c/4 orthogonal

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c/4 orthogonal
46p4h1v0.png
Spaceship Yes
Puffer Yes
Rake Yes
Wickstretcher Yes
Gun Yes

c/4 orthogonal is an orthogonal speed that is equivalent to one fourth of the speed of light.

Spaceships

See also category Spaceships with speed c/4

The first c/4 orthogonal spaceship, 119P4H1V0, was discovered by Dean Hickerson in December 1989. Hickerson then found a small tagalong for this spaceship which could be attached in two different ways. These three spaceships were the only known c/4 orthogonal spaceships until Hartmut Holzwart discovered 163P4H1V0 (shown below) in July 1992. The searches conducted by Holzwart also turned up the first method of creating arbitrarily large c/4 orthogonal spaceships by repeatedly attaching a tagalong to the back of 103P4H1V0 (shown below). Holzwart also found the first orthogonal non-monotonic spaceship, non-monotonic spaceship 1, during this search. In May 1996 Tim Coe discovered 46P4H1V0, which was the smallest known spaceship of this speed until April 2012, when Josh Ball discovered 37P4H1V0. From February to March 2006, Hartmut Holzwart found several ways to create c/4 orthogonal greyships (one shown below).

x = 40, y = 17, rule = B3/S23 20bo$7b2o8b4o8b2o$7bo2b3o2b4o5b4obo$6bo7b2o2bo4bo7bo5bo$5b4obobo3bo2bo 4b2o4b4obo2b2o$5b2o8bo2b2obo2bo2bobobob3o$4bo10b2obo9bo2bo$b3obo5bobo 5bobob3o6b2o$o2bo7bo9bob3o$b3obo5bobo5bobob3o6b2o$4bo10b2obo9bo2bo$5b 2o8bo2b2obo2bo2bobobob3o$5b4obobo3bo2bo4b2o4b4obo2b2o$6bo7b2o2bo4bo7bo 5bo$7bo2b3o2b4o5b4obo$7b2o8b4o8b2o$20bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]
163P4H1V0 discovered by Hartmut Holzwart in 1992
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 27, y = 15, rule = B3/S23 10b2o$5b3o2b3o$7bo2b2obobo4bo$5b2o5b3o6bo$b2o2bo2b3obo3b4obo4bo$2ob2o 5bo4b2o3b3obobo$bo3bo9bo8bobo$2o3bo$bo3bo9bo8bobo$2ob2o5bo4b2o3b3obobo $b2o2bo2b3obo3b4obo4bo$5b2o5b3o6bo$7bo2b2obobo4bo$5b3o2b3o$10b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]
103P4H1V0: repeatedly attaching a tagalong can produce arbitrarily large c/4 orthogonal spaceships
