Over-unity reaction

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An over-unity reaction is a reaction that produces strictly more output signals than input signals. By implication, "over-unity" refers to the ratio of outputs to inputs. This is an important concept in gun and macro-spaceship construction.

Such a reaction involves some input signals (e.g. gliders) as well as an optional sustained reaction (usually a catalyst, sparker, hassled object, or reburnable fuse). An over-unity reaction can be made self-sustaining by connecting outputs to inputs.

In the stationary case, mechanisms (reflectors, conduits, etc.) can usually be added to produce a gun, where the excess signal(s) become the output stream(s). If all signal outputs must be used up to sustain a stationary reaction, it can lead to an emu instead, for instance the Simkin's p60.

In a macro-spaceship, the synchronized reactions between two or more active fuses produce additional output signals, for example the 31c/240 Herschel-pair climber. Here "over-unity" implies that cleaning up the reburnable reactions does not use up all of the outputs; there are leftovers to build the fuse-supporting track.

Glider duplicators and glider-emitting Herschel conduits can be considered degenerate examples of over-unity reactions (with one input and two or more outputs).

4g-to-5g reaction

In July 1992, Dieter Leithner found the following 4g-to-5g reaction where four gliders react to produce five gliders. The first two produce a traffic light and a glider, and then the other two react symmetrically with the evolving traffic light to form four gliders.

x = 65, y = 49, rule = B3/S23 obo$b2o$bo22$17bo$15bobo22bo$16b2o22bobo$40b2o19$63bo$62b2o$62bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 400 WIDTH 480 ZOOM 6 GPS 20 PAUSE 2 LOOP 256 THEME Book ]]
4g-to-5g over-unity reaction
(click above to open LifeViewer)
RLE: here Plaintext: here

It is the driving mechanism in the following (not optimized) period-132 glider gun. However, the long recovery time renders the mechanism of less practical value.

