OCA:Star Wars

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Star Wars
Star Wars rule
Rulestring 345/2/4
B2/S345/C4
B2/S345/G4
Character Explosive

Star Wars, also known as MirekGro, is a Generations rule devised by Mirek Wójtowicz in March 1999. In this rule, a state-0 cell will become state 1 iff it has two state-1 neighbours. A state-1 cell does not change if it has 3, 4 or 5 state-1 neighbours, otherwise it will enter state 2 next tick and then state 3 before dying.

Named after its behaviour that resembles deep space battle scenes, the rule can be described as follows:

A collection of patterns in Star Wars rule is in Mirek's Cellebration. The rule can also run in modern simulators (e.g. Golly and LifeViewer) that support Generations rules.

Patterns

x = 100, y = 79, rule = 345/2/4 98.A$97.3A$98.A$98.A$98.2A$98.A$2.A5.A5.A5.A10.A5.A5.A11.A2.A2.A6.A2. A2.A6.A10.A5.A$.3A3.3A3.3A3.3A8.3A3.3A3.3A9.9A4.9A4.3A8.3A4.2A$2.A5.A 5.A5.A10.A5.A5.A11.A5.A6.A5.A6.A10.A5.A$8.A5.A5.A10.A5.A5.A11.A5.A6.A 5.A6.A10.A5.A$7.3A3.3A3.3A9.2A4.2A4.2A9.2A5.2A4.2A5.2A4.2A9.2A5.2A$8. A5.A5.A10.A5.A5.A11.A5.A6.2A4.A6.2A9.2A4.A$14.A5.A10.A5.A5.A11.A5.A7. 2A3.A7.2A3.A5.2A3.A$13.3A3.3A8.3A4.2A4.2A9.9A7.6A7.6A5.6A$14.A5.A10.A 5.A5.A11.A2.A2.A9.A2.A9.A2.A7.A2.A$20.A16.A5.A$19.3A14.3A4.2A$20.A16. A5.A$43.A$42.3A$43.A4$61.A2.A2.A$60.9A$59.2A3.A3.2A$2.A2.A6.A2.A6.A2. A6.A2.A2.A6.A2.A2.A6.2A9.2A$.6A4.6A4.6A4.9A4.9A4.2A11.2A$2.A2.A6.A2.A 6.A2.A6.A2.A2.A6.2A3.2A6.A11.A$2.A2.A6.A2.A6.A2.A6.A2.A2.A6.A5.A6.A 11.A$.6A5.4A5.6A4.9A4.2A5.2A4.3A9.3A$2.A2.A6.A2.A6.A2.A6.A2.A2.A6.A5. A6.A11.A$12.A2.A6.A2.A6.A2.A2.A6.2A3.2A6.A11.A$11.6A4.6A4.9A4.9A4.2A 11.2A$12.A2.A6.A2.A6.A2.A2.A6.A2.A2.A6.2A9.2A$59.2A3.A3.2A$60.9A$61.A 2.A2.A5$2.A4.A7.A11.A$.3A2.3A5.3A9.3A$2.A.2A.A7.A11.A3.A$2.A.2A.A7.3A 9.6A39.A20.A$.3A2.3A5.2A.2A6.A.A.A.A39.24A$2.A4.A7.3A6.6A42.A.18A.A$ 16.A8.A3.A42.2A18.2A$28.3A41.2A18.2A$29.A42.2A18.2A$72.2A18.2A$72.2A 18.2A$72.2A18.2A$72.2A18.2A$54.A2.A14.2A18.2A$31.A10.A10.6A13.2A18.2A $11.A9.A8.3A8.3A8.2A3.A14.2A18.2A$3.A6.3A7.3A6.2A.2A6.2A.2A6.2A4.A14. 