## Perfect and Semiperfect Orthogonal Speeds Rule Mashup

For discussion of other cellular automata.

### Perfect and Semiperfect Orthogonal Speeds Rule Mashup

Version history:
0.2
0.3
0.4
0.5
0.6
--
1.0
1.1 - too big, may host on wiki if desired enough
1.2
1.3
1.9pre1
2.0
2.00
--
2.01
2.01+0.1i
2.02
2.03
2.04
2.05

Out of boredom I decided to compile this mashup rule from all the rules from my Perfect Orthogonal Speeds list thread, as a tool to aid in visualizing the many perfect speeds not yet discovered in Life. Each rule contains a spaceship which moves at a speed from c/1 to c/50, and every single ship's period is equal to its speed (with the exception of c/42).

I'll let this pattern do all the talking:
x = 1970, y = 12, rule = RainbowASOv1.02B43.3A15.3A21.2A.A30.A49.A7.A25.3A10.3A21.A39.C2.C36.D39.2A2.2A32.E.E38.4F38.2G.2G35.2H35.I3.2I36.J40.K36.L7.L35.4M36.N37.O.O37.2P2.2P36.Q41.R37.S37.4T36.U.U39.5V33.3W37.X5.X34.pA.pA38.pB2.pB35.4pC34.2pD42.3pE33.2pF2.2pF36.4pG37.pH41.pI3.pI34.pJ.pJ35.pK.pK36.9pL32.4pM36.3pN39.2pO.pO.2pO32.pP2.pP35.4pQ38.pR36.pS.pS39.4pT$44.A3.A13.A3.A17.2A.A.2A.3A26.A8.A34.2A.A.A.2A3.2A.A.A.2A14.3A.A7.2A7.A.3A15.A.A76.D3.D39.2A35.E39.F2.F39.G.G35.4H35.3I37.J.J38.K.K39.L39.M2.M34.2N.2N36.O37.P.P2.P.P75.R.R.R35.S37.T2.T36.U.U40.V.V32.W.3W.W35.2X.X.2X34.3pA37.2pB2.2pB72.2pD2.pD75.6pF35.2pG2.2pG78.pI3.pI33.pJ.pJ.pJ33.2pK.2pK33.2pL9.2pL28.8pM32.2pN.pN.2pN37.pO5.pO30.8pP33.pQ2.pQ36.pR3.pR32.4pS38.2pT4.2pT$B42.2A4.A11.A4.2A13.4A2.2A6.A24.A.A5.A3.A29.3A.A.3A9.3A.A.3A15.A3.A2.A2.A2.A3.A19.A2.A36.2C2.2C77.2A75.4F36.G.5G.G31.6H74.J.J38.K.K37.L.L.L116.O39.P2.P34.2Q.Q.2Q37.3R35.S.S35.T4.T35.U.U39.V3.V32.5W35.3X3.3X31.pA5.pA35.2pB2.2pB34.pC2.pC73.2pE3.pE.pE3.2pE69.pG.2pG.pG75.pI2.pI3.pI2.pI69.pK.pK36.pL.5pL.pL31.pM4.pM78.pO.pO.pO31.pP.pP2.pP.pP33.4pQ36.pR3.pR33.pS2.pS$42.A.A.2A.2A3.3A3.2A.2A.A.A11.A4.A3.A3.2A33.A3.2A28.A3.A.A5.A.A5.A.A3.A15.A5.A4.A5.A20.2A77.D.D37.A.A2.A.A72.F2.F36.2G5.2G32.H2.H117.K37.L5.L37.2M35.N.N.N35.O.O79.Q38.7R33.S.S36.T2.T35.U3.U40.V33.W5.W38.X117.4pC38.pD34.2pE4.pE4.2pE30.2pF116.2pI2.pI5.pI2.2pI28.2pJ.2pJ33.2pK.2pK33.2pL9.2pL27.10pM31.pN5.pN40.pO32.pP2.4pP2.pP72.pR.pR.pR32.pS2.pS38.pT6.pT$41.2A.A4.A.2A.3A.2A.A4.A.2A11.2A42.A.2A5.2A30.2A6.A.A6.2A25.2A2.2A145.A6.A32.E80.G.3G.G313.O.O119.5R35.S36.2T2.2T35.3U39.V3.V73.X5.X33.pA3.pA77.2pC116.4pF37.4pG35.pH3.pH33.4pI9.4pI29.pJ36.3pK36.pL.2pL.2pL.pL31.6pM33.7pN39.pO.pO34.4pP34.pQ4.pQ35.pR.pR.pR33.pS.2pS39.4pT$40.A4.A3.A4.A.A4.A3.A4.A50.6A2.A6.A26.2A9.A.A9.2A19.A3.A2.A3.A22.A5.A235.G3.G196.L116.O3.O38.2P77.7R72.T2.T198.pA238.4pG194.pL4.pL4.pL28.pM.pM4.pM.pM31.7pN37.3pO.3pO29.3pP4.3pP72.2pR.2pR32.2pS40.3pT2.3pT$52.A5.A63.2A6.A3.3A26.2A.2A15.2A.2A19.A.A6.A.A23.A3.A.A112.A6.A274.K279.7R72.4T237.6pB34.4pC356.2pL.pL.2pL33.4pM35.pN.pN.pN76.6pP76.pR37.pS$40.2A7.2A9.2A7.2A59.A3.A.2A29.A15.A24.10A23.2A3.A2.A112.2A2.2A274.K.K158.O121.3R554.pH.pH.pH235.pN.pN.pN157.3pR76.pT4.pT$133.A76.A4.A25.A3.2A2.A113.4A274.2K.2K278.R.R.R555.pH400.pR$138.A69.A8.A423.K.K.K279.3R556.pH$137.A69.A10.A145.2A560.R$137.A70.A8.A146.2A560.R! Rule table: (pretty massive) @RULE RainbowASOv1.0@TABLEn_states:45neighborhood:Mooresymmetries:rotate4reflectvar aa=1var ab=2var ac=3var ad=4var ae=5var af=6var ag=7var ah=8 var ai=9 var aj=10var ak=11var al=12var am=13var an=14var ao=15var ap=16var aq=17var ar=18var as=19var at=20var au=21var av=22var aw=23var ax=24var ay=25var az=26var ba=27var bb=28var bc=29var bd=30var be=31var bf=32var bg=33var bh=34var bi=35var bj=36var bk=37var bl=38var bm=39var bn=40var bo=41var bp=42var bq=43var br=44var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44}var b=avar d=avar e=avar f=avar g=avar i=avar j=avar 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0 0 01 255 255 2552 255 0 03 0 255 04 0 0 2555 0 255 2556 255 0 2557 255 255 08 255 127 09 127 255 010 255 0 12711 127 0 25512 0 255 12713 0 127 25514 127 0 015 0 127 016 0 0 12717 0 127 12718 127 0 12719 127 127 020 255 127 12721 127 255 12722 127 127 25523 127 255 25524 255 127 25525 255 255 12726 255 191 027 191 255 028 255 0 19129 191 0 25530 0 255 19131 0 191 25532 191 0 033 0 191 034 0 0 19135 0 191 19136 191 0 19137 191 191 038 191 255 25539 255 191 25540 255 255 19141 255 191 19142 191 255 19143 191 191 25544 191 191 191 Last edited by muzik on August 6th, 2017, 12:11 pm, edited 6 times in total. 2c/n spaceships project Current priorities: see here muzik Posts: 2612 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) bprentice Posts: 407 Joined: September 10th, 2009, 6:20 pm Location: Coos Bay, Oregon ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) Definitely interesting, but I can't seem to get speeds of c/even in the first rule, and the second rule doesn't seem to support true period ships. 2c/n spaceships project Current priorities: see here muzik Posts: 2612 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) Beautiful! If you run it it looks like an exponential graph. It's great to have the ones I found hehe Everyone, please stop posting B/S about CA x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

