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## Free Star (0345/2/10)

For discussion of other cellular automata.

### Free Star (0345/2/10)

This rule is a combination of "Live Free or Die" and "Star Wars".

Here are some interesting patterns:

Some oscillators:

x = 3, y = 3, rule = 0345/2/10A$.A$2.A!

x = 5, y = 5, rule = 0345/2/104.A2$A$.A$2.A! x = 5, y = 5, rule = 0345/2/10.BA$C.A$D3A$E.A.I$.FGH! x = 4, y = 4, rule = 0345/2/10GHA$D2AH$F2AC$CD.B!

A c/2 spaceship:

x = 5, y = 3, rule = 0345/2/10HFDBA$.HFDB$HFDBA!

Guns:

x = 5, y = 5, rule = 0345/2/10GHDC$D2A.B$F4A$E.A.A$.DCB!

x = 5, y = 5, rule = 0345/2/10.AIH$H2A.G$B3A$A.A.G$2.IH!

A sample puffer:

x = 7, y = 18, rule = 0345/2/10A3$.2A$A2I$I$3.IHG$3.G.GI$AC2GH.H$C2E2H2G$.CGDBCF$BC.BFCE$.2ACD.D$AB.2D2C$2.C2A.B$3.AB2A$2.3A$3.2A! An interesting "growing puffer": x = 8, y = 28, rule = 0345/2/103.A$3.2IH$3.EGF$3.FED$3.ACB$2.IBA$4.A$2.G2A$2.H.A$2.E2A$2.F.A$2.C2A$2ID.A$2H3A$2GB.A$2FI2A$2E2.A$2DG2A$2CHIA.2I$2BE2A.2H$2AFGA.2G$2.C2A.2F$2.DEA.2E$2.3A.2D$2.BCA.2C$3.2A.2B$2.3A.2A$3.2A!

A breeder:

x = 5, y = 5, rule = 0345/2/10DECB$3A.A$C3A$B.A.I$.A.IA!

Another interesting pattern:

x = 15, y = 6, rule = 0345/2/1014.A2$IHGFEDCBA$IHGFEDCBA2$13.A! You might also want to visit this thread. There you can find a similar (but a bit more explosive) rule. There are 10 types of people in the world: those who understand binary and those who don't. Alexey_Nigin Posts: 323 Joined: August 4th, 2014, 12:33 pm Location: Ann Arbor, MI ### Re: Free Star (0345/2/10) Some "tractor beams": x = 92, y = 23, rule = 0345/2/10CD.I$.2A.H$B3AGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.I$A.A.GFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IA$2.IH4$CD.I$.2A.H$B3AGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFDC$A.A.GFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFCD$2.IH70.EFACD$74.AEF4$BCA$.2A.IECA5.IGECA5.IGECA5.IGECA5.IGECA5.IGECA5.IGECA5.IGECA5.IGEDCBA$D3A2GECA5.IGECA5.IGECA5.IGECA5.IGECA5.IGECA5.IGECA5.IGECA5.IGEDCBA$C.A.IECA5.IGECA5.IGECA5.IGECA5.IGECA5.IGECA5.IGECA5.IGECA5.IG.FEDCBA$.BA81.FGFEDCBA$84.AFG! Edit: 2c/3 signal: x = 71, y = 5, rule = 0345/2/102.AI2.ACD3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A$2.I.I.CDC$A2.IGFDCA$4.FGF2.A$4.AFG3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A! C signal: x = 33, y = 4, rule = 0345/2/10.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A$33A$.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A$IHGFEDCBA!
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: 1862
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

### Re: Free Star (0345/2/10)

An interesting gun produces rare 2c/3 spaceships:

x = 19, y = 5, rule = 0345/2/10BCA13.ACB$.2A.I9.I.2A$D3A11.3AD$C.A.I9.I.A.C$.BA13.AB!

Here is a sawtooth (it uses one of the tractor beams created by Aidan F. Pierce):

x = 11, y = 5, rule = 0345/2/10.CBA$D.A3.HFDBA$E3A3.HFDB$.2A.A.HFDBA$IECB!

I'll publish more patterns soon, so stay tuned.
There are 10 types of people in the world: those who understand binary and those who don't. Alexey_Nigin

Posts: 323
Joined: August 4th, 2014, 12:33 pm
Location: Ann Arbor, MI

### Re: Free Star (0345/2/10)

This is a very cool rule. Here's a pretty frightening puffer/breeder of ever-increasing complexity.
x = 9, y = 13, rule = 0345/2/10I2A4.GF$H.2A3.FE$G2A.GHFED$F.2A2IHDC$E2A.EFDCB$D.2A2GFBA$C2A.CDBA$B.2A2ED$3A.ABA$2.2A2CB$2.A.2A$3.4A$4.2A! lukebradford

Posts: 100
Joined: October 11th, 2013, 8:07 pm
Location: Cambridge, MA

### Re: Free Star (0345/2/10)

Oscillators like this one:

x = 11, y = 11, rule = 0345/2/10DCA5.ACD$CDC5.CDC$ACD5.DCA2$4.DCA$4.CDC$4.ACD2$ACD5.DCA$CDC5.CDC$DCA5.ACD!

occur in several Generations rules. Some of the best examples can be found in rule 03467/25/6 which is briefly discussed here:

http://www.conwaylife.com/forums/viewtopic.php?f=11&t=1015&p=7395#p7395

Brian Prentice
bprentice

Posts: 555
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Free Star (0345/2/10)

Luke Bradford wrote:This is a very cool rule.