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 177, y = 183, rule = B3/S23 6bo$5bobo$7bo$4b2o$3b3o$2b2o3bo$6bobo$4bo2b2o$5b2o$5bo2$6b2o$bobobo2bo 33bo$bo3b3obo30b4o$bobob2o33b4o$6b2o28bo2b2o$8bo27b2o$5bo2bo27bo3b2o$ 4bo34b3o$3b3o34b2o$2bo3b2o31b2o2bo$40b2o$3b2o$5bobo32b2o$7bo31b2o2bo$ 6bo33b2o$7b4o25b3ob2o$11bo19bo9bo4b2o$30bo3bo4bo5b2o$8b2o7bo11b2o3b3o 2b7o2bo$8b2o2bobobobo5b2o2bobo14bo3bo2b2o$8b2o3b2obobo4b3o2b2ob14ob2ob o2bobo$9b2o2bo2bob2o2bo7bo18bo2b2o$14b2ob3o3bobo3b21o2bo$19bo2b2o30bo 2b2o$20b3ob29ob3o2bo$24bo29b4o$25b30o2bo$57bobob3o$25b32o$24bo37b2o$ 17b4obob36o2bo4bo$17bo2b4o38b2o3bo$24b38o4bo$17b3o43bo3b2o$24b40o2bo$ 17bo2b4o43b2o2b2o$17b4obob43obo2bobo$24bo43bo2b2o$25b44o2bo$73bo2b2o$ 25b47ob3o2bo$24bo48b4o$17b4obob50o2bo$17bo2b4o52bobob3o$24b52o$17b3o 61b2o$24b55o2bo4bo$17bo2b4o57b2o3bo$17b4obob57o4bo$24bo57bo3b2o$25b58o 2bo$86b2o2b2o$25b61obo2bobo$20b2o2bo62bo2b2o$14b2o3bob3ob63o2bo$9b3o2b 4o4b2o68bo2b2o$11bo2b4o3b3ob66ob3o2bo$9b2o5b2o6bo67b4o$5b2o2bo2b3o4bob o4b67o2bo$4b2ob2o5bo3bo2bo3bo69bobob3o$5bo3bo8bo2bo4b69o$4b2o3bo90b2o$ 5bo3bo8bo2bo4b72o2bo4bo$4b2ob2o5bo3bo2bo3bo74b2o3bo$5b2o2bo2b3o4bobo4b 74o4bo$9b2o5b2o6bo76bo3b2o$11bo2b4o3b3ob77o2bo$9b3o2b4o4b2o81b2o2b2o$ 14b2o3bob3ob80obo2bobo30bobo$20b2o2bo81bo2b2o29b2o3b2o$25b82o2bo30bobo $111bo2b2o26bo$25b85ob3o2bo22bo15bobo$20b2o2bo86b4o24b2o3bo8b2o3b2o$ 14b2o3bob3ob87o2bo30bo7bobo$9b3o2b4o4b2o90bobob3o21b2ob2o8bo$11bo2b4o 3b3ob89o29bob2o5bo$9b2o5b2o6bo94b2o21b2obo6b2o3bo$5b2o2bo2b3o4bobo4b 91o2bo4bo20bo12bo$4b2ob2o5bo3bo2bo3bo93b2o3bo16bo2bo10b2ob2o$5bo3bo8bo 2bo4b93o4bo17bo2b2o10bob2o$4b2o3bo110bo3b2o16b2o11b2obo$5bo3bo8bo2bo4b 95o2bo34bo$4b2ob2o5bo3bo2bo3bo98b2o2b2o24bo2bo$5b2o2bo2b3o4bobo4b98obo 2bobo9b3o11bo2b2o$9b2o5b2o6bo100bo2b2o12b3o10b2o$11bo2b4o3b3ob101o2bo 12bobo$9b3o2b4o4b2o106bo2b2o6bobo$14b2o3bob3ob104ob3o2bo5b2o10b3o$20b 2o2bo105b4o8bo12b3o$25b106o2bo20bobo$133bob2o2b2ob2o10bobo$25b108o6b2o 13b2o$24bo114b2o14bo$17b4obob112o4b2o$17bo2b4o113bobob2o9b2ob2o$24b 115o2bo10b2o$17b3o123bo2b2o4b2o$24b117o2bo2b2o5b2o$17bo2b4o120bo5bobob 2o14bobo$17b4obob128o2bo12b6o2b2o$24bo131bo2b2o4b4o5bo$25b129o2bo2b2o 4b2obobo$157bo5bo2bo$25b140o$24bo$17b4obob141o$17bo2b4o133bo5bo2bo$24b 130o2bo2b2o4b2obobo$17b3o136bo2b2o4b4o5bo$24b128o2bo12b6o2b2o$17bo2b4o 120bo5bobob2o14bobo$17b4obob117o2bo2b2o5b2o$24bo118bo2b2o4b2o$25b114o 2bo10b2o$35bo16bo16bo16bo16bo16bo16bobob2o9b2ob2o$8bobo14b6obo3b12obo 3b12obo3b12obo3b12obo3b12obo3b12obo5b2o$7bo2bo13bobo4b2o3bo2bo3bo4b2o 3bo2bo3bo4b2o3bo2bo3bo4b2o3bo2bo3bo4b2o3bo2bo3bo4b2o3bo2bo3bo4b2o4b2o 14bo$2b2obo2bo10b3ob2o3bo6b3o2bo4bo6b3o2bo4bo6b3o2bo4bo6b3o2bo4bo6b3o 2bo4bo6b3o2bo4bo8b2o13b2o$o4bo3b2o3bo4b2ob2o4b2o5bo5b2o2b2o5bo5b2o2b2o 5bo5b2o2b2o5bo5b2o2b2o5bo5b2o2b2o5bo5b2o2b2o7b2ob2o10bobo$o12bobo7b2o 