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Free Star (0345/2/10)

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Free Star (0345/2/10)

Postby Alexey_Nigin » November 23rd, 2014, 11:43 am

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 = 0345/2/10
A$.A$2.A!

x = 5, y = 5, rule = 0345/2/10
4.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 = 0345/2/10
GHA$D2AH$F2AC$CD.B!


A c/2 spaceship:

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


Guns:

x = 5, y = 5, rule = 0345/2/10
GHDC$D2A.B$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 = 0345/2/10
A3$.2A$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 = 0345/2/10
3.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 = 0345/2/10
DECB$3A.A$C3A$B.A.I$.A.IA!


Another interesting pattern:

x = 15, y = 6, rule = 0345/2/10
14.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.
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Re: Free Star (0345/2/10)

Postby A for awesome » November 23rd, 2014, 1:17 pm

Some "tractor beams":
x = 92, y = 23, rule = 0345/2/10
CD.I$.2A.H$B3AGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDC
BA.IHGFEDCBA.IHGFEDCBA.I$A.A.GFEDCBA.IHGFEDCBA.IHGFEDCBA.IHGFEDCBA.IH
GFEDCBA.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$.2A.IECA5.IGECA5.IGECA5.IGECA5.IGECA
5.IGECA5.IGECA5.IGECA5.IGEDCBA$D3A2GECA5.IGECA5.IGECA5.IGECA5.IGECA5.
IGECA5.IGECA5.IGECA5.IGEDCBA$C.A.IECA5.IGECA5.IGECA5.IGECA5.IGECA5.IG
ECA5.IGECA5.IGECA5.IG.FEDCBA$.BA81.FGFEDCBA$84.AFG!

Edit: 2c/3 signal:
x = 71, y = 5, rule = 0345/2/10
2.AI2.ACD3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A3.A$2.I.I.CDC$A2.I
GFDCA$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)

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

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Re: Free Star (0345/2/10)

Postby Alexey_Nigin » November 24th, 2014, 3:49 pm

An interesting gun produces rare 2c/3 spaceships:

x = 19, y = 5, rule = 0345/2/10
BCA13.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.
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Re: Free Star (0345/2/10)

Postby lukebradford » November 24th, 2014, 5:51 pm

This is a very cool rule. Here's a pretty frightening puffer/breeder of ever-increasing complexity.
x = 9, y = 13, rule = 0345/2/10
I2A4.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!
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Re: Free Star (0345/2/10)

Postby bprentice » November 25th, 2014, 6:50 am

Oscillators like this one:

x = 11, y = 11, rule = 0345/2/10
DCA5.ACD$CDC5.CDC$ACD5.DCA2$4.DCA$4.CDC$4.ACD2$ACD5.DCA$CDC5.CDC$DCA
5.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

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Re: Free Star (0345/2/10)

Postby Alexey_Nigin » November 25th, 2014, 1:41 pm

Luke Bradford wrote:This is a very cool rule.


Thank you!

Here is a nice gun:

x = 16, y = 5, rule = 0345/2/10
GHDC8.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 = 0345/2/10
HFDBA$.HFDB5.A$HFDBA!

x = 15, y = 14, rule = 0345/2/10
3.IHGFEDCBA$3.IHGFEDCBA$.IHGFEDCBA$IHGFEDCBA2$13.2A$13.2B$13.2C$13.2D
$13.2E$13.2F$13.2G$13.2H$13.2I!
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Re: Free Star (0345/2/10)

Postby A for awesome » November 25th, 2014, 5:40 pm

Interesting wickstretcher for which there is probably a better end stabilization:
x = 22, y = 17, rule = 0345/2/10
5.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)

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

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Re: Free Star (0345/2/10)

Postby flipper77 » November 25th, 2014, 6:25 pm

A for awesome wrote:Interesting wickstretcher for which there is probably a better end stabilization:
x = 22, y = 17, rule = 0345/2/10
5.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 = 0345/2/10
3.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!
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Re: Free Star (0345/2/10)