Thank you!

Here is a nice gun:

x = 16, y = 5, rule = 0345/2/10GHDC8.CDHG$D2A.B6.B.2AD$F4A6.4AF$E.A.A6.A.A.E$.DCB8.BCD!

A couple of simple reactions:

x = 11, y = 3, rule = 0345/2/10HFDBA$.HFDB5.A$HFDBA!

x = 15, y = 14, rule = 0345/2/103.IHGFEDCBA$3.IHGFEDCBA$.IHGFEDCBA$IHGFEDCBA2$13.2A$13.2B$13.2C$13.2D$13.2E$13.2F$13.2G$13.2H$13.2I!
There are 10 types of people in the world: those who understand binary and those who don't. Alexey_Nigin

Posts: 323
Joined: August 4th, 2014, 12:33 pm
Location: Ann Arbor, MI

### Re: Free Star (0345/2/10)

Interesting wickstretcher for which there is probably a better end stabilization:
x = 22, y = 17, rule = 0345/2/105.A$4.3A$3.2A.2A$2.2A3.2A$.2A.A.A.2A$2.7A2$3.3A.A$2.4A$.2A$2A.2A$.4A.A2.A3.A3.A$2.A9.G.G.C.C.A$5.A.2A.3AH3AD4A$7.4A.3AF3AB2A$8.A.I.I.E.E.A.A$11.A3.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: 1862 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### Re: Free Star (0345/2/10) A for awesome wrote:Interesting wickstretcher for which there is probably a better end stabilization: x = 22, y = 17, rule = 0345/2/105.A$4.3A$3.2A.2A$2.2A3.2A$.2A.A.A.2A$2.7A2$3.3A.A$2.4A$.2A$2A.2A$.4A.A2.A3.A3.A$2.A9.G.G.C.C.A$5.A.2A.3AH3AD4A$7.4A.3AF3AB2A$8.A.I.I.E.E.A.A$11.A3.A!

Yes there most certainly is:
x = 16, y = 6, rule = 0345/2/103.A3.A3.A$6.G.G.C.C.A$2.5AH3AD4A$A.3A.3AF3AB2A$4.I.I.E.E.A.A$2.A2.A3.A! flipper77 Posts: 197 Joined: October 24th, 2010, 3:25 am Location: Spokane, WA ### Re: Free Star (0345/2/10) flipper77 wrote:Yes there most certainly is: [RLE for an end stabilization in which 7 cells do not have the state they had in the unstabilized wickstretcher] Here is a 6-cell end stabilization (that is, 6 cells do not have the state they had in the unstabilized wickstretcher). x = 17, y = 6, rule = 0345/2/102.A2.A2.A3.A$7.G.G.C.C.A$A.2A.3AH3AD4A$2.4A.3AF3AB2A$3.A.I.I.E.E.A.A$6.A3.A!

Alexey_Nigin wrote:Here is a nice gun:

Here is a smaller c/2 ship gun.
x = 7, y = 5, rule = 0345/2/103.A$2.3A$.2A.2A$2A.A.2A$.5A!
c0b0p0

Posts: 645
Joined: February 26th, 2014, 4:48 pm

### Re: Free Star (0345/2/10)

Here's a cool growing rake/spacefiller:
x = 15, y = 62, rule = 0345/2/1010.2A$9.3A.2A$10.2A.2B$9.BCA.2C$9.3A.2D$9.DEA.2E$9.C2A.2F$7.2AFGA.2G$7.2BE2A.2H$7.2CHIA.2I$7.2DG2A$7.2E2.A$7.2FI2A$7.2GB.A$7.2H3A$7.2ID.A$9.C2A$3.2A4.F.A$2.4A3.E2A$3.2A4.H.A$2.B2CB3.G2A$2.A2BA5.A$2.D2ED3.I2A$.AB2DBA2.B.A$ABF2GFB3.2A$BCD2FDC2BD.A$CDH2IHDCAC2A$DEF2HFDC.F.A$EF4.F3.2A$FGH2.HG2FH.A$GH4.HGAG2A$HI4.HG3.A$I9.2A$9.A.A$8.C.2A$7.AC2.A$7.2BD2A$6.A.AE.A$6.ABGD2A$5.ACDGC.A$5.CD2FH2A$5.DE2CI.A$6.EF.H2A$5.EGH.G.A$5.GH2.B2A$5.HI2GC.A$6.I2.B2A$5.I5.A$9.F2A$9.G.A$9.F2A$9.D.A$10.2A$9.A.A$10.2A$9.H.A$9.D2A$8.AE.A$8.ADABC$9.BCFE$10.IHG$10.H.I! lukebradford Posts: 100 Joined: October 11th, 2013, 8:07 pm Location: Cambridge, MA ### Re: Free Star (0345/2/10) c0b0p0 wrote: Alexey_Nigin wrote:Here is a nice gun: Here is a smaller c/2 ship gun. x = 7, y = 5, rule = 0345/2/103.A$2.3A$.2A.2A$2A.A.2A$.5A! My gun actually produces lightspeed ships... As for c/2 spaceship guns, a 5x5 example is contained in my first post. However, your gun is in some sense neater - it is perfectly symmetric and consists only of state-1 cells. There are 10 types of people in the world: those who understand binary and those who don't. Alexey_Nigin Posts: 323 Joined: August 4th, 2014, 12:33 pm Location: Ann Arbor, MI ### Re: Free Star (0345/2/10) I'm surprised at the lack of interest in this rule. Some more guns: x = 5, y = 84, rule = 0345/2/102.HCB$.3AH$.G2AC$.FBFE$2.2D$2.2C$2.2B$2.2A12$2.2I$2.2H$2.2G$2.2F$2.2E$2.2D$2.2C$2.2B$2.2A14$3.A5$.2A$.2B$.2C$.2D$.2E$.2F$.2G$.2H$.2I12$.2A$.2B$.2C$.2D$.2E$.2F$.2G$.2H$.2I6$EFBF$C2AG$H3A$BCH!