129bobo$obob2o5bo9b3o11bobo14bobo14bobo14bobo14bobo14bobo19bo12b3o$3b 2o7b2ob2o3b2o12bo2bo13bo2bo13bo2bo13bo2bo13bo2bo13bo2bo18b2o10b3o$5b2o 5bo3b2ob3o11b3o14b3o14b3o14b3o14b3o14b3o20bobo$18b3o120bobo$18bo14b2o 15b2o15b2o15b2o15b2o15b2o22b3o10b2o$33b3o14b3o14b3o14b3o14b3o14b3o19b 3o11bo2b2o$30b2o15b2o15b2o15b2o15b2o15b2o37bo2bo$30bobo14bobo14bobo14b obo14bobo14bobo40bo$30bobo14bobo14bobo14bobo14bobo14bobo24b2o11b2obo$ 32b2o15b2o15b2o15b2o15b2o15b2o22bo2b2o10bob2o$29b2ob2o12b2ob2o12b2ob2o 12b2ob2o12b2ob2o12b2ob2o22bo2bo10b2ob2o$28b3obo12b3obo12b3obo12b3obo 12b3obo12b3obo27bo12bo$29bobo2bo11bobo2bo11bobo2bo11bobo2bo11bobo2bo 11bobo2bo22b2obo6b2o3bo$28b3ob2obo9b3ob2obo9b3ob2obo9b3ob2obo9b3ob2obo 9b3ob2obo22bob2o5bo$33bo16bo16bo16bo16bo16bo23b2ob2o8bo$27b2ob2obo10b 2ob2obo10b2ob2obo10b2ob2obo10b2ob2obo10b2ob2obo26bo7bobo$27b2o2bob2o9b 2o2bob2o9b2o2bob2o9b2o2bob2o9b2o2bob2o9b2o2bob2o19b2o3bo8b2o3b2o$28bob 2ob2o10bob2ob2o10bob2ob2o10bob2ob2o10bob2ob2o10bob2ob2o19bo15bobo$28bo b2o13bob2o13bob2o13bob2o13bob2o13bob2o25bo$27b2ob2o12b2ob2o12b2ob2o12b 2ob2o12b2ob2o12b2ob2o23bobo$29bo16bo16bo16bo16bo16bo25b2o3b2o$29bo16bo 16bo16bo16bo16bo27bobo$30bo3bobo10bo3bobo10bo3bobo10bo3bobo10bo3bobo 10bo3bobo$28bo2bo13bo2bo13bo2bo13bo2bo13bo2bo13bo2bo$27bo3bobo2bo7bo3b obo2bo7bo3bobo2bo7bo3bobo2bo7bo3bobo2bo7bo3bobo2bo$28bo5b2o9bo5b2o9bo 5b2o9bo5b2o9bo5b2o9bo5b2o$29b2obo13b2obo13b2obo13b2obo13b2obo13b2obo$ 34bobo14bobo14bobo14bobo14bobo14bobo$33bo16bo16bo16bo16bo16bo$28bo3b2o 2bo8bo3b2o2bo8bo3b2o2bo8bo3b2o2bo8bo3b2o2bo8bo3b2o2bo$28bo4b2o10bo4b2o 10bo4b2o10bo4b2o10bo4b2o10bo4b2o$27b2o2bo12b2o2bo12b2o2bo12b2o2bo12b2o 2bo12b2o2bo$28bob2o13bob2o13bob2o13bob2o13bob2o13bob2o$28bob2o13bob2o 13bob2o13bob2o13bob2o13bob2o$28bob2o13bob2o13bob2o13bob2o13bob2o13bob 2o$27b2o2bo12b2o2bo12b2o2bo12b2o2bo12b2o2bo12b2o2bo$28bo16bo16bo16bo 16bo16bo$28bo3b2o11bo3b2o11bo3b2o11bo3b2o11bo3b2o11bo3b2o$32b2o15b2o 15b2o15b2o15b2o15b2o$33bo2bo13bo2bo13bo2bo13bo2bo13bo2bo13bo2bo2$33bob 2o13bob2o13bob2o13bob2o13bob2o13bob2o$33bo3bo12bo3bo12bo3bo12bo3bo12bo 3bo12bo3bo$33b3o14b3o14b3o14b3o14b3o14b3o$34b2obo13b2obo13b2obo13b2obo 13b2obo13b2obo2$36bo16bo16bo16bo16bo16bo$36bo16bo16bo16bo16bo16bo$34b 2o15b2o15b2o15b2o15b2o15b2o$35bobo14bobo14bobo14bobo14bobo14bobo$36bo 16bo16bo16bo16bo16bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 2 ]]
A greyship created by Hartmut Holzwart using several methods of stabilization
(click above to open LifeViewer)
RLE: here Plaintext: here