2A18.2A$2.3A4.2A.2A5.2A.2A4.2A.A.2A4.2A.A.2A4.2A5.2A13.2A18.2A$.3A6. 3A5.2A.2A6.2A.2A4.2A.A.2A6.A4.2A14.2A18.2A$2.A8.A7.3A8.3A6.2A.2A7.A3. 2A15.2A18.2A$20.A10.A8.3A7.6A16.2A18.2A$41.A9.A2.A17.2A18.2A$72.2A18. 2A$72.2A18.2A$72.A.18A.A$71.24A$72.A20.A2$2.A11.A9.A11.A10.A11.A$.15A 7.15A8.15A$2A.A.A.A.A.A.A.2A5.2A.A.A.A.A.A.A.2A6.2A.A.A.A.A.A.A.2A$. 2A.A.A.A.A.A.2A5.2A.A.A.A.A.A.A.A.2A4.2A2.A.A.A.A.A.A2.2A$2.13A7.2A.A .A.A.A.A.A.2A6.3A.A.A.A.A.A.3A$3.A9.A9.2A.A.A.A.A.A.2A8.2A.A.A.A.A.A. 2A$24.13A10.13A$25.A9.A12.A9.A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Generations ZOOM 6 WIDTH 640 HEIGHT 560 ]]
Example still lives in Star Wars
(click above to open LifeViewer)
x = 181, y = 195, rule = 345/2/4 .A9.A29.A4.A2.A10.ABC7.CBA8.A4.A2.A12.BC$3A7.3A27.3A2.6A10.A9.A8.3A2. 6A10.C.A$.A9.A29.A4.A2.A10.3A7.3A8.A4.A2.A10.B.A.A$.A39.A4.A2.A11.A9. A9.A7.A10.4AB$.2A38.2A2.2A2.2A10.3A7.3A7.2A6.2A11.A2.C$.A39.A4.A2.A 10.2A.2A5.2A.2A6.A7.A12.3A$.A39.A4.A2.A11.3A7.3A7.A7.A12.A.2A.A4.C$. 2A38.2A2.2A2.2A11.A9.A8.2A6.2A10.2A2.2A.A2.A.B$.A39.A4.A2.A11.CBA7.AB C7.A7.A12.A3.8A$.A39.A4.A2.A31.A7.A12.A4.A3.A$.2A38.2A2.2A2.2A30.2A6. 2A10.3A6.C$.A39.A4.A2.A31.A7.A12.A$.A39.A4.A2.A16.ABC2.A9.A7.A$3A37. 3A2.6A11.A3.ABC.3A7.3A5.3A$.A39.A4.A2.A11.3A7.A9.A7.A$60.C.A7.CBA$61. BA14$.A10.B6.A3.A5.A2.A2.A5.A4.A34.A4.A2.A14.ABC$3A7.ACAC4.7A3.9A3.3A 2.3A14.A2.A.C12.3A2.6A11.A2.A$.A8.2B2.B4.A.A.A3.2A2.A2.A.2A3.A4.A14. 6AB13.A4.A2.A11.6A$.A8.ACAC5.A3.A4.A.A.CBA.A4.A4.A13.A.2A.A.A13.A4.A 2.A12.A2.A$2A10.B6.2A.2A4.2A.CBA2.A4.2A3.2A12.B.A18.2A2.2A2.2A$.A17.A 3.A3.2A.CBA.C.2A3.A4.A13.C3A17.A4.A2.A$.A2.A14.A.A.A4.A.BA.CB.A4.A4.A 15.A18.A4.A2.A$6A5.CB5.7A3.3A.CBA.A4.2A3.2A33.2A2.6A$.A2.A5.2A.A5.A3. A3.2A7.2A3.A4.A34.A4.A2.A$4.A6.2A15.9A4.A4.A34.A4.A2.A$4.2A4.BA.C15.A 2.A2.A5.2A3.2A33.2A2.2A2.2A$4.A5.A.CB6.A4.A15.A4.A34.A4.A2.A$4.A14.8A 14.A4.A34.A4.A2.A$3.3A14.A2.A.A14.3A2.3A32.3A2.6A$4.A15.3A2.A15.A4.A 