x = 26, y = 16, rule = 0345/2/1023.HCB$22.3AH$22.G2AC$22.FBFE$23.2D$23.2C$23.2B$23.2A6$.A2.A2.A2.A2.A2.A2.A2.A$24A$.A2.A2.A2.A2.A2.A2.A2.A!

x = 28, y = 16, rule = 0345/2/10BCH22.HCB$H3A20.3AH$C2AG20.G2AC$EFBF20.FBFE$.2D22.2D$.2C22.2C$.2B22.2B$.2A22.2A6$3.A2.A2.A2.A2.A2.A2.A2.A$2.24A$3.A2.A2.A2.A2.A2.A2.A2.A!

x = 13, y = 30, rule = 0345/2/1011.A$10.3A$11.A$11.A$10.3A$11.A$11.A$10.3A$11.A$11.A$10.3A$11.A$ABHG7.A$H2A.F5.3A$.3AEDCBA2.A$I.A.EDCBA2.A$.HGF6.3A$11.A$11.A$10.3A$11.A$11.A$10.3A$11.A$11.A$10.3A$11.A$11.A$10.3A$11.A! x = 28, y = 6, rule = 0345/2/10.A2.A2.A2.A2.A2.A2.A2.A$24A$.A2.A2.A2.A2.A2.A2.A2.A$13.ABCDEFGHI4.A$25.3A$26.A!

and oscillators:

x = 88, y = 59, rule = 0345/2/10A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A2$A28.A2$4.A28.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A2$AHI26.AHI$HIH26.HIH$IHA26.IHA3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A!