Saka

Posts: 2267
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!)

ah, so that's what that was called. Had it in my head somewhere.

Also, when I add the remaining rules in the other thread to the mashup rule, the ruletable becomes too big to post here.
2c/n spaceships project

Current priorities: see here
muzik

Posts: 2612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!)

muzik wrote:ah, so that's what that was called. Had it in my head somewhere.

Also, when I add the remaining rules in the other thread to the mashup rule, the ruletable becomes too big to post here.

Try pastebin
x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo! (Check gen 2) Saka Posts: 2267 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) muzik wrote:I'll let this pattern do all the talking: Fun fact: if you stretch a rectangular hyperbola in the x-direction, it is indistinguishable from a rectangular hyperbola being stretched in the y-direction. Corollary: this pattern, which only works since you were sufficiently helpful as to place them equally-spaced and in order... x = 2144, y = 2086, rule = RainbowASOv1.0122.pT.pT.pT$120.pT.pT3.pT$122.2pT3.pT$123.pT3.pT$123.pT3.pT$122.2pT3.pT$120.pT.pT3.pT$122.pT.pT.pT38$123.pS.pS.pS$121.pS.2pS.pS$126.2pS$122.2pS.2pS$122.pS.pS.pS9$64.pT.pT.pT$62.pT.pT3.pT$64.2pT3.pT$65.pT3.pT$65.pT3.pT$64.2pT3.pT$62.pT.pT3.pT$64.pT.pT.pT17$122.5pR$120.pR.pR$119.3pR.2pR2.pR$120.pR.pR$122.5pR17$65.pS.pS.pS$63.pS.2pS.pS$68.2pS$64.2pS.2pS$64.pS.pS.pS9$6.pT.pT.pT$4.pT.pT3.pT$6.2pT3.pT$7.pT3.pT$7.pT3.pT$6.2pT3.pT$4.pT.pT3.pT112.pQ$6.pT.pT.pT114.3pQ$125.pQ.pQ$125.pQ.pQ$125.3pQ$123.pQ13$64.5pR$62.pR.pR$61.3pR.2pR2.pR$62.pR.pR$64.5pR15$122.pP.pP$122.pP2.2pP$7.pS.pS.pS109.2pP3.pP$5.pS.2pS.pS110.pP.5pP$10.2pS109.pP.2pP.pP$6.2pS.2pS110.pP.2pP.pP$6.pS.pS.pS110.pP.5pP$121.2pP3.pP$122.pP2.2pP$122.pP.pP12$65.pQ$67.3pQ$67.pQ.pQ$67.pQ.pQ$67.3pQ$65.pQ13$6.5pR111.pO3.2pO$4.pR.pR115.pO2.pO.pO$3.3pR.2pR2.pR110.2pO$4.pR.pR117.2pO.pO$6.5pR111.2pO$122.pO2.pO.pO$122.pO3.2pO13$64.pP.pP$64.pP2.2pP$63.2pP3.pP$63.pP.5pP$63.pP.2pP.pP$63.pP.2pP.pP$63.pP.5pP$63.2pP3.pP$64.pP2.2pP$64.pP.pP12$7.pQ$9.3pQ$9.pQ.pQ$9.pQ.pQ$9.3pQ110.3pN.pN$7.pQ112.4pN2.pN$122.2pN3.pN$120.4pN2.2pN$122.2pN3.pN$120.4pN2.pN$122.3pN.pN8$64.pO3.2pO$64.pO2.pO.pO$64.2pO$66.2pO.pO$64.2pO$64.pO2.pO.pO$64.pO3.2pO13$6.pP.pP$6.pP2.2pP$5.2pP3.pP$5.pP.5pP$5.pP.2pP.pP$5.pP.2pP.pP111.pM.pM$5.pP.5pP112.pM.pM$5.2pP3.pP111.5pM$6.pP2.2pP110.pM.2pM.2pM$6.pP.pP112.pM.2pM.2pM$121.pM.2pM.2pM$121.pM.2pM.2pM$122.5pM$124.pM.pM$122.pM.pM11$64.3pN.pN$62.4pN2.pN$64.2pN3.pN$62.4pN2.2pN$64.2pN3.pN$62.4pN2.pN$64.3pN.pN8$6.pO3.2pO$6.pO2.pO.pO$6.2pO$8.2pO.pO112.pL.pL$6.2pO114.pL.pL.pL$6.pO2.pO.pO111.pL.pL.pL$6.pO3.2pO109.pL5.pL$121.pL.pL.pL.pL$123.pL.pL.pL$121.2pL2.pL.pL$123.pL.pL.pL$121.pL.pL.pL.pL$121.pL5.pL$123.pL.pL.pL$122.pL.pL.pL$124.pL.pL9$64.pM.pM$66.pM.pM$64.5pM$63.pM.2pM.2pM$63.pM.2pM.2pM$63.pM.2pM.2pM$63.pM.2pM.2pM$64.5pM$66.pM.pM$64.pM.pM11$6.3pN.pN$4.4pN2.pN$6.2pN3.pN$4.4pN2.2pN$6.2pN3.pN$4.4pN2.pN113.pK.pK$6.3pN.pN112.5pK$123.pK$123.5pK$124.pK.pK8$66.pL.pL$64.pL.pL.pL$65.pL.pL.pL$63.pL5.pL$63.pL.pL.pL.pL$65.pL.pL.pL$63.2pL2.pL.pL$65.pL.pL.pL$63.pL.pL.pL.pL$63.pL5.pL$65.pL.pL.pL$64.pL.pL.pL$66.pL.pL9$6.pM.pM$8.pM.pM$6.5pM$5.pM.2pM.2pM$5.pM.2pM.2pM$5.pM.2pM.2pM112.pJ.pJ$5.pM.2pM.2pM112.pJ2.pJ$6.5pM112.pJ2.pJ$8.pM.pM113.pJ2.pJ$6.pM.pM115.pJ.pJ16$66.pK.pK$65.5pK$65.pK$65.5pK$66.pK.pK8$8.pL.pL112.pI$6.pL.pL.pL112.2pI$7.pL.pL.pL111.2pI$5.pL5.pL111.pI.pI$5.pL.pL.pL.pL$7.pL.pL.pL112.pI$5.2pL2.pL.pL113.3pI$7.pL.pL.pL$5.pL.pL.pL.pL$5.pL5.pL$7.pL.pL.pL113.3pI$6.pL.pL.pL113.pI$8.pL.pL$123.pI.pI$123.2pI$123.2pI$123.pI10$66.pJ.pJ$66.pJ2.pJ$65.pJ2.pJ$66.pJ2.pJ$66.pJ.pJ16$8.pK.pK$7.5pK$7.pK$7.5pK$8.pK.pK109.pH2.pH2$118.3pH6.pH2$120.pH2.pH4$65.pI$65.2pI$65.2pI$65.pI.pI2$66.pI$67.3pI4$67.3pI$66.pI2$65.pI.pI$65.2pI$65.2pI$65.pI10$8.pJ.pJ$8.pJ2.pJ$7.pJ2.pJ$8.pJ2.pJ$8.pJ.pJ$125.2pG$122.2pG2.2pG$122.2pG.pG.pG$122.2pG.pG.pG$122.2pG2.2pG$125.2pG14$62.pH2.pH2$60.3pH6.pH2$62.pH2.pH4$7.pI$7.2pI$7.2pI$7.pI.pI2$8.pI$9.3pI4$9.3pI$8.pI2$7.pI.pI$7.2pI117.2pF$7.2pI114.pF2.2pF$7.pI115.2pF.pF$123.2pF.pF$123.pF2.2pF$126.2pF12$67.2pG$64.2pG2.2pG$64.2pG.pG.pG$64.2pG.pG.pG$64.2pG2.2pG$67.2pG12$124.2pE$124.2pE$4.pH2.pH2$2.3pH6.pH$125.pE.pE$4.pH2.pH116.pE2.pE$125.pE.pE4$124.2pE$124.2pE12$68.2pF$65.pF2.2pF$65.2pF.pF$65.2pF.pF$65.pF2.2pF$68.2pF12$9.2pG$6.2pG2.2pG$6.2pG.pG.pG$6.2pG.pG.pG$6.2pG2.2pG$9.2pG$124.pD.pD3$126.2pD$126.2pD7$66.2pE$66.2pE4$67.pE.pE$66.pE2.pE$67.pE.pE4$66.2pE$66.2pE12$10.2pF$7.pF2.2pF$7.2pF.pF$7.2pF.pF$7.pF2.2pF109.pC2.2pC.pC$10.2pF109.pC.2pC2.pC$121.pC.2pC2.pC$121.pC2.2pC.pC16$66.pD.pD3$68.2pD$68.2pD7$8.2pE$8.2pE4$9.pE.pE$8.pE2.pE$9.pE.pE$121.pB3.2pB$121.pB3.3pB$121.pB$8.2pE111.pB$8.2pE111.pB3.3pB$121.pB3.2pB15$63.pC2.2pC.pC$63.pC.2pC2.pC$63.pC.2pC2.pC$63.pC2.2pC.pC16$8.pD.pD2$125.pA$10.2pD111.pA$10.2pD114.2pA$122.pA3.pA$126.2pA$123.pA$125.pA11$63.pB3.2pB$63.pB3.3pB$63.pB$63.pB$63.pB3.3pB$63.pB3.2pB15$5.pC2.2pC.pC$5.pC.2pC2.pC113.X$5.pC.2pC2.pC111.X.3X$5.pC2.2pC.pC113.2X2$124.X.X2$125.2X$123.X.3X$125.X12$67.pA$65.pA$68.2pA$64.pA3.pA$68.2pA$65.pA$67.pA11$5.pB3.2pB$5.pB3.3pB$5.pB$5.pB$5.pB3.3pB$5.pB3.2pB$124.W.W$125.W$125.3W$125.3W$125.3W$125.W$124.W.W9$67.X$65.X.3X$67.2X2$66.X.X2$67.2X$65.X.3X$67.X12$9.pA$7.pA$10.2pA$6.pA3.pA112.V.V.V$10.2pA114.2V$7.pA116.V2.V$9.pA116.2V$123.V.V.V16$66.W.W$67.W$67.3W$67.3W$67.3W$67.W$66.W.W9$9.X$7.X.3X$9.2X2$8.X.X2$9.2X$7.X.3X$9.X114.U$123.U.3U$123.U$123.U.3U$124.U11$65.V.V.V$68.2V$66.V2.V$68.2V$65.V.V.V16$8.W.W$9.W$9.3W$9.3W$9.3W111.T.T$9.W111.4T.2T$8.W.W110.T5.T$121.T5.T$121.4T.2T$123.T.T14$66.U$65.U.3U$65.U$65.U.3U$66.U11$7.V.V.V$10.2V$8.V2.V$10.2V$7.V.V.V3$124.2S$123.S2.2S$124.2S15$65.T.T$63.4T.2T$63.T5.T$63.T5.T$63.4T.2T$65.T.T14$8.U112.2R.R$7.U.3U107.R.4R.R$7.U110.R.6R$7.U.3U104.12R$8.U109.R.6R$119.R.4R.R$121.2R.R16$66.2S$65.S2.2S$66.2S15$7.T.T$5.4T.2T$5.T5.T$5.T5.T113.Q$5.4T.2T113.Q$7.T.T$124.2Q.Q2$125.Q$125.Q10$63.2R.R$61.R.4R.R$60.R.6R$58.12R$60.R.6R$61.R.4R.R$63.2R.R16$8.2S$7.S2.2S114.P$8.2S117.P$125.3P$122.P$122.P$125.3P$127.P$126.P12$67.Q$67.Q2$66.2Q.Q2$67.Q$67.Q10$5.2R.R$3.R.4R.R$2.R.6R$12R$2.R.6R$3.R.4R.R$5.2R.R2$122.O$123.2O2.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It's quite frightening to watch. What do you do with ill crystallographers? Take them to the mono-clinic! calcyman Posts: 1370 Joined: June 1st, 2009, 4:32 pm ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) Here's an updated version, in which I've removed all of the rules that exist solely to provide even-speed ships, thanks to the recent discovery made by AbhpzTa. Some of these replacement ships are bigger than the previous ships, but the size of the ruletable is crunched down by a lot as any even speed can be simulated besides c/2. The entire ruletable can fit in a single forum post once again: @RULE RainbowASOv1.2@TABLEn_states:36neighborhood:Mooresymmetries:rotate4reflectvar aa=1var ab=2var ac=3var ad=4var ae=5var af=6var ag=7var ah=8 var ai=9 var aj=10var ak=11var al=12var am=13var an=14var ao=15var ap=16var aq=17var ar=18var as=19var at=20var au=21var