Period multiplier

A period multiplier is a conduit that can accept an uniformly spaced period-p stream (typically consisting of gliders, spaceships or Herschels) and produce an output stream with period pn, for some positive integer n > 1.

The term "period multiplier" is often used for a pulse divider, because dividing the number of signals in a regular stream by n necessarily multiplies the period by n. The term "period multiplier" can be somewhat misleading in this context, because most such circuits can accept input streams where the signals are not uniformly spaced.

For Herschel signals and glider guns, a number of small stable 2×, 3×, and 4× pulse-dividing mechanisms are known. For example, the first one of the following conduits produces one output glider after accepting four input Herschels from B-heptominoes passing a BFx59H converter. For a period-doubling conduit, see L156.

#C Period multiplier example based on NW31 x = 44, y = 29, rule = B3/S23 19bo$19b3o$22bo$11b2o8b2o$12bo$12bobo$b2o10b2o$2bo$bo$b2o3$42b2o$42b2o 2$o3b2o$2o2b2o$b2o$2o9$32b2o$32b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 640 HEIGHT 500 ]] An NW31 4× pulse divider (click above to open LifeViewer) RLE: here Plaintext: here

x = 43, y = 49, rule = B3/S23 34b2o$34bo$32b3o16$32b2o$23b2o7b2o$24bo$24bobo$19b2o4b2o$b2o17bo20b2o$ 2bo17bobo18bo$bo19b2o16bobo$b2o36b2o6$o3b2o$2o2b2o$b2o$2o2$35b2o$35bo$ 36b3o$38bo5$21b2o$22bo$21bo$21b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 640 HEIGHT 500 ZOOM 8 ]] An L112 4× pulse divider (click above to open LifeViewer) RLE: here Plaintext: here

x = 44, y = 27, rule = B3/S23 20bo$19bobo$20bo2$18b5o$17bo4bo$16bo2bo$13bo2bob2o13b2o$b2o9bobobo5bo 10b2o$2bo10bo2bo4bobo$bo14b2o2bo2bo$b2o18b2o2$40bob2o$38b3ob2o$38bo$ 38bo$o3b2o$2o2b2o$b2o$2o5$33b2o$33b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 640 HEIGHT 500 ]] An Fx70 4× pulse divider requiring a subsequent dependent conduit. It can be turned to a non-period multiplying conduit with Jubjub reflector. (click above to open LifeViewer) RLE: here Plaintext: here

Additional examples for glider streams are semi-Snark, tremi-Snark, quadri-Snark, unnamed x5 reflector, unnamed x12 reflector, unnamed x11 and x(6n+4) reflectors, and crystal-based devices requiring same input parity. As of October 2023, stable and elementary reactions have also been found to double or triple the output period of some rakes in a relatively small space, enabling an exponential increase in period for a linear increase in size.

"Period multiplication" may also refer to a technique of producing a stream of period pn from two or more input streams with periods p (i.e. colliding glider streams), or a way of stabilizing an engine so that the period of the reaction is multiplied by a positive integer n > 1, for example the usage of a half-bakery/Ship-tie to restore a ship.

x = 34, y = 23, rule = B3/S23 4b2o13b2o$3bobo10bo2bobo$3b2o9b3o5bo2b2o$b2o10bo6b2obo2bo$obo10b2o4bo bob2o$2o4b2o12bo$5bobo22b2o$5b2o23bo$10b3o8b3o4bobo$9bo3bo6bo3bo3b2o$ 8bo5bo4bo5bo$8bo5bo4bo5bo$8bo5bo4bo5bo$4b2o3bo3bo6bo3bo$3bobo4b3o8b3o $3bo23b2o$2b2o22bobo$13bo12b2o4b2o$9b2obobo4b2o10bobo$7bo2bob2o6bo10b 2o$7b2o2bo5b3o9b2o$12bobo2bo10bobo$13b2o13b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 HEIGHT 480 WIDTH 480 GPS 19 THEME Book AUTOSTART STARTFROM 38 ]]

p38, found by Period1GliderGun on February 22, 2024, based on a partial by iNoMed. The honey farm regions oscillate with period 19, but this stabilization doubles the period. Nevertheless, a variant, Goban is known that is period-19. (click above to open LifeViewer) RLE: here Plaintext: here

See also

• Pulse divider
• Filter
• Toggle circuit
• LCM oscillator

External links

• Period multiplier at the Life Lexicon
• I'm looking for period multiplicating Herschel Tracks. (discussion thread) at the ConwayLife.com forums
• "period multiplier". ConwayLife.com.