x = 177, y = 116, rule = 0345/2/1016.GE.I57.GE.I$16.H2AE57.H2AE$16.D2A58.D2A$16.CICB57.CICB3$17.2I59.2I$17.2H59.2H$17.2G59.2G$17.2F59.2F$17.2E19.A39.2E79.A$17.2D18.3A38.2D78.3A$17.2C19.A39.2C79.A$17.2B59.2B$17.2A59.2A2$11.A6.IHGFEDCBA11.A13.CDHG16.A6.IHGFEDCBA11.IHGFEDCBA11.IHGFEDCBA11.IHGFEDCBA11.A13.CDHG$10.3A3.A.IHGFEDCBA14.ABCDEFGHI2.I2AE15.3A3.A.IHGFEDCBA11.IHGFEDCBA11.IHGFEDCBA11.IHGFEDCBA14.ABCDEFGHI2.I2AE$11.A26.2I.ABCDEFGHI2.C2A17.A86.2I.ABCDEFGHI2.C2A$38.2H12.B.EI103.2H12.B.EI$38.2G119.2G$38.2F119.2F$38.2E119.2E$38.2D119.2D$38.2C119.2C$38.2B119.2B$38.2A119.2A3$16.2A59.2A$16.2B59.2B$16.2C59.2C$16.2D59.2D$16.2E59.2E$16.2F59.2F$16.2G59.2G$IE.B12.2H59.2H$.2AC2.IHGFEDCBA.2I26.A32.2I$E2AI2.IHGFEDCBA14.ABCDEFGHI.A3.3A113.2I$GHDC13.A11.ABCDEFGHI6.A114.2H$159.2G$37.2A120.2F$37.2B120.2E$17.A19.2C120.2D$16.3A18.2D120.2C$17.A19.2E120.2B$37.2F120.2A$37.2G$37.2H$37.2I38.2A$77.2B$77.2C$36.BCIC37.2D$37.2AD37.2E$36.E2AH37.2F$36.I.EG37.2G$77.2H$77.2I$159.2I$159.2H$159.2G$159.2F$159.2E$159.2D$159.2C$159.2B$159.2A3$77.2A$77.2B$77.2C$77.2D$77.2E$77.2F$77.2G$77.2H$77.2I$159.2I$159.2H$159.2G$159.2F$159.2E$159.2D$159.2C$159.2B$159.2A3$77.2A$77.2B$77.2C$77.2D$77.2E$77.2F$77.2G$61.IE.B12.2H$62.2AC2.IHGFEDCBA.2I86.A$61.E2AI2.IHGFEDCBA14.ABCDEFGHI11.ABCDEFGHI11.ABCDEFGHI11.ABCDEFGHI.A3.3A$61.GHDC13.A11.ABCDEFGHI11.ABCDEFGHI11.ABCDEFGHI11.ABCDEFGHI6.A2$158.2A$158.2B$78.A79.2C$77.3A78.2D$78.A79.2E$158.2F$158.2G$158.2H$158.2I3$157.BCIC$158.2AD$157.E2AH$157.I.EG! x = 26, y = 49, rule = 0345/2/109.IHGFEDCBA$2.A2.A2.A2.A2.A2.A2.A2.A$.24A$2.A2.A2.A2.A2.A2.A2.A3.2A$24.A$24.A$23.3A$24.A$24.A$23.3A$24.A$24.A$23.3A$24.A$24.A$23.3A$24.A$24.A$23.3A$24.A$24.A$23.3A$24.A$24.A$2.A2.A2.A2.A2.A2.A2.A3.2A$.24A$2A3.A2.A2.A2.A2.A2.A2.A$.A$.A$3A$.A$.A$3A$.A$.A$3A$.A$.A$3A$.A$.A$3A$.A$.A$3A$.A$.A$3A$.A! Brian Prentice bprentice Posts: 555 Joined: September 10th, 2009, 6:20 pm Location: Coos Bay, Oregon ### Re: Free Star (0345/2/10) A few more guns: x = 32, y = 55, rule = 0345/2/108.IHGFEDCBA$.A2.A2.A2.A2.A2.A2.A2.A$24A$.A2.A2.A2.A2.A2.A2.A2.A$26.A2.A$25.6A$26.A3.2A$30.A$30.A$29.3A$30.A13$8.IHGFEDCBA$.A2.A2.A2.A2.A2.A2.A2.A$24A$.A2.A2.A2.A2.A2.A2.A2.A$26.A2.A$25.6A$26.A3.2A$30.A$30.A$29.3A$30.A$30.A$29.3A$30.A$30.A$29.3A$30.A$30.A$29.3A$30.A$30.A$29.3A$30.A$30.A$29.3A$30.A$30.A$29.3A$30.A$30.A$29.3A$30.A! x = 50, y = 23, rule = 0345/2/1030.A$29.3A$30.A11$8.IHGFEDCBA$.A2.A2.A2.A2.A2.A2.A2.A$24A$.A2.A2.A2.A2.A2.A2.A2.A$26.A21.A$25.3A19.3A$26.A21.A$48.A$47.3A$48.A! x = 89, y = 14, rule = 0345/2/105.IHGFEDCBA$.A2.A2.A2.A2.A2.A2.A2.A$24A$.A2.A2.A2.A2.A2.A2.A2.A35.A$26.A2.A27.3A$25.6A27.A$26.A3.2A26.A$30.A26.2A3.A$30.A27.6A$29.3A27.A2.A$30.A35.A2.A2.A2.A2.A2.A2.A2.A$65.24A$66.A2.A2.A2.A2.A2.A2.A2.A$75.ABCDEFGHI!

x = 32, y = 15, rule = 0345/2/108.IHGFEDCBA$.A2.A2.A2.A2.A2.A2.A2.A$24A$.A2.A2.A2.A2.A2.A2.A2.A$26.A2.A$25.6A$26.A3.2A$30.A$30.A$29.3A$30.A$30.A$26.A3.2A$25.6A$26.A2.A!

x = 33, y = 14, rule = 0345/2/10.A5.A2.A2.A2.A2.A2.A$24A$.A2.A2.A2.A2.A2.A2.A2.A$26.A2.A$25.6A.A$26.A3.2AB$30.A.C$30.A.D$29.3AE$30.A.F$30.A.G$26.A3.2AH$25.6A.I$26.A2.A! x = 23, y = 10, rule = 0345/2/1010.F.F$9.G.A.G$8.GH3AHG$7.F.A.A.A.F$6.B.2A3.2A.B$3.GHCH2A.E.E.2AHCHG$ABC3A2.A2.A2.A2.3ACBA$ABCG2A.9A.2AGCBA$3.DECH.A2.A2.A.HCED$7.GFED.DEFG!

x = 5, y = 6, rule = 0345/2/102.A$.3A$2A.2A$.A.A$.3A$2.A! Brian Prentice bprentice Posts: 555 Joined: September 10th, 2009, 6:20 pm Location: Coos Bay, Oregon ### Re: Free Star (0345/2/10) A breeder that fires growing spaceships: x = 15, y = 15, rule = 0345/2/108.DCB$4.2A.E.A.A$3.A2BDF3A$2.AB2CDH2A.I$.ABCDFG3.B$.ABCFGI.A.C$2.2DGIE3ADF$.EFH2.A.A.AG$D.2A.3A.2A$C3A2.A.A.A.CB$B.A.BCD3A.2A.A$.A.I2.FG2.A.2A$9.C3A.I$9.B.A$10.A.I! 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: 1862 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### Re: Free Star (0345/2/10) Five more guns: x = 12, y = 26, rule = 0345/2/109.HCB$8.3AH$8.G2AC$8.FBFE$9.2D$.A7.2C$3A6.2B$.A7.2A$.A$2A3.A2.A$.9A$2.A2.A2.A3$2.A2.A2.A$.9A$2A3.A2.A$.A$.A7.2A$3A6.2B$.A7.2C$9.2D$8.FBFE$8.G2AC$8.3AH$9.HCB!