av=22var aw=23var za=24var zb=25var zd=26var zf=27var zi=28var zk=29var zl=30var zm=31var zo=32var zp=33var zs=34var zz=35var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35}var b=avar d=avar e=avar f=avar g=avar i=avar j=avar 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0 0 01 255 255 2552 255 0 03 0 255 04 0 0 2555 0 255 2556 255 0 2557 255 255 08 255 127 09 127 255 010 255 0 12711 127 0 25512 0 255 12713 0 127 25514 127 0 015 0 127 016 0 0 12717 0 127 12718 127 0 12719 127 127 020 255 127 12721 127 255 12722 127 127 25523 127 255 25524 255 127 25525 255 255 12726 255 191 027 191 255 028 255 0 19129 191 0 25530 0 255 19131 0 191 25532 191 0 033 0 191 034 0 0 19135 191 191 191 2c/n spaceships project Current priorities: see here muzik Posts: 2612 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) Saka wrote:Beautiful! If you run it it looks like an exponential graph. It's great to have the ones I found hehe It's actually a graph of y = t/x, where t is the generation number. An easy way to tell that it's not an exponential function is to observe that the ratio between the displacement of the nth and (n + 1)st spaceships differs as the value of n changes. As Calcyman pointed out, this results in a section of a hyperbola turned by 45 degrees. As the pattern runs -- say from generation t0 to t1 -- it gets stretched along the y-axis by a factor of F = t1/t0. Equivalently, one can also view this as being stretched along the x-axis by the same factor, or even as being magnified by a factor of sqrt(F). In fact, for any nonzero value A, the transformation described by the matrix: ⎡F/A 0⎤⎣0 A⎦ produces the same result. gameoflifeboy Posts: 457 Joined: January 15th, 2015, 2:08 am Location: New Mexico Tech ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) 1.3 is here, mercilessly stealing a smaller c/13 from this rule. @RULE RainbowASOv1.3@TABLEn_states:36neighborhood:Mooresymmetries:rotate4reflectvar aa=1var ab=2var ac=3var ad=4var ae=5var af=6var ag=7var ah=8 var ai=9 var aj=10var ak=11var al=12var am=13var an=14var ao=15var ap=16var aq=17var ar=18var as=19var at=20var au=21var av=22var aw=23var za=24var zb=25var zd=26var zf=27var zi=28var zk=29var zl=30var zm=31var zo=32var zp=33var zs=34var zz=35var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35}var b=avar d=avar e=avar f=avar g=avar i=avar j=avar 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0 0 01 255 255 2552 255 0 03 0 255 04 0 0 2555 0 255 2556 255 0 2557 255 255 08 255 127 09 127 255 010 255 0 12711 127 0 25512 0 255 12713 0 127 25514 127 0 015 0 127 016 0 0 12717 0 127 12718 127 0 12719 127 127 020 255 127 12721 127 255 12722 127 127 25523 127 255 25524 255 127 25525 255 255 12726 255 191 027 191 255 028 255 0 19129 191 0 25530 0 255 19131 0 191 25532 191 0 033 0 191 034 0 0 19135 191 191 191 and here they all are: x = 1974, y = 55, rule = RainbowASOv1.32B43.3A15.3A21.2A.A30.A49.A7.A25.3A10.3A26.A33.3pK38.C41.2A34.D.D38.3pK38.E38.3pK37.F3.2F34.3pK40.G36.3pK40.4H33.3pK38.I.I36.3pK40.J36.3pK40.K36.3pK38.L.L36.3pK38.3M36.3pK39.N.N35.3pK39.4O34.3pK41.3P33.3pK39.4Q34.3pK42.R3.R30.3pK39.S.S35.3pK39.4T34.3pK41.2U.U.2U39.3pK39.4V34.3pK38.W.W36.3pK$44.A3.A13.A3.A17.2A.A.2A.3A26.A8.A34.2A.A.A.2A3.2A.A.A.2A14.3A.A7.2A7.A.3A20.A.A33.pK37.C3.C38.A2.A34.D40.pK38.3E38.pK39.3F37.pK40.G.G36.pK41.H2.H34.pK40.I38.pK79.pK41.K37.pK39.L.L37.pK37.M.3M.M35.pK40.3N36.pK79.pK79.pK39.2Q2.2Q34.pK43.R3.R31.pK39.2S.2S35.pK38.8T33.pK42.U5.U40.pK40.V2.V35.pK37.4W38.pK$B42.2A4.A11.A4.2A13.4A2.2A6.A24.A.A