34.A4.A2.A$19.2A2.C.2A$20.A.2B.A$20.A2.A.A$19.8A$20.A4.A11$.A2.A7.CB 27.A4.A2.A12.AB17.A2.A4.A2.A10.AB.A16.C12.C$6A4.B2A.A25.3A2.6A11.A.C 15.6A2.6A7.C2.3A.C$.A2.A6.3A15.C11.A4.A2.A11.3A17.A2.A4.A2.A10.2A.3A$ .A10.A16.B11.A7.A12.A21.A4.A2.A7.A.2A.2A.B15.ABA6.ABA$2A9.CAC15.A11. 2A6.2A33.2A2.2A2.2A6.B2A3.3A14.BCACBA2.ABCACB$.A10.B14.5A9.A7.A34.A4. A2.A8.A.A.2A14.A.A.A.A4.A.A.A.A$.A2.A22.CA.AC9.A4.A2.A31.A2.A4.A2.A7. 6A15.B16AB$6A21.B3.B9.2A2.6A29.6A2.2A2.2A8.A.A2.C14.A.A.A.A2.A.A.A.A$ .A2.A23.BCB10.A4.A2.A31.A2.A4.A2.A8.CABA17.A2.A2.A2.A2.A2.A$4.A23.BCB 10.A4.A34.A7.A2.A28.18A$4.2A12.A8.B3.B9.2A2.2A33.2A6.2A2.2A28.A2.A2.A 2.A2.A2.A$4.A11.ABCBA6.CA.AC9.A4.A34.A7.A2.A$.A2.A6.A5.A.A3.A3.5A9.A 4.A2.A31.A2.A4.A2.A$6A4.15A4.A10.3A2.6A29.6A2.6A$.A2.A6.A2.A2.A2.A2.A 5.B11.A4.A2.A31.A2.A4.A2.A$29.C15$.A2.A7.AB27.A4.A2.A13.A17.A2.A4.A 12.A2.C7.C2.A14.A14.A$6A6.A.C25.3A2.6A11.3A2.A12.6A2.3A10.4A.B5.B.4A 12.3A12.3A$.A2.A6.3A27.A4.A2.A10.3A.5AC11.A2.A4.A10.2A2.A.CA3.AC.A2. 2A12.A14.A$.A8.C.A28.A7.A10.B.3A2.A.B14.A4.A11.A.3A.B3.B.3A.A13.A14.A $2A9.BA28.2A6.2A9.C.A5.A15.2A2.2A11.3A.3A3.3A.3A12.2A14.2A$.A39.A7.A 11.3A20.A4.A10.C2.3A7.3A2.C12.A2.ABC.A2.CBA2.A$.A2.A36.A4.A2.A12.A18. A2.A4.A2.A8.BC.A9.A.CB13.A.ABC.AB2A.CBA.A$6A35.2A2.6A29.6A2.6A8.ABA4. A4.ABA13.2A.ABC.AB2A.CBA.2A$.A2.A36.A4.A2.A31.A2.A4.A2.A15.3A20.A2.AB C.A2.CBA2.A$.A2.A36.A7.A31.A10.A14.2A.2A19.A14.A$2A2.2A35.2A6.2A29.2A 10.2A14.3A19.2A14.2A$.A2.A36.A7.A31.A10.A9.ABA4.A4.ABA14.A14.A$.A2.A 36.A4.A2.A31.A2.A7.A8.BC.A9.A.CB13.A14.A$6A34.3A2.6A29.6A5.3A6.C2.3A 7.3A2.C11.3A12.3A$.A2.A36.A4.A2.A11.B7.B11.A2.A7.A8.3A.3A3.3A.3A13.A 14.A$60.C.A5.A.C30.A.3A.B3.B.3A.A$61.3A3.3A30.2A2.A.CA3.AC.A2.2A$62.A 2.A2.A32.4A.B5.B.4A$61.ABCBCBCBA32.A2.C7.C2.A$64.B.B$65.A10$.A2.A5.C. A28.A4.A26.A7.A2.A4.A2.A38.A2.A18.A2.A$6A4.B4A25.3A2.3A24.A.B5.6A2.6A 36.6A7.C8.6A$.A2.A5.A.A.B26.A4.A16.ABC5.3ACA5.A2.A4.A2.A38.A2.A7.B10. A2.A$4.A7.A.C26.A4.A16.ABC6.A2.B8.A4.A2.A12.BC9.CB14.2A9.C10.2A$4.2A 5.3A27.2A2.2A14.A.A10.C9.2A2.2A2.2A12.A.A5.A.A15.2A14.C5.2A$4.A7.A28. A4.A13.3A21.A4.A2.A10.B.3A.B3.B.3A.B12.2A12.A7.2A$4.A7.A28.A4.A2.A11. A.A17.A2.A4.A2.A10.C2A.2AC3.C2A.2AC12.2A10.ABCBA5.2A$4.2A4.C3A27.2A2. 