The first higher period c/4 orthogonal spaceship was discovered by David Bell in September 2000. It had a period of 20 and consisted of a block puffer found by Jason Summers and a side sparker used to delete the blocks. In the following month Summers found period 8 and 12 spaceships based off of a failed blinker puffer and a spaceship with a forward domino spark. Several other periods were achieved by perturbing the output of a period 168 puffer discovered by Paul Tooke in November 2003.

Puffers

Jason Summers found the first c/4 orthogonal puffer, which had period 9732 and was extremely dirty, in January 1999. In November 2003 Paul Tooke discovered a versatile period 168 puffer the output of which could be perturbed by sparkers to produce puffers of lower periods.

Rakes

The lowest period c/4 orthogonal rakes are based on Paul Tooke's p168 puffer. A method of rake construction is also known for all periods above about 800.

Wickstretchers

c/4 orthogonal was the first speed known to contain a wickstretcher, wickstretcher 1. It was discovered by Hartmut Holzwart in October 1992 and stretched ants from an ant stabilizer found by Dean Hickerson.

Guns

The first c/4 orthogonal spaceship for which a complete glider synthesis was found was 46P4H1V0 by Tanner Jacobi and Martin Grant on February 4, 2019 with 105 gliders.[1] This was later reduced to 88 gliders with a repeat time of 572 ticks due to optimizations by various people.[2] Goldtiger997 constructed a 46P4H1V0 gun based on this optimized synthesis on October 22.[3]

Waves

The following is an example of a c/4 orthogonal wave that can be supported by various spaceships. This one was found by Bullet51 on March 19, 2016:[4]

4bo$3bobo$2bo4bo6bo$3o4bo5bobo$2o2b2obo4bo4bo6bo$2o4bo3b3o4bo5bobo$5bo 4b2o2b2obo4bo4bo6bo$6bo3b2o4bo3b3o4bo5bobo$15bo4b2o2b2obo4bo4bo6bo69bo $16bo3b2o4bo3b3o4bo5bobo67b3o$25bo4b2o2b2obo4bo4bo6bo58b3o$26bo3b2o4bo 3b3o4bo5bobo59bo$35bo4b2o2b2obo4bo4bo6bo47b4o$36bo3b2o4bo3b3o4bo5bobo 45bobob2o$45bo4b2o2b2obo4bo4bo6bo36bo$46bo3b2o4bo3b3o4bo5bobo36bo$55bo 4b2o2b2obo4bo4bo6bo31b3o$56bo3b2o4bo3b3o4bo5bobo30b3o$65bo4b2o2b2obo4b o4bo6bo20bobo$66bo3b2o4bo3b3o4bo5bobo16bobo$75bo4b2o2b2obo4bo4bo6bo7bo $76bo3b2o4bo3b3o4bo5bobo5bo2bo$85bo4b2o2b2obo4bo4bo5b2o$86bo3b2o4bo3b 3o4bo4b3o$95bo4b2o2b2obo$96bo3b2o4bo3bobo$105bo4bo$106bo3b2o3bo$111bo 3b2o$112bo3bo$112bobo$115bo$113bo2b2o$113bo4bo$118bo$115b2o$116bo$116b o2bo$115bo2bo2$114bo3bo$114b2ob2o3$115b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ TRACKLOOP 4 0 -1/4 THUMBSIZE 2 GPS 4 HEIGHT 480 WIDTH 480 THUMBSIZE 2 ]]
A c/4 orthogonal wave
(click above to open LifeViewer)
RLE: here Plaintext: here


See also

References

  1. Martin Grant (February 4, 2019). Re: Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
  2. Matthias Merzenich (February 10, 2019). Re: Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
  3. Goldtiger997 (October 22, 2019). Re: Stable signal converters (discussion thread) at the ConwayLife.com forums
  4. Bullet51 (March 19, 2016). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums

External links