5.A3.A29.3A.A.3A9.3A.A.3A15.A3.A2.A2.A2.A3.A23.A2.A33.pK80.A2.A75.pK37.E3.E37.pK79.pK40.G.G36.pK79.pK40.I38.pK38.2J.J.2J34.pK40.K.K36.pK39.L.L37.pK38.5M36.pK38.N5.N34.pK40.O2.O35.pK37.2P3.P.P3.2P29.pK39.Q.2Q.Q34.pK40.R2.R3.R2.R28.pK40.S.S36.pK39.T4.T34.pK43.U.U.U41.pK40.4V35.pK38.W2.W37.pK$42.A.A.2A.2A3.3A3.2A.2A.A.A11.A4.A3.A3.2A33.A3.2A28.A3.A.A5.A.A5.A.A3.A15.A5.A4.A5.A24.2A34.pK38.C.C38.A4.A74.pK79.pK79.pK41.G37.pK42.2H35.pK39.I.I37.pK41.J37.pK40.K.K36.pK38.L3.L36.pK37.M5.M35.pK79.pK40.4O35.pK37.2P4.P4.2P29.pK79.pK38.2R2.R5.R2.2R26.pK39.2S.2S35.pK37.10T32.pK45.U43.pK79.pK37.W2.W38.pK$41.2A.A4.A.2A.3A.2A.A4.A.2A11.2A42.A.2A5.2A30.2A6.A.A6.2A25.2A2.2A66.pK79.A4.A33.D40.pK79.pK79.pK79.pK79.pK39.I.I37.pK79.pK41.K37.pK39.3L37.pK79.pK39.N3.N35.pK41.2O36.pK79.pK40.4Q35.pK37.4R9.4R25.pK40.3S36.pK39.6T34.pK44.U.U42.pK39.V4.V34.pK38.W.2W37.pK$40.A4.A3.A4.A.A4.A3.A4.A50.6A2.A6.A26.2A9.A.A9.2A19.A3.A2.A3.A23.A5.A32.pK.pK79.4A75.pK79.pK79.pK79.pK79.pK38.I3.I36.pK79.pK79.pK79.pK79.pK41.N37.pK79.pK79.pK40.4Q35.pK79.pK79.pK37.T.T4.T.T32.pK42.3U.3U40.pK79.pK37.2W40.pK$52.A5.A63.2A6.A3.3A26.2A.2A15.2A.2A19.A.A6.A.A22.A.A3.A34.pK79.2A2.2A74.pK79.pK79.pK41.G37.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK40.4O35.pK79.pK79.pK79.pK79.pK40.4T35.pK89.pK79.pK40.W38.pK$40.2A7.2A9.2A7.2A59.A3.A.2A29.A15.A24.10A22.A2.A3.2A113.A4.A73.pK.pK78.pK79.pK40.G.G36.pK79.pK40.I38.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$133.A76.A4.A24.A2.2A3.A113.A4.A74.pK78.pK.pK78.pK39.2G.2G35.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$138.A69.A8.A304.pK78.pK.pK38.G.G.G35.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$137.A69.A10.A383.pK78.pK.pK78.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$137.A70.A8.A145.4A315.pK78.pK.pK78.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$364.2A396.pK78.pK.pK78.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$842.pK78.pK.pK78.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$922.pK78.pK.pK78.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$1002.pK78.pK.pK78.pK79.pK79.pK79.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$1082.pK78.pK.pK78.pK79.pK79.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$1162.pK78.pK.pK78.pK79.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$1242.pK78.pK.pK78.pK79.pK79.pK79.pK79.pK89.pK79.pK79.pK$1322.pK78.pK.pK78.pK79.pK79.pK79.pK89.pK79.pK79.pK$1402.pK78.pK.pK78.pK79.pK79.pK89.pK79.pK79.pK$1482.pK78.pK.pK78.pK79.pK89.pK79.pK79.pK$1562.pK78.pK.pK78.pK89.pK79.pK79.pK$1642.pK78.pK.pK88.pK79.pK79.pK$1722.pK88.pK.pK78.pK79.pK$1812.pK78.pK.pK78.pK$1892.pK78.pK.pK$1972.pK13$4.3X35.pA5.pA37.2pB37.pC3.pC32.pD.pD2.pD.pD46.pE.pE.pE21.pF.8pF.pF30.pG2.pG34.5pH36.2pI.2pI37.pJ.pJ$4.3X35.2pA3.2pA37.2pB37.2pC.2pC33.2pD2.2pD47.pE3.pE63.4pG35.3pH36.pI5.pI$2.3X.3X33.7pA36.4pB35.pC.pC.pC.pC32.2pD2.2pD47.pE3.pE21.4pF4.4pF28.pG2.2pG2.pG30.2pH.3pH.2pH34.5pI36.5pJ$42.pA5.pA34.8pB34.5pC32.2pD4.2pD71.pF12.pF27.pG2.2pG2.pG32.pH.pH.pH35.pI5.pI$.X.X.X.X.X32.3pA.3pA34.8pB33.7pC86.3pE22.pF2.6pF2.pF27.2pG6.2pG29.2pH2.pH2.2pH34.5pI34.2pJ.3pJ.2pJ$.9X35.pA37.8pB32.9pC108.2pF12.2pF25.2pG2.2pG2.2pG31.5pH35.pI5.pI31.2pJ9.2pJ$.3X.X.3X73.8pB32.9pC110.5pF2.5pF27.3pG4.3pG30.pH.3pH.pH34.2pI.pI.2pI33.pJ2.3pJ2.pJ$2.7X74.8pB32.9pC31.pD4.pD71.2pF12.2pF25.pG.pG4.pG.pG69.2pI7.2pI29.2pJ9.2pJ$2.2X.X.2X73.10pB31.3pC.pC.3pC110.pF2.6pF2.pF29.pG.2pG.pG73.2pI3.2pI33.3pJ.pJ.3pJ$4.3X76.8pB32.pC2.3pC2.pC109.pF12.pF105.2pI7.2pI$83.8pB151.12pF108.2pI3.2pI$85.4pB$244.2pF4.2pF111.5pI2$246.4pF113.5pI!
2c/n spaceships project

