the p8 bouncer.
One of the phases of the oscillator, which led to both of its names
Construction
x = 11, y = 11, rule = B3/S23
b2o$o2bo$o2bo$b3o$9b2o$8b2o$10bo2$5bo$4b2o$4bobo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THEME Book ZOOM 12 GPS 10 AUTOSTART T 0 PAUSE 3 T 24 PAUSE 1 LOOP 25 ]]
A diagonally symmetric collision between two gliders and a teardrop, which costs two gliders, produces a figure eight cleanly, leading to its 4-glidersynthesis.
A four-object 21-cell one-glider seed for figure eight with bounding box 14 × 14 is known.^{[4]}
x = 46, y = 44, rule = B3/S23
34bo$34bobo$34b2o6$17bo$18b2o$17b2o$31bobo$31b2o$32bo5$40b3o$40b3o$40b
3o$43b3o$43b3o$43b3o15$3o$2bo$bo$4b2o$3bobo$5bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ HEIGHT 400 THEME Book ZOOM 10 X 4 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 88 PAUSE 2 LOOP 89 ]]
An alternate 5G synthesis^{[3]} (click above to open LifeViewer)
x = 30, y = 14, rule = B3/S23
bo9b2o$2bo7bo2bo$3o8bobo$12bo$24b2o$24b2obo$28bo$7b2o16bo$2o4bo2bo16bo
b2o$2o5b2o19b2o3$4b2o$4b2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ HEIGHT 400 THEME Book ZOOM 10 AUTOSTART GPS 12 T 0 PAUSE 3 T 56 PAUSE 2 LOOP 57 ]]
A 4-object 1G seed^{[4]} (click above to open LifeViewer)
↑The headerless RLEs of the two collisions are 2b2o$2b2o3$4b2o2b2o$2o2b2o2b2o2b2o$2o9b2o$13bo$7b2o$7b2o! and 3b2o$3b2o2b2o$7b2o4$bo5b2o$obo3bo2bo$obo4b2o$bo$9bo$8b2o$8bobo!