6A10.CB17.6A2.6A11.2A.A5.A.2A14.2A10.ABCBA5.2A$4.A5.B.A.A26.A4.A2.A 31.A2.A4.A2.A11.A.3A2.A2.3A.A13.2A12.A7.2A$4.A5.A.A.B26.A7.A34.A4.A2. A12.BC2.2A.2A2.CB14.2A14.C5.2A$4.2A5.3AC26.2A6.2A33.2A2.2A2.2A15.A.A. A18.2A9.C10.2A$4.A7.A28.A7.A34.A4.A2.A15.A.A.A.A16.A2.A7.B10.A2.A$4.A 7.A28.A7.A31.A2.A4.A2.A16.A.A.A16.6A7.C8.6A$3.3A5.3A26.3A5.3A29.6A2. 6A11.BC2.2A.2A2.CB13.A2.A18.A2.A$4.A5.C.A28.A7.A31.A2.A4.A2.A11.A.3A 2.A2.3A.A$10.B.A.A90.2A.A5.A.2A$10.4AB88.C2A.2AC3.C2A.2AC$12.A.C88.B. 3A.B3.B.3A.B$106.A.A5.A.A$105.BC9.CB10$61.BC$.A2.A36.A4.A2.A10.A.A.C$ 6A16.C2.A2.C11.3A2.6A10.3AB$.A2.A7.AB9.5A13.A4.A2.A12.A.A4.ABC$.A2.A 7.A.C8.A3.A13.A4.A23.A$2A2.2A5.3A8.2A3.2A12.2A2.2A22.3A$.A2.A5.2A.2A 8.A3.A13.A4.A21.A.2AB$.A2.A6.3A9.5A13.A4.A2.A19.BC$6A4.C.A9.C2.A2.C 12.2A2.6A$.A2.A6.BA28.A4.A2.A$.A2.A36.A7.A14.ABA$2A2.2A35.2A6.2A11.AB C.CBA$.A2.A36.A7.A12.BC3.CB$.A2.A36.A4.A2.A11.C3.A3.C$6A34.3A2.6A9.B. A.3A.A.B$.A2.A36.A4.A2.A10.4A.A.4A$62.A.B.B.A$63.A.A.A14$.A2.A5.A.A2. A.C23.A4.A2.A31.A2.A4.A2.A8.A2.A71.A2.A$6A4.B6AB22.3A2.6A29.6A2.6A6. 6A33.ABA33.6A$.A2.A5.C.A2.A.A23.A4.A2.A12.AB17.A2.A4.A2.A8.A2.A32.ABC .CBA32.A2.A$.A2.A36.A4.A15.A.C16.A7.A12.2A31.ABC.A.A.CBA31.2A$2A2.2A 35.2A2.2A14.3A16.2A6.2A12.2A29.ABC.A.CBC.A.CBA29.2A$.A2.A36.A4.A13.2A .2A16.A7.A12.2A27.ABC.ABC.ABA.CBA.CBA27.2A$.A2.A36.A4.A2.A11.3A17.A2. A4.A2.A9.2A25.ABC17.CBA25.2A$6A35.2A2.6A11.A17.6A2.6A8.2A25.ABC17.CBA 25.2A$.A2.A36.A4.A2.A31.A2.A4.A2.A9.2A27.ABC.ABC.ABA.CBA.CBA27.2A$4.A 36.A4.A2.A31.A2.A4.A2.A9.2A29.ABC.A.CBC.A.CBA29.2A$4.2A35.2A2.2A2.2A 29.2A2.2A2.2A2.2A8.2A31.ABC.A.A.CBA31.2A$4.A36.A4.A2.A31.A2.A4.A2.A8. A2.A32.ABC.CBA32.A2.A$.A2.A36.A4.A2.A31.A2.A4.A2.A7.6A33.ABA33.6A$6A 34.3A2.6A29.6A2.6A7.A2.A71.A2.A$.A2.A36.A4.A2.A31.A2.A4.A2.A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Generations ZOOM 2 WIDTH 640 HEIGHT 560 ]]