Current priorities: see here
muzik

Posts: 2612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!)

muzik wrote:1.3 is here, mercilessly stealing a smaller c/13 from this rule.

Thanks for doing all this work. It makes for a really interesting sample pattern. Golly 3.0 should have at least one mashup rule example, and this is down under 15K in ZIP form now, pattern and all:

unit-fraction-orthogonal-spaceships.zip
collection extended to c/150, with Calcyman's hyperbolic stunt-flying trick re-created

One 10-cell spacing discrepancy had crept in, over toward the right side -- should be fixed in the attachment. Unfortunately at high periods the even-period spaceships get too long to stay out of the way of the wide c/2 and c/5, so I had to adapt the hyperbolic spaceship stunt pattern a little to avoid those collisions. The c/53 through c/141 ships have been included in their appropriate spots in the long row at the bottom, but the stunt flying is mostly done with four copies of the c/1 through c/50 lineup.
dvgrn
Moderator

Posts: 4033
Joined: May 17th, 2009, 11:00 pm

### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!)

I have found smaller c/9 and c/21 ships posted on the sssss thread, which I can't yet add to the rule due to lack of access to a desktop computer, so you might want to wait a couple days unless you're in a hurry.

If someone's willing to use isotrop.py to generate the ruletables for these, though, I could update this in a matter of minutes:

x = 2, y = 3, rule = B2e3-cjy4ai/S23cqr4o$2o$o!

x = 2, y = 3, rule = B2ek3-cjy4ai/S23cqr4o$2o$o!
2c/n spaceships project

Current priorities: see here
muzik

Posts: 2612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!)

...and here we have a ruletable that can simulate any "perfect" speed ever, using a set of 4 different isotropic rules, taking up a laughably much smaller amount of space than previously.

@RULE RainbowASOv2.01@TABLEn_states:5neighborhood:Mooresymmetries:rotate4reflectvar l=1var u=2var v=3var pp=4var a={0,1,2,3,4}var b=avar d=avar e=avar f=avar g=avar i=avar j=avar k=a#life0,l,l,l,0,0,0,0,0,l0,l,l,0,l,0,0,0,0,l0,l,l,0,0,l,0,0,0,l0,l,l,0,0,0,l,0,0,l0,l,l,0,0,0,0,l,0,l0,l,l,0,0,0,0,0,l,l0,l,0,l,0,l,0,0,0,l0,l,0,l,0,0,l,0,0,l0,l,0,0,l,0,l,0,0,l0,0,l,0,l,0,l,0,0,ll,l,l,0,0,0,0,0,0,ll,l,0,l,0,0,0,0,0,ll,l,0,0,l,0,0,0,0,ll,l,0,0,0,l,0,0,0,ll,0,l,0,l,0,0,0,0,ll,0,l,0,0,l,0,0,0,ll,0,l,0,0,0,l,0,0,ll,l,l,l,0,0,0,0,0,ll,l,l,0,l,0,0,0,0,ll,l,l,0,0,l,0,0,0,ll,l,l,0,0,0,l,0,0,ll,l,l,0,0,0,0,l,0,ll,l,l,0,0,0,0,0,l,ll,l,0,l,0,l,0,0,0,ll,l,0,l,0,0,l,0,0,ll,l,0,0,l,0,l,0,0,ll,0,l,0,l,0,l,0,0,l#universal-odd0,0,u,0,u,0,0,0,0,u0,u,u,u,0,0,0,0,0,u0,u,u,0,0,0,0,u,0,u0,u,u,u,0,u,0,0,0,u0,u,u,0,u,0,0,0,u,u0,u,u,0,0,u,0,0,u,u0,u,u,u,u,u,0,0,0,u0,u,u,u,u,u,0,u,0,u0,u,u,u,u,u,u,u,0,u0,u,u,u,u,u,u,0,u,u0,u,u,u,u,u,u,u,u,uu,0,u,0,0,0,0,0,0,uu,u,u,0,0,0,0,0,0,uu,u,0,u,0,0,0,0,0,uu,u,0,0,u,0,0,0,0,uu,u,0,0,0,u,0,0,0,uu,0,u,0,u,0,0,0,0,uu,0,u,0,0,0,u,0,0,uu,u,u,0,u,0,0,0,0,uu,u,u,0,0,u,0,0,0,uu,u,0,u,0,u,0,0,0,uu,u,u,u,u,0,0,0,0,uu,u,u,0,0,u,0,0,u,uu,u,0,u,0,u,0,u,0,uu,u,u,u,u,0,u,0,0,uu,u,u,u,u,0,0,u,0,uu,u,u,u,u,0,0,0,u,uu,u,u,u,0,u,0,u,0,uu,u,u,0,u,u,u,0,0,uu,u,u,0,u,u,0,u,0,uu,u,u,0,u,0,u,u,0,uu,u,u,0,u,0,u,0,u,uu,u,u,u,u,u,u,0,0,uu,u,u,u,u,u,0,u,0,uu,u,u,u,u,0,u,u,0,uu,u,u,u,u,0,u,0,u,uu,u,u,u,0,u,u,u,0,uu,u,u,0,u,u,u,0,u,uu,u,u,u,u,u,u,u,0,uu,u,u,u,u,u,u,0,u,u#universal-even0,0,v,0,v,0,0,0,0,v0,v,v,v,0,0,0,0,0,v0,v,0,v,0,v,0,0,0,v0,v,v,v,v,0,0,0,0,v0,v,v,0,v,v,0,0,0,v0,v,v,v,v,v,0,0,0,v0,v,v,v,v,0,v,0,0,v0,v,v,v,v,0,0,v,0,v0,v,v,v,v,0,0,0,v,v0,v,v,v,0,v,v,0,0,v0,v,v,v,0,v,0,v,0,v0,v,v,0,v,v,v,0,0,v0,v,v,0,v,v,0,v,0,v0,v,v,0,v,0,v,v,0,v0,v,v,0,v,0,v,0,v,v0,v,v,v,v,v,0,v,0,vv,v,v,0,0,0,0,0,0,vv,v,0,v,0,0,0,0,0,vv,v,0,0,0,v,0,0,0,vv,0,v,0,v,0,0,0,0,vv,v,v,v,0,0,0,0,0,vv,v,v,0,0,v,0,0,0,vv,v,v,0,0,0,0,v,0,vv,v,v,0,0,0,0,0,v,vv,v,0,v,0,0,v,0,0,vv,v,0,0,v,0,v,0,0,vv,0,v,0,v,0,v,0,0,vv,v,v,v,v,0,0,0,0,vv,v,v,v,0,v,0,0,0,vv,v,v,v,0,0,v,0,0,vv,v,v,0,v,v,0,0,0,vv,v,v,0,v,0,v,0,0,vv,v,v,0,v,0,0,v,0,vv,v,v,0,v,0,0,0,v,vv,v,v,0,0,v,v,0,0,vv,v,v,0,0,v,0,v,0,vv,v,v,0,0,v,0,0,v,vv,v,v,0,0,0,v,v,0,vv,v,0,v,0,v,0,v,0,vv,0,v,0,v,0,v,0,v,v#photons0,pp,pp,0,0,0,0,0,0,pp0,pp,pp,0,0,pp,0,0,0,pp#deatha,b,d,e,f,g,i,j,k,0@COLORS0 0 0 01 255 255 2552 170 170 1703 85 85 854 255 0 0