x = 7, y = 23, rule = 0345/2/102.A2.A$.6A$.A3.A$2A$.A$.2A$.A$.A$3A$.A$.A$3A$.A$.A$3A$.A$.A$.2A$.A$2A$.A3.A$.6A$2.A2.A!

x = 35, y = 23, rule = 0345/2/102.A2.A23.A2.A$.6A21.6A$.A3.A23.A3.A$2A31.2A$.A31.A$.2A29.2A$.A31.A$.A31.A$3A29.3A$.A31.A$.A31.A$3A29.3A$.A31.A$.A31.A$3A29.3A$.A31.A$.A31.A$.2A29.2A$.A31.A$2A31.2A$.A3.A23.A3.A$.6A21.6A$2.A2.A23.A2.A!

x = 55, y = 97, rule = 0345/2/1045.A$44.3A$45.A5$46.A$45.3A5.A$46.A5.3A$26.A19.A6.A$25.3A17.3A$26.A19.A$19.A2.A$18.6A6.A$19.A2.A$18.BA12$18.BA$19.A2.A$18.6A6.A$19.A2.A$26.A19.A$25.3A17.3A$26.A19.A6.A$46.A5.3A$45.3A5.A$46.A5$45.A$44.3A$45.A8$45.A$44.3A$45.A5$46.A$45.3A5.A$46.A5.3A$26.A19.A6.A$25.3A17.3A$26.A19.A$.A2.A2.A2.A2.A2.A2.A2.A$24A6.A$.A2.A2.A2.A2.A2.A2.A2.A$11.IHGFEDCBA12$11.IHGFEDCBA$.A2.A2.A2.A2.A2.A2.A2.A$24A6.A$.A2.A2.A2.A2.A2.A2.A2.A$26.A19.A$25.3A17.3A$26.A19.A6.A$46.A5.3A$45.3A5.A$46.A5$45.A$44.3A$45.A! x = 39, y = 33, rule = 0345/2/1012.CAFE$12.D3A$13.2AF$12.IEIH$13.2G$13.2F$13.2E$13.2D$13.2C$13.2B$13.2A2$23.IHGFEDCBA$3.A2.A2.A2.A10.IHGFEDCBA$2.12A8.IHGFEDCBA$3.A5.A2.A8.IHGFEDCBA3.2A$19.IHGFEDCBA5.2B$9.I8.IHGFEDCBA6.2C$9.HI22.2D$9.GH2I20.2E$9.FG2H20.2F$9.EF2G20.2G$9.DE2F19.HIEI$9.CD2E19.F2A$9.BC2D19.3AD$9.AB2C19.EFAC$10.A2B$11.2A$D.EG17.A$E2AHFEDCBA10.3A$.2ADFEDCBA11.A8.A6.A$BCIH25.3A4.3A$30.A6.A!

Brian Prentice
bprentice

Posts: 555
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

### Re: Free Star (0345/2/10)

I have constructed a really high-period gun. One of its components was found by Brian Prentice - thank you, Brian!

x = 229, y = 92, rule = 0345/2/10214.A$213.3A$214.A5$215.A$214.3A4.A$215.A4.3A$206.A3.A4.A5.A$205.3A6.3A4.A$206.A8.A5.2A$37.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A18.A$36.168A5.A11.A$37.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A18.2A$201.IA18.A$221.A$221.2A$203.A8.A8.A$202.12A7.A$203.A2.A2.A2.A8.2A$221.A5.A$221.A4.3A$203.A2.A2.A2.A8.2A4.A$202.12A7.A5.A$203.A8.A8.A5.2A$221.2A4.A$221.A5.A$201.IA18.A5.2A$28.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A18.2A4.A$27.177A5.A11.A5.A$28.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A18.A5.2A$206.A8.A5.2A4.A$205.3A6.3A4.A5.A$206.A3.A4.A5.A5.2A$215.A4.3A4.A$214.3A4.A5.A$215.A11.2A$227.A$208.A18.A$207.3A17.2A$208.A18.A$208.A5.A12.A$207.2A4.3A11.2A$208.A5.A12.A$208.A5.A12.A$207.2A4.3A11.2A$208.A5.A12.A$208.A18.A$207.3A17.2A$208.A18.A$227.A$215.A11.2A$214.3A4.A5.A$215.A4.3A4.A$206.A3.A4.A5.A5.2A$205.3A6.3A4.A5.A$206.A8.A5.2A4.A$19.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A18.A5.2A$18.186A5.A11.A5.A$19.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A18.2A4.A$201.IA18.A5.2A$221.A5.A$221.2A4.A$203.A8.A8.A5.2A$202.12A7.A5.A$203.A2.A2.A2.A8.2A4.A$221.A4.3A$221.A5.A$203.A2.A2.A2.A8.2A$202.12A7.A$203.A8.A8.A$221.2A$221.A$201.IA18.A$.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A18.2A$204A5.A11.A$.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A18.A$206.A8.A5.2A$205.3A6.3A4.A$206.A3.A4.A5.A$215.A4.3A$214.3A4.A$215.A5$214.A$213.3A$214.A! Its period is about 10M generations, although I have not calculated the exact value yet. There are 10 types of people in the world: those who understand binary and those who don't. Alexey_Nigin Posts: 323 Joined: August 4th, 2014, 12:33 pm Location: Ann Arbor, MI ### Re: Free Star (0345/2/10) Alexey_Nigin wrote:I have constructed a really high-period gun. Well done! oscar.py reports a period of 13,214,880 for your gun. Brian Prentice Last edited by bprentice on November 29th, 2014, 9:57 am, edited 2 times in total. bprentice Posts: 555 Joined: September 10th, 2009, 6:20 pm Location: Coos Bay, Oregon ### Re: Free Star (0345/2/10) Here is a 7-cell gun. x = 3, y = 4, rule = 0345/2/102.G$C2A$.2A$2.A!
c0b0p0