Example oscillators in Star Wars
(click above to open LifeViewer)
x = 75, y = 108, rule = 345/2/4 35.CBA16.CBA$36.CBA6.CBA7.CBA5.CBA$38.CBA6.CBA6.CBA5.CBA4.CBA$38.CBA 6.CBA6.CBA5.CBA4.CBA$36.CBA6.CBA7.CBA5.CBA$35.CBA16.CBA7$49.CBA17.CBA $47.C.A.CBA8.CBA2.CBA.CBA$49.CBA.CBA6.C.A6.CBA$54.CBA5.C.AB5A$54.CBA 5.C.AB5A$49.CBA.CBA6.C.A6.CBA$47.C.A.CBA8.CBA2.CBA.CBA$49.CBA17.CBA7$ 46.CBA$44.BC.A.A$45.C.AB2A7.CBA$45.C.AB2A5.BC.A.A$45.C.A.A7.C.AB2A6.C BA$45.C.A.A7.C.AB2A3.C.AB.A$45.C.AB2A6.C.A.A7.BC3A$45.C.AB2A6.C.A.A7. BC3A$45.C.A.A7.C.AB2A3.C.AB.A$45.C.A.A7.C.AB2A6.CBA$45.C.AB2A5.BC.A.A $45.C.AB2A7.CBA$44.BC.A.A$46.CBA6$68.CBA$66.BC.A.A$65.C2.BC3A$67.ABC 3A$67.C.A.A$68.CBA9$20.BA25.C.ABC.AB.A$18.BCBC11.A14.ABC.ABC3A6.BC.AB C.A$17.C.A.A3.B2.ACA.B.B11.2C.BC.ABC3A7.C2.A.AB2A$17.BC.C.3A.3A.3AC3A 12.BA.C.A.A10.2B.4A$20.C2A.3A.3A.5A9.ACBC2.B.A.A10.AC.C.A$17.C2.B.B.B .C.C2.A2.A11.2B3.C.AC3A11.B$21.A.A3.B3.C14.AC2.C.ABC3A$19.C30.BC.AB.A $17.CB6$55.A$54.BAB9.AC.AB.A$54.3C.A3.B2.3A.AC3A$57.BA.A2CA.B.3AC3A$ 54.CA.AC2A2.B2.A2.A2.A$54.2B2.A.2A.2A.2A.2A$54.CA.AC2A2.B2.A2.A2.A$ 57.BA.A2CA.B.3AC3A$54.3C.A3.B2.3A.AC3A$54.BAB9.AC.AB.A$55.A7$24.CBA$ 25.CBA$6.CBA12.C.AB2.CBA15.CBA$3.BC.A.CBA11.B2.CBA.CBA14.CBA14.CBA$2. C2.BC.A.CBA10.CBA4.CBA9.C.AB2.CBA11.B2.CBA$3.B.A.CBA.CBA17.CBA9.B2.CB A.CBA8.C.AB2.CBA$CB2.CBA.CBA.CBA17.CBA9.CBA4.CBA11.CBA.CBA$2.CBA.CBA. CBA.CBA16.CBA16.CBA9.CBA3.CBA$15.CBA16.CBA16.CBA16.CBA$15.CBA16.CBA 16.CBA16.CBA$2.CBA.CBA.CBA.CBA16.CBA16.CBA9.CBA3.CBA$CB2.CBA.CBA.CBA 17.CBA9.CBA4.CBA11.CBA.CBA$3.B.A.CBA.CBA17.CBA9.B2.CBA.CBA8.C.AB2.CBA $2.C2.BC.A.CBA10.CBA4.CBA9.C.AB2.CBA11.B2.CBA$3.BC.A.CBA11.B2.CBA.CBA 14.CBA14.CBA$6.CBA12.C.AB2.CBA15.CBA$25.CBA$24.CBA! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Generations ZOOM 4 WIDTH 640 HEIGHT 560 ]]
Example spaceships in Star Wars (Mirek Wójtowicz, May 1999)
(click above to open LifeViewer)