Our next courses of action:

- Isotropic rules that can simulate all semiperfect (2c/n) speeds
- Isotropic rules that can simulate all 3c/n, 4c/n, etc. orthogonal speeds
- Can diagonal speeds be infinitely extended in this way? Here's something that might be a start:
drc wrote:EDIT2: Maybe a bit too weird:
x = 6, y = 4, rule = B2-a3-ai4-a5-a678/S1235-i6782bo$b3o$3ob2o$bo2b2o! - Same goes for knightwise, camelwise, giraffewise, ibiswise, flamingowise, etc. - How about improving the rules we currently have for the perfect speeds, so that ships of speeds c/2, c/3 and c/5 can be created in a systematic way? 2c/n spaceships project Current priorities: see here muzik Posts: 2612 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) I was working on an isotropic version of my All_Speeds rule, or do you want two state rules? I don't think any 2-state rule has infinite directions that are not done with self-constructing spaceships. Things to work on: - An Isotropic version of All_Speeds - Find more ships in B2ek3-ajny4ajqr5a/S02ack3ackny4aq5y - Find a (3,1)c/5 ship in a Non-totalistic rule (someone please search the rules) AforAmpere Posts: 289 Joined: July 1st, 2016, 3:58 pm ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) I'm pretty much meaning that every state is an isotropic rule in its own right and does not interact with any other states. 2c/n spaceships project Current priorities: see here muzik Posts: 2612 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) muzik wrote:...and here we have a ruletable that can simulate any "perfect" speed ever, using a set of 4 different isotropic rules, taking up a laughably much smaller amount of space than previously. Well, here's a 4-state version: @RULE RainbowASOv2.01+0.1i@TABLEn_states:4neighborhood:Mooresymmetries:rotate4reflectvar l=1var u=2var v=3var a={0,1,2,3}var b=avar d=avar e=avar f=avar g=avar i=avar j=avar k=a#life0,l,l,l,0,0,0,0,0,l0,l,l,0,l,0,0,0,0,l0,l,l,0,0,l,0,0,0,l0,l,l,0,0,0,l,0,0,l0,l,l,0,0,0,0,l,0,l0,l,l,0,0,0,0,0,l,l0,l,0,l,0,l,0,0,0,l0,l,0,l,0,0,l,0,0,l0,l,0,0,l,0,l,0,0,l0,0,l,0,l,0,l,0,0,ll,l,l,0,0,0,0,0,0,ll,l,0,l,0,0,0,0,0,ll,l,0,0,l,0,0,0,0,ll,l,0,0,0,l,0,0,0,ll,0,l,0,l,0,0,0,0,ll,0,l,0,0,l,0,0,0,ll,0,l,0,0,0,l,0,0,ll,l,l,l,0,0,0,0,0,ll,l,l,0,l,0,0,0,0,ll,l,l,0,0,l,0,0,0,ll,l,l,0,0,0,l,0,0,ll,l,l,0,0,0,0,l,0,ll,l,l,0,0,0,0,0,l,ll,l,0,l,0,l,0,0,0,ll,l,0,l,0,0,l,0,0,ll,l,0,0,l,0,l,0,0,ll,0,l,0,l,0,l,0,0,l#universal-odd0,0,u,0,u,0,0,0,0,u0,u,u,u,0,0,0,0,0,u0,u,u,0,0,0,0,u,0,u0,u,u,u,0,u,0,0,0,u0,u,u,0,u,0,0,0,u,u0,u,u,0,0,u,0,0,u,u0,u,u,u,u,u,0,0,0,u0,u,u,u,u,u,0,u,0,u0,u,u,u,u,u,u,u,0,u0,u,u,u,u,u,u,0,u,u0,u,u,u,u,u,u,u,u,uu,0,u,0,0,0,0,0,0,uu,u,u,0,0,0,0,0,0,uu,u,0,u,0,0,0,0,0,uu,u,0,0,u,0,0,0,0,uu,u,0,0,0,u,0,0,0,uu,0,u,0,u,0,0,0,0,uu,0,u,0,0,0,u,0,0,uu,u,u,0,u,0,0,0,0,uu,u,u,0,0,u,0,0,0,uu,u,0,u,0,u,0,0,0,uu,u,u,u,u,0,0,0,0,uu,u,u,0,0,u,0,0,u,uu,u,0,u,0,u,0,u,0,uu,u,u,u,u,0,u,0,0,uu,u,u,u,u,0,0,u,0,uu,u,u,u,u,0,0,0,u,uu,u,u,u,0,u,0,u,0,uu,u,u,0,u,u,u,0,0,uu,u,u,0,u,u,0,u,0,uu,u,u,0,u,0,u,u,0,uu,u,u,0,u,0,u,0,u,uu,u,u,u,u,u,u,0,0,uu,u,u,u,u,u,0,u,0,uu,u,u,u,u,0,u,u,0,uu,u,u,u,u,0,u,0,u,uu,u,u,u,0,u,u,u,0,uu,u,u,0,u,u,u,0,u,uu,u,u,u,u,u,u,u,0,uu,u,u,u,u,u,u,0,u,u#universal-even0,0,v,0,v,0,0,0,0,v0,v,v,v,0,0,0,0,0,v0,v,0,v,0,v,0,0,0,v0,v,v,v,v,0,0,0,0,v0,v,v,0,v,v,0,0,0,v0,v,v,v,v,v,0,0,0,v0,v,v,v,v,0,v,0,0,v0,v,v,v,v,0,0,v,0,v0,v,v,v,v,0,0,0,v,v0,v,v,v,0,v,v,0,0,v0,v,v,v,0,v,0,v,0,v0,v,v,0,v,v,v,0,0,v0,v,v,0,v,v,0,v,0,v0,v,v,0,v,0,v,v,0,v0,v,v,0,v,0,v,0,v,v0,v,v,v,v,v,0,v,0,vv,v,v,0,0,0,0,0,0,vv,v,0,v,0,0,0,0,0,vv,v,0,0,0,v,0,0,0,vv,0,v,0,v,0,0,0,0,vv,v,v,v,0,0,0,0,0,vv,v,v,0,0,v,0,0,0,vv,v,v,0,0,0,0,v,0,vv,v,v,0,0,0,0,0,v,vv,v,0,v,0,0,v,0,0,vv,v,0,0,v,0,v,0,0,vv,0,v,0,v,0,v,0,0,vv,v,v,v,v,0,0,0,0,vv,v,v,v,0,v,0,0,0,vv,v,v,v,0,0,v,0,0,vv,v,v,0,v,v,0,0,0,vv,v,v,0,v,0,v,0,0,vv,v,v,0,v,0,0,v,0,vv,v,v,0,v,0,0,0,v,vv,v,v,0,0,v,v,0,0,vv,v,v,0,0,v,0,v,0,vv,v,v,0,0,v,0,0,v,vv,v,v,0,0,0,v,v,0,vv,v,0,v,0,v,0,v,0,vv,0,v,0,v,0,v,0,v,v#photons0,1,2,0,0,0,0,0,0,10,0,1,2,1,0,0,0,0,20,0,1,2,1,0,0,1,0,1#deatha,b,d,e,f,g,i,j,k,0@COLORS0 0 0 01 255 255 2552 170 170 1703 85 85 854 255 0 0 x = 146, y = 10, rule = RainbowASOv2.01+1.0i85.A7.A$79.2A.A.A.2A3.2A.A.A.2A$10.3A15.3A45.3A.A.3A9.3A.A.3A5.3C4.B.B4.3C4.B.B4.3C4.B.B$9.A3.A13.A3.A15.A.2A.3A11.3C7.A3.A.A5.A.A5.A.A3.A6.C6.B6.C6.B6.C6.B$ABA5.2A4.A11.A4.2A13.2A.2A4.2A.A8.C12.2A6.A.A6.2A10.C6.B6.C6.B6.C6.B$7.A.A.2A.2A3.3A3.2A.2A.A.A11.A2.A.A2.A3.3A7.C9.2A9.A.A9.2A7.C6.B6.C6.B6.C6.B$.A4.2A.A4.A.2A.3A.2A.A4.A.2A11.A5.A3.A3.A5.C.C8.2A.2A15.2A.2A6.C.C4.3B5.C6.B6.C6.B$5.A4.A3.A4.A.A4.A3.A4.A23.A7.C13.A15.A11.C12.C.C4.3B5.C6.B$17.A5.A99.C12.C.C4.3B$5.2A7.2A9.2A7.2A101.C!