Posts: 645
Joined: February 26th, 2014, 4:48 pm

### Re: Free Star (0345/2/10)

I always liked Star Wars, but this rule adds complexity with easily formed spaceships of other velocities.
Compact gun for 7w-2c3 spaceship (7 cells wide, 2c/3 velocity):
x = 18, y = 21, rule = 0345/2/107.GHDC3.DEGF$7.C2A.B.C.2AD$7.H3A.5AH$7.G.A.CBC.A.G$8.FEDABADEF2$.A$3A$.A2$9.A5.A2$.A$3A$.A2$8.FEDABADEF$7.G.A.CBC.A.G$7.H3A.5AH$7.C2A.B.C.2AD$7.GHDC3.DEGF!

I wouldn't doubt there exists a smaller "natural" gun for this spaceship.

EDIT:
Sliding gun / splitter:
x = 32, y = 21, rule = 0345/2/107.GHDC3.DEGF$7.C2A.B.C.2AD$7.H3A.5AH$7.G.A.CBC.A.G$8.FEDABADEF2$.A$3A$.A29.A4$.A$3A$.A2$8.FEDABADEF$7.G.A.CBC.A.G$7.H3A.5AH$7.C2A.B.C.2AD$7.GHDC3.DEGF! knightlife Posts: 566 Joined: May 31st, 2009, 12:08 am ### Re: Free Star (0345/2/10) The variety of guns that can be constructed with this rule is fascinating. Some more examples: x = 71, y = 14, rule = 0345/2/1010.A2.A2.A2.A31.A2.A2.A2.A$9.12A29.12A$10.A2.A2.A2.A31.A2.A2.A2.A$3.A2.A16.A2.A17.A2.A16.A2.A$A.6A14.6A.A11.A.6A14.6A.A$B2A3.A16.A3.2AB11.B2A3.A16.A3.2AB$C.A24.A.C11.C.A24.A.C$D.A24.A.D11.D.A24.A.D$E3A22.3AE11.E3A22.3AE$F.A24.A.F11.F.A24.A.F$G.A24.A.G11.G.A24.A.G$H2A3.A16.A3.2AH11.H2A3.A16.A3.2AH$I.6A14.6A.I11.I.6A14.6A.I$3.A2.A16.A2.A17.A2.A16.A2.A!

x = 5, y = 55, rule = 0345/2/10.HIG$G.3A$F3AG$E.A.F$.2DE$.2C$.2B$.2A2$.2A$.2B$.2C$.2DE$E.A.F$F3AG$G.3A$.HIG8$GE.I$H2AE$D2A$CICB3$.2I$.2H$.2G$.2F$.2E$.2D$.2C$.2B$.2A2$.2A$.2B$.2C$.2D$.2E$.2F$.2G$.2H$.2I3$CICB$D2A$H2AE$GE.I! x = 20, y = 20, rule = 0345/2/10.FAC$3AD3.IHGFEDCBA$F2A4.IHGFEDCBA$HIED$17.2A$17.2B$17.2C$17.2D$17.2E$17.2F$17.2G$17.2H$17.2I4$16.D.DC$16.E3A$16.I2AF$16.HFA! x = 14, y = 75, rule = 0345/2/10HDIA$I2AB.IHGFEDCBA$D2AH.IHGFEDCBA$FGCB$10.2A$10.2B$10.2C$10.2D$10.2E$10.2F$10.2G$10.2H$10.2I8$9.GHDH$9.E2AI$10.2AC$9.DE.B8$9.DE.B$10.2AC$9.E2AI$9.GHDH8$10.2I$10.2H$10.2G$10.2F$10.2E$10.2D$10.2C$10.2B$10.2A$HDIA$I2AB.IHGFEDCBA$D2AH.IHGFEDCBA$FGCB$10.2A$10.2B$10.2C$10.2D$10.2E$10.2F$10.2G$10.2H$10.2I8$9.GHDH$9.E2AI$10.2AC$9.DE.B! x = 151, y = 44, rule = 0345/2/109.EFAC46.CAFE26.EFAC45.CAFE$9.3AD46.D3A26.3AD45.D3A$9.F2A48.2AF26.F2A47.2AF$9.HIEI46.IEIH26.HIEI45.IEIH9$10.2I48.2I28.2I47.2I$10.2H48.2H28.2H47.2H$10.2G48.2G28.2G47.2G$10.2F48.2F28.2F47.2F$10.2E48.2E28.2E47.2E$10.2D48.2D28.2D47.2D$10.2C48.2C28.2C47.2C$10.2B11.IHGFEDCBA8.ABCDEFGHI11.2B28.2B11.IHGFEDCBA7.ABCDEFGHI11.2B$IE.B6.3A11.IHGFEDCBA6.ABCDEFGHI11.3A6.B.EI8.IE.B6.3A11.IHGFEDCBA5.ABCDEFGHI11.3A6.B.EI$.2AC2.IHGFEDCBA11.IHGFEDCBA2.ABCDEFGHI11.ABCDEFGHI2.C2A10.2AC2.IHGFEDCBA11.IHGFEDCBA.ABCDEFGHI11.ABCDEFGHI2.C2A$E2AI2.IHGFEDCBA11.IHGFEDCBA2.ABCDEFGHI11.ABCDEFGHI2.I2AE8.E2AI2.IHGFEDCBA11.IHGFEDCBA.ABCDEFGHI11.ABCDEFGHI2.I2AE$GHDC6.3A11.IHGFEDCBA6.ABCDEFGHI11.3A6.CDHG8.GHDC6.3A11.IHGFEDCBA5.ABCDEFGHI11.3A6.CDHG$10.2B11.IHGFEDCBA8.ABCDEFGHI11.2B28.2B11.IHGFEDCBA7.ABCDEFGHI11.2B$10.2C48.2C28.2C47.2C$10.2D48.2D28.2D47.2D$10.2E48.2E28.2E47.2E$10.2F48.2F28.2F47.2F$10.2G48.2G28.2G47.2G$10.2H48.2H28.2H47.2H$10.2I48.2I28.2I47.2I9$9.HIEI46.IEIH26.HIEI45.IEIH$9.F2A48.2AF26.F2A47.2AF$9.3AD46.D3A26.3AD45.D3A$9.EFAC46.CAFE26.EFAC45.CAFE!