Postby c0b0p0 » November 25th, 2014, 6:34 pm

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 = 0345/2/10
2.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 = 0345/2/10
3.A$2.3A$.2A.2A$2A.A.2A$.5A!
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Re: Free Star (0345/2/10)

Postby lukebradford » November 26th, 2014, 11:14 am

Here's a cool growing rake/spacefiller:
x = 15, y = 62, rule = 0345/2/10
10.2A$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!
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Re: Free Star (0345/2/10)

Postby Alexey_Nigin » November 26th, 2014, 4:57 pm

c0b0p0 wrote:
Alexey_Nigin wrote:Here is a nice gun:

Here is a smaller c/2 ship gun.
x = 7, y = 5, rule = 0345/2/10
3.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.
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Re: Free Star (0345/2/10)

Postby bprentice » November 27th, 2014, 4:12 pm

I'm surprised at the lack of interest in this rule.

Some more guns:

x = 5, y = 84, rule = 0345/2/10
2.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 = 0345/2/10
23.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 = 0345/2/10
BCH22.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 = 0345/2/10
11.A$10.3A$11.A$11.A$10.3A$11.A$11.A$10.3A$11.A$11.A$10.3A$11.A$ABH
G7.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 = 0345/2/10
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$4.A
28.A2$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 = 0345/2/10
16.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.C
DHG$10.3A3.A.IHGFEDCBA14.ABCDEFGHI2.I2AE15.3A3.A.IHGFEDCBA11.IHGFED
CBA11.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$38.2A119.2A
3$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.IHGFED
CBA14.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$37.2A
D37.2E$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.A
BCDEFGHI11.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 = 0345/2/10
9.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!


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Re: Free Star (0345/2/10)

Postby bprentice » November 28th, 2014, 7:55 am

A few more guns:

x = 32, y = 55, rule = 0345/2/10
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.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 = 0345/2/10
30.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 = 0345/2/10
5.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 = 0345/2/10
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$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 = 0345/2/10
10.F.F$9.G.A.G$8.GH3AHG$7.F.A.A.A.F$6.B.2A3.2A.B$3.GHCH2A.E.E.2AHCH
G$ABC3A2.A2.A2.A2.3ACBA$ABCG2A.9A.2AGCBA$3.DECH.A2.A2.A.HCED$7.GFED
.DEFG!


x = 5, y = 6, rule = 0345/2/10
2.A$.3A$2A.2A$.A.A$.3A$2.A!


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Re: Free Star (0345/2/10)

Postby A for awesome » November 28th, 2014, 10:38 am

A breeder that fires growing spaceships:
x = 15, y = 15, rule = 0345/2/10
8.DCB$4.2A.E.A.A$3.A2BDF3A$2.AB2CDH2A.I$.ABCDFG3.B$.ABCFGI.A.C$2.2DGI
E3ADF$.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

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Re: Free Star (0345/2/10)

Postby bprentice » November 28th, 2014, 2:03 pm

Five more guns:

x = 12, y = 26, rule = 0345/2/10
9.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.F
BFE$8.G2AC$8.3AH$9.HCB!


x = 7, y = 23, rule = 0345/2/10
2.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 = 0345/2/10
2.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 = 0345/2/10
45.A$44.3A$45.A5$46.A$45.3A5.A$46.A5.3A$26.A19.A6.A$25.3A17.3A$26.A
19.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.A
2.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 = 0345/2/10
12.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.GH
2I20.2E$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!


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Re: Free Star (0345/2/10)

Postby Alexey_Nigin » November 28th, 2014, 5:04 pm

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 = 0345/2/10
214.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.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.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.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A18.2A$201.IA18.A$221.A$221.2A$203.A
8.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.A
5.2A$28.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A18.2A4.A$27.177A5.A11.A
5.A$28.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.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.A
11.2A$227.A$208.A18.A$207.3A17.2A$208.A18.A$208.A5.A12.A$207.2A4.3A
11.2A$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.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.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.A
5.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.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.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.
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Re: Free Star (0345/2/10)

Postby bprentice » November 28th, 2014, 9:10 pm

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

Postby c0b0p0 » November 29th, 2014, 12:26 am

Here is a 7-cell gun.
x = 3, y = 4, rule = 0345/2/10
2.G$C2A$.2A$2.A!
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Re: Free Star (0345/2/10)

