Period multiplier

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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.

Reactions have also been found to period double or period triple the output of some rakes to create high-period rakes in a relatively small space (i.e., an exponential increase in period for a linear increase in size).

For Herschel signals and glider guns, a number of small period doubler, tripler, and quadrupler mechanisms are known. For example, the following conduit produces one output glider after accepting four input B-heptominoes, or four Herschels if a conduit such as F117 is prepended that includes the same BFx59H converter.

#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 4x period multiplier.
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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 4x period multiplier.
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RLE: here Plaintext: here
x = 60, y = 35, rule = B3/S23 52bo$50b3o$49bo$49b2o$37bo$37b3o$40bo$39b2o$8bo$7bobo$8bo44b2o$53b2o$ 6b5o$5bo4bo$4bo2bo$bo2bob2o13b2o$obobo5bo10b2o$bo2bo4bobo$4b2o2bo2bo$ 9b2o$58b2o$28bob2o26b2o$26b3ob2o$26bo$26bo$9bo$9bobo$9b3o43b2o$11bo43b o$56bo$55b2o3$21b2o$21b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 640 HEIGHT 640 ]]
An Fx70 4x period multiplier.
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RLE: here Plaintext: here

Also see the L156 for a period-doubling variant of that conduit.

See semi-Snark and tremi-Snark for additional examples using glider streams. As of March 2019 no stable period-multiplying elementary conduits are known for a multiplication factor of five or higher, though it is easy to construct composite ones.

External links