x = 59, y = 18, rule = 0345/2/109.ECHG$.A7.F2AC33.CDIA$3A6.B2AH33.I2AB7.A$.A7.AGA34.D2AH6.3A$.A44.FGCG7.A$2A45.2E8.A$.A45.2D8.2A$.A3.H.I6.I.H30.2C8.A$2A2.AIH8.HIA27.AB2ABA6.A$.A3.H.I6.I.H29.B2.B7.2A$.A27.A15.AB2ABA6.A$2A45.2C8.A$.A45.2D8.2A$.A7.AGA35.2E8.A$3A6.B2AH33.FGCG7.A$.A7.F2AC33.D2AH6.3A$9.ECHG33.I2AB7.A$46.CDIA! This pattern which is based on one of the guns above beautifully illustrates the complexity of this rule. x = 85, y = 83, rule = 0345/2/1014$58.FGBD$58.B2AE3.A$58.G3A2.ACA$58.I.F3.CEC$64.EGE$64.GIG$64.I.I5$71.IGECA$72.IGECA$71.IGECA$34.A2$75.AED$37.A36.F2AB$75.2AG$58.A15.IGBF19$20.FBGI15.A$20.G2A$20.B2AF36.A$20.DEA2$63.A$22.ACEGI$21.ACEGI$22.ACEGI5$31.I.I$31.GIG$31.EGE$31.CEC3.F.I$31.ACA2.3AG$32.A3.E2AB$36.DBGF! Brian Prentice Last edited by bprentice on November 30th, 2014, 10:39 am, edited 1 time in total. bprentice Posts: 555 Joined: September 10th, 2009, 6:20 pm Location: Coos Bay, Oregon ### Re: Free Star (0345/2/10) Wow. x = 7, y = 8, rule = 0345/2/103.A$2.3A$.A3.A$7A$.A.A.A$3.A$2.3A$3.A!

P50 gun:
x = 9, y = 15, rule = 0345/2/10.AB3.BA$2.5A$I2A.A.2AI$H.2A.2A.H$.G.3A.G$2.F.A.F$3.E.E$3.AEA$3.F.F$2.G.A.G$.H.3A.H$I.2A.2A.I$.2A.A.2A$A.5A.A$.BC3.CB!

Gun that fires 13-wide 2c/3 spaceships:
x = 7, y = 7, rule = 0345/2/103.A$2.3A$.A.A.A$2A3.2A$.2A.2A$2.3A$3.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: 1862
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

### Re: Free Star (0345/2/10)

Variable period gun for any even period 12 or more:
x = 89, y = 36, rule = 0345/2/1057.A7.A$IHGFEDCBA47.3A5.3A$IHGFEDCBA48.A7.A$57.A7.A$56.3A5.3A$57.A7.A25$57.A23.A5.A$IHGFEDCBA47.3A21.3A3.3A$IHGFEDCBA48.A23.A5.A$57.A23.A$56.3A21.3A$57.A23.A! A plus can block one barrel as in Star Wars rule. EDIT: Space invaders x = 15, y = 20, rule = 0345/2/10.2A9.2A$3A9.3A$.3A7.3A$BCA9.ACB$2ABD7.DB2A$D2E2A5.2A2ED$CACDA5.ADCAC$FGCA2.ABA2.ACGF$2EFH.2A.2A.HF2E$H2I.FC3ACF.2IH$GAGHEDEAEDEHGAG$2.G.GD3.DG.G$2I2.HG3CGH2.2I$3.2IHD.DH2I$.A2.HGFEFGH2.A$3.IA.I.I.AI$4.HGF.FGH$6.EDE$6.BDB$6.ABA!
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Free Star (0345/2/10)