Still lifes

Still lives of population 5, 8, 10, 12 and above exists. The only 5-cell still life is the X-pentomino, or cross, which is a common extendable segment in larger still lives.

A group of still lives in the shape of rectangular boxes are invincible from inside, limiting the evolution similar to a finite plane; for a m×n plane the exterior has a bounding box of (m+4)×(n+4). An example with m=n=16 is shown above at lower-right corner.

Oscillators

Due to the two dying states, oscillators of period 2 and 3 are impossible.

Many oscillators consist of one or more lightspeed signals, with a leading state-1 cell each, that are running on the surface of the stator. These oscillators are referred to as railroads because they look like trains running on railways. The mechanism provides at least one specimen for every period p ≥ 4. Specifically, jointing q copies of the X-pentomino orthogonally will give a still life with circumference 6q+6 cells (which has exactly one state-1 cell each in their Moore neighbourhoods). If 6q+6 = kp for some integer k, then k copies of the signal can be put in the circumference evenly to yield a period-p oscillator. The period-7 example is constructed accordingly.

Spaceships

The spaceships in Star Wars are all at c orthogonal, thus are also referred to as photons. The structure is extensible to various degrees.

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Guns of period 4, 5 (right), 6 and 7 (left) in Star Wars
(Stephen Silver, May 1999) (click above to open LifeViewer)
x = 107, y = 47, rule = 345/2/4 CBA4.A18.2C27.A21.A19.A$CBA3.3A45.3A19.3A17.3A4.A$7.A12.CBA4.A25.2A. 2A12.CBA4.A2.C9.CBA4.A4.3A.C$20.CBA3.3A25.3A13.CBA4.A2.C9.CBA10.A2.C$ 27.A28.A19.3A$55.3A19.A$31.A21.C2.A$30.3A20.C$31.A18.CBA$50.CBA21$CBA 3.2C30.2C17.A$CBA53.3A$7.A22.CBA6.A17.2A.A$6.3A21.CBA5.3A16.A.3A$7.A 31.A17.2A.A$50.CBA3.3A$11.A38.CBA4.A6.A$10.3A50.3A.C$11.A26.2A24.A2.C $16.ABC19.2B$11.2C3.ABC19.2C4$55.2A$55.2B$55.2C! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Generations ZOOM 6 WIDTH 720 HEIGHT 560 ]]
Simple photon conduits in Star Wars, with state-3 cells marking output location.
Top, left to right: eater,90-degree reflector, 180-degree reflector, 3-tick delay, 2-tick delay
Bottom: XOR gate with two outputs, AND gate, OR gate (click above to open LifeViewer)

Linear growth patterns

Guns (or rather, lasers) firing the smallest photon exist at all periods above 4, which can be constructed by connecting two still lives to the aforementioned adjustable oscillator.

Usually, abundant guns, puffers, rakes, wickstretchers and wavestretchers emerge from sufficiently large soups.

Signal circuits

Technologies based on the smallest photon have been extensively developed. For instance, shooting the photon at the edge of a still life can split it into two lightspeed signals, which travel on the edge and merge into a photon elsewhere, or are turned into other signals. A small portion of photon conduits is shown above.

Further constructions are possible, for instance an adder.[1]

Miscellaneous

The domino in this rule expands in a diamond shape, while the block grows quadratically generating wickstretchers.

References

  1. Jeremy Tan (March 22, 2015). An Amsterdam Adder (discussion thread) at the ConwayLife.com forums

External links