x = 303, y = 185, rule = B3/S23 68b2o5b2o$53b2o12bo2bobobobo$53bobo11b2o3bobo$49b5obo18bo$48bo2bo2b2o 7bo7b3o$48b3o4bo6bobo$50bo4b3o3bo2bo7b4o$50b2o2bo2bo4b2o12bo177b2o$50b ob5o14bo3bobo175bobo$50bobo17bobo2bobo169b2o4bo$51b2o17bobo3bo168bo2bo 2b2ob4o$71bo173b2obobobo4bo$248bobobob2o$248bob4o$249b2obo$252bobo$72b o179b3o7b2o$71b2o177b2obo8bo$71bobo176b2o8bobo$249b4o7b2o$248b2o2bo$ 247b2o5$207b2o41b2o$207bobo41bo$209bo4b2o32b3o$41bo163b4ob2o2bo2bo30bo $40bo164bo2bobobobob2o$40b3o165bobobobo$209b2obobo$213bo2$199b2o$200bo 7b2o70b2o$200bobo5b2o70bo$201b2o79bo$262b2o14b5o$263bo13bo$263bobo12b 3o$264b2o15bo$278b4o$273b2o3bo3b2o$83b2o126b2o60b2o4b3o2bo$83b2o126bo 69bob2o$201b2o9b3o50b2o14bo$202b2o10bo51b2o12b2o$105bo95bo63bo$104b2o$ 104bobo165b2o$216bo55bo$214b2o57b3o$67b2o14bo131b2o58bo$67b2o12b2ob2o$ 81b2o$2o5b2o71bobo3bo$bo5b2o224bo$bobo81bo148b2o10bo$2b2o78b3o148b2o9b 3o$6b2o74b2o159bo$5bobo3bo75b2o154b2o$6bo5b2o$11b2o$6bo79bo2bo$6bo82bo $88bo$4bo3bo69bo10b3o$2b3obob3o65b2o13bo116b2o23b2o$bo3b2o4bo65b2o129b 2o22bobo5b2o$bob2o2b2obobo219bo7b2o$2bo2b2o2b2obo218b2o$3b2o2b2obob2o 193b2o$5bo2bobobo2bo188bo4bo35bo$5b4ob2o2b2o182b2o4bo5bo30b2obobo$9bo 112bo74bo2bo3bob2ob2o29bobobobo$7bobo113bo69bo4bob2o35bo2bobobobob2o$ 7b2o112b3o68bo5bobo6bo16b2o11b4ob2o2bo2bo$192b3o2b3o7bo16b2o15bo4b2o$ 168b2o27bo10bo30bobo$169b2o38b2o28b2o$63b2o73bo29bo39bo$62bobo15b2o55b 2o70b2o$62bo6bo10b2o7b2o46bobo$61b2o6b3o17bo93bo77b2o$60bo11bo14bobo 91b2o77b4o15bo$60b3o8b2o14b2o93b2o75bobo2bo12b3o$63bo195b2o2bobo10bo$ 50bo11b2o200bobo9b2o$48b3o15bo136b2o61b2o$47bo21bo134bo60b3o5bo$47b2o 20b3ob3o8b2o115b3o60bobo5bobo$32b2o31bo3b5o2bo7b2o115bo62b2o6bob2o$33b o32bo4b2o4bo195bo$33bob2o7bo29bobo$34bo2bo7b2o24b2obo196bo$35b2o7b2o 26b3o9b2obo181b2o$50b2o21b3o8b2ob3o180b2o$50b2o23b2o13bo$75bo8b2ob3o$ 76b3o6bobo$60bo17bo6bobo136bo$59bo3b2o21bo9b2o127b2o$58bo5bo30b4o15bo 109b2o$57bob2o2bo30bobo2bo12b3o$53b2obobo3bo31b2o2bobo10bo116b2o$53b2o bo2b4obo34bobo9b2o98b2o15bobo$57bobo3bobo35b2o99b2o7b2o10bo6bo$53b2ob 2o2bo2bobo34b3o4bo47bo47bo8bo8b3o6b2o66b2o$54bobo2b2o3bo34bobo4bobo47b o3bo42bobo6b3o5bo11bo65bo$42b2o10bobo42b2o4bo2bo45b3o2bo44b2o5bo2bo5b 2o8b3o67bo$42b2o11bo50b2o51b3o33b2o14b2obo14bo50b2o14b5o$139b2o54bo33b 2o11bo38bo13bo$140b2o51bobo46b3o36bobo12b3o$139bo53b2o50bo36b2o15bo$ 183bobo21b2o35b2o50b4o$184b2o21b2o50b2o30b2o3bo3b2o$154bo29bo4b2o68bo 31b2o4b3o2bo$152b2o34bo2bo64b2obo39bob2o$153b2o33bobo64bo2bo40bo$189bo 7bo7bob2o47b2o40b2o$195b3o5b3ob2o37bo3bo$194bo7bo13b2o28bo3b2o2bo25b3o $195bo7b3ob2o8bo27bo6bo29bo7b2o$181bobo4b2o2bo2bo9bobo6b3o29b2ob2obo 28bo8bo$182b2o4b2o2bo12bobo6bo27b3o8bo37b3o$182bo9bobo11bo21b2o3bo9b2o 4b2obo40bo$91bobo28b2o69bobo32bo3bobo9bob3o2bo$91b2o29bobo70bo33bo3bob o10bo$92bo29bo72b2o33bo3bobob2o8bobo$228bob4o2bob2o8bobo$227bobo3bobo 12b3o$227bobo2bo2b2ob2o$228bo3b2o2bobo$236bobo10b2o$237bo11b2o5$132b2o $125b2o4bo2bo$124bo2bo4bobo$127bo5bo$59b2o66bo$60bo45b2o13bo3bobo9b2o 19bo$60bobo44b2o11bo3bobo10bo19bo$61b2o43bo13bo4bo12b3o16b3o$121b4o15b o2$65b2o$64bo2bo$65bobo$66bo2$247b3o$249bo$62b4o10bo137bobo31bo$61bo4b o10bo137b2o$60bobo3bo8b3o137bo$59bobo3bo$59bo$59bo$59bo2bo$60b2o4$243b 2o$85b2o157bo$84bo2bo4b2o148bo$84bobo5b2o146b4o$85bo153bo4bo$238bob5o$ 80b2o9b3o144bobobo2b2o$81bo9b2obo2b2o127b2o9b2o2bob2o2bo$78b3o12b2o2b 2o127b2o2b2o4bo3b2o2bob2o$78bo14b2o135bobo3b2obobo2bo$125bo105bo4bo4bo b2o$124bo112b2obobo$124b3o101b2o8bobobo$229bo8bo2bo$226b3o10b2o$226bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 800 WIDTH 1250 ZOOM 4 GPS 55 LOOP 132 ]]
Period-132 glider gun driven by 4g-to-5g reaction
(click above to open LifeViewer)
RLE: here Plaintext: here

Other glider collisions

There are other 4-glider collisions that can also yield 5 output gliders. In 2019, Paul Callahan found the following reaction:[1]

x = 67, y = 65, rule = B3/S23 2$60bobo$60b2o$61bo42$18b2o$17bobo$19bo3$25b3o$25bo$26bo5$6b2o$5bobo$ 7bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 600 WIDTH 480 ZOOM 6 GPS 20 PAUSE 2 LOOP 300 THEME Book ]]
Another 4g-to-5g reaction
(click above to open LifeViewer)
RLE: here Plaintext: here

There is also a 4g-to-6g reaction:

x = 89, y = 66, rule = B3/S23 obo$b2o$bo18$39bo$37bobo$38b2o37$86bobo$87b2o$87bo2$85b2o$84b2o$86bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 600 WIDTH 480 ZOOM 4 X 28 Y 35 GPS 60 PAUSE 2 LOOP 380 THEME Book ]]
4g-to-6g reaction
(click above to open LifeViewer)
RLE: here Plaintext: here

References

  1. Paul Callahan (February 27, 2019). Re: Refactoring DRH's cyclotron with stable components? (discussion thread) at the ConwayLife.com forums

External links