The outer layer of this "orb" seems totally indestructible (I need confirmation). New parts may be added or destroyed by random events (An exterior intervention may burst it), but the structure seems to last forever. At the center is a 90 degree bounce of a photon over a diagonal "mirror"
x = 18, y = 18, rule = 0345/2/103.FI9.I$2.G.10A.H$.H.2A2.A2.A2.2A.G$I.2A.A.A2.A.A.2A.F$.2A.A.6A.A.2AI$.A.A.2A4.2A.A.A$.A2.2A.FGFC.2A2.A$.4A.GHGFDB.4A$.A2.A5.2C.A2.A$.A2.A5.2B.A2.A$.4A5.A2.4A$.A2.2A6.2A2.A$.A.A.2A4.2A.A.A$I2A.A.6A.A.2A$F.2A.A.A2.A.A.2A.I$.G.2A2.A2.A2.2A.H$2.H.10A.G$3.I9.IF! And as this one has a similar proprety for the inside, it opens the billard-table world! x = 21, y = 19, rule = 0345/2/104.IB2.A2.A2.CB$5.10A.A$2.A.2A8.2A$.B.2A4.FGHIA.2A.I$.C2A4.E.A2.2A.2AB$2.A5.D4A.2A.A$2.A5.C.A.2A.I.A$.2A6.BA2.A.H.2A$2.A7.5AG.A$2.A.AF5.B.A.F.A$.2A.F2.IA3.CDE2.2A$2.A.GCH.I8.A$2.A.2A.H9.A$.B2A.2AC.F6.2AC$.I.2A.AGFA5.2A.B$4.2A8.2A.A$3.A.10A$4.BC2.A2.A2.BI!
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towerator

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### Re: Free Star (0345/2/10)

towerator wrote:The outer layer of this "orb" seems totally indestructible (I need confirmation)

The first pattern is 100% indestructible, both from the inside and outside, and I'll show why
Consider the pattern below:
x = 18, y = 18, rule = 0345/2/103.2E8I2E$2.EI10AIE$.EI2A2.A2.A2.2AIE$EI2A.A.A2.A.A.2AIE$E2A.A.6A.A.2AE$IA.A.2A4I2A.A.AI$IA2.2AIE2.EI2A2.AI$I4AIE4.EI4AI$IA2.AI6.IA2.AI$IA2.AI6.IA2.AI$I4AIE4.EI4AI$IA2.2AIE2.EI2A2.AI$IA.A.2A4I2A.A.AI$E2A.A.6A.A.2AE$EI2A.A.A2.A.A.2AIE$.EI2A2.A2.A2.2AIE$2.EI10AIE$3.2E8I2E! Here, state 9 cells represent the exterior region where births CANNOT happen because the only birth rule is with 2 neighbors, no more, no less, unless the existing structure is destroyed, this takes us to the next part Next, state 5 cells represent the only cells that can turn ON while bordering the exterior of the pattern, and when you turn all of those cells on, the most neighbors any one cell in the structure can get is 5, which is one of the survival conditions set by the rule. Now as long as cells in the 9 region remains relatively clear, the pattern will stick around indefinitely. When I say "relatively", I mean don't have anything like this: x = 18, y = 18, rule = 0345/2/103.2EI3A4I2E$2.EI10AIE$.E3A2.A2.A2.2AIE$EI2A.A.A2.A.A.3AE$E2A.A.6A.A.2AE$IA.A.2A4I2A.A.AI$IA2.2AIE2.EI2A2.AI$5AIE4.EI4AI$2A2.AI6.IA2.AI$2A2.AI6.IA2.2A$I4AIE4.EI5A$IA2.2AIE2.EI2A2.2A$IA.A.2A4I2A.A.AI$E2A.A.6A.A.2AE$EI2A.A.A2.A.A.3AE$.EI2A2.A2.A2.2AIE$2.E12AE$3.2E8I2E!

EDIT: In addition to billiard tables, one thing you could do is create a big box with an indestructible interior, draw some random lines or put a random soup of sorts inside the box, and observe what happens. Sometimes you'll see very interesting things going on. I did that once with star wars, and a certain gun popped up with the ability to create chains of plusses of up to 20 plusses long, the post is here if you want to see. flipper77

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Joined: October 24th, 2010, 3:25 am
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### Re: Free Star (0345/2/10)

Tiny breeder:
x = 5, y = 5, rule = 0345/2/10.FG.E$E.2AF$D4A$C.A$.BA!

Edit: p20 gun for the smallest 2c/3 spaceship:
x = 23, y = 21, rule = 0345/2/10.A19.A$3A7.A.A7.3A$.A6.AB.A.BA6.A$.A6.BC3ACB6.A$2A6.CD.A.DC6.2A$.A5.B.A.A.A.B5.A$.A5.9A5.A$2A7.A3.A7.2A$.A6.IHGFGHI6.A$.A19.A$3A17.3A$.A19.A2$6.A9.A$5.13A$6.A2.A.A.A2.A$10.A.A$10.A.A$9.2A.2A$10.3A\$11.A!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

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

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Aidan F. Pierce A for awesome

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