Period multiplier

Period multiplier is a term commonly 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 that are not strictly periodic.

For Herschel signals and glider guns, a number of small stable period doubler, tripler, and quadrupler 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 640 ]] An NW31 4× period multiplier. (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 640 ]] An L112 4× period multiplier. (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 640 ]] An Fx70 4× period multiplier requiring a subsequent dependent conduit. (click above to open LifeViewer) RLE: here Plaintext: here

Additional examples for glider streams are semi-Snark, tremi-Snark, quadri-Snark, and crystal-based devices requiring same input parity. As of August 2021 no fully stable period-multiplying elementary conduits are known for a multiplication factor of five or higher, though it is easy to construct composite ones.

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.

See also

• Filter
• Toggle circuit

External links

• Period multiplier at the Life Lexicon

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