But I'm sure that's not at all what you were intending.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

A for awesome

Posts: 1442
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!)

Definitely not, but still definitely interesting:

x = 18, y = 6, rule = RainbowASOv2.01+0.1iABA2.ABA2.ABA2.ABA2$3.2A3.2A3.2A$4.A3.2A3.A$7.A2.A$7.A2.A!
2c/n spaceships project

Current priorities: see here
muzik

Posts: 2612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

x = 7, y = 5, rule = RainbowASOv2.01+0.1iABA.ABA2$.A3.A$3A.3A$2.A.A! x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce A for awesome Posts: 1442 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) x = 33, y = 4, rule = RainbowASOv2.01+0.1iABA15.ABA9.ABA2$.A17.A11.A$.2A27.3A! Everyone, please stop posting B/S about CA x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

Saka

Posts: 2267
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!)

Huh. I had a rule like this but with Life and DotLife.
x = 12, y = 7, rule = RainbowASOv2.01+0.1iA$B$A2$9.A.A$9.B.B$9.A.A! This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.) Current rule interest: B2ce3-ir4a5y/S2-c3-y drc Posts: 1665 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: Perfect Orthogonal Speeds Rule Mashup (simulates c to c/50!) Currently working on integrating semiperfect speeds to the rule. Since we font have a systematic spaceship series for 2c/odd, this will bump the size up a bit until one comes. As to not get it too big, 2c/even will be left out and other spaceships can be used to simulate these instead until someone finds out a rule with a true infinite series of 2c/even speeds. I need sleep. @RULE RainbowASOv2.03@TABLEn_states:16neighborhood:Mooresymmetries:rotate4reflectvar l=1var u=2var v=3var aa=4var ab=5var ac=6var ad=7var ae=8var af=9var ag=10var ah=11var ai=12var aj=13var ak=14var al=15var a={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}var b=avar d=avar e=avar f=avar g=avar i=avar j=avar 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0 0 01 255 255 2552 170 170 1703 85 85 854 255 0 05 0 255 06 0 0 2557 0 255 2558 255 0 2559 255 255 010 255 127 011 127 255 012 255 0 12713 127 0 25514 0 255 12715 0 127 255 x = 1164, y = 58, rule = 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2c/n spaceships project

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muzik

Posts: 2612
Joined: January 28th, 2016, 2:47 pm
Location: Scotland