Postby knightlife » November 29th, 2014, 5:56 pm

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 = 0345/2/10
7.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 = 0345/2/10
7.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!
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Re: Free Star (0345/2/10)

Postby bprentice » November 30th, 2014, 9:46 am

The variety of guns that can be constructed with this rule is fascinating. Some more examples:

x = 71, y = 14, rule = 0345/2/10
10.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$B2A3.A16.A3.2AB
11.B2A3.A16.A3.2AB$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 = 0345/2/10
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.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 = 0345/2/10
9.EFAC46.CAFE26.EFAC45.CAFE$9.3AD46.D3A26.3AD45.D3A$9.F2A48.2AF26.F
2A47.2AF$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$10.2B11.IHGFEDCBA
8.ABCDEFGHI11.2B28.2B11.IHGFEDCBA7.ABCDEFGHI11.2B$IE.B6.3A11.IHGFED
CBA6.ABCDEFGHI11.3A6.B.EI8.IE.B6.3A11.IHGFEDCBA5.ABCDEFGHI11.3A6.B.
EI$.2AC2.IHGFEDCBA11.IHGFEDCBA2.ABCDEFGHI11.ABCDEFGHI2.C2A10.2AC2.I
HGFEDCBA11.IHGFEDCBA.ABCDEFGHI11.ABCDEFGHI2.C2A$E2AI2.IHGFEDCBA11.I
HGFEDCBA2.ABCDEFGHI11.ABCDEFGHI2.I2AE8.E2AI2.IHGFEDCBA11.IHGFEDCBA.
ABCDEFGHI11.ABCDEFGHI2.I2AE$GHDC6.3A11.IHGFEDCBA6.ABCDEFGHI11.3A6.C
DHG8.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.HIEI
46.IEIH26.HIEI45.IEIH$9.F2A48.2AF26.F2A47.2AF$9.3AD46.D3A26.3AD45.D
3A$9.EFAC46.CAFE26.EFAC45.CAFE!


x = 59, y = 18, rule = 0345/2/10
9.ECHG$.A7.F2AC33.CDIA$3A6.B2AH33.I2AB7.A$.A7.AGA34.D2AH6.3A$.A44.F
GCG7.A$2A45.2E8.A$.A45.2D8.2A$.A3.H.I6.I.H30.2C8.A$2A2.AIH8.HIA27.A
B2ABA6.A$.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.ECH
G33.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 = 0345/2/10
14$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.IGB
F19$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.DBG
F!


Brian Prentice
Last edited by bprentice on November 30th, 2014, 10:39 am, edited 1 time in total.
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Re: Free Star (0345/2/10)

Postby A for awesome » November 30th, 2014, 10:00 am

Wow.
x = 7, y = 8, rule = 0345/2/10
3.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 = 0345/2/10
3.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)

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

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Re: Free Star (0345/2/10)

Postby knightlife » November 30th, 2014, 8:29 pm

Variable period gun for any even period 12 or more:
x = 89, y = 36, rule = 0345/2/10
57.A7.A$IHGFEDCBA47.3A5.3A$IHGFEDCBA48.A7.A$57.A7.A$56.3A5.3A$57.A7.A
25$57.A23.A5.A$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.GD
3.DG.G$2I2.HG3CGH2.2I$3.2IHD.DH2I$.A2.HGFEFGH2.A$3.IA.I.I.AI$4.HGF.FG
H$6.EDE$6.BDB$6.ABA!
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Re: Free Star (0345/2/10)

Postby towerator » December 1st, 2014, 5:12 pm

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 = 0345/2/10
3.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$.A2.A
5.2B.A2.A$.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 = 0345/2/10
4.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!
This is game of life, this is game of life!
Loafin' ships eaten with a knife!
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Re: Free Star (0345/2/10)

Postby flipper77 » December 1st, 2014, 7:05 pm

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 = 0345/2/10
3.2E8I2E$2.EI10AIE$.EI2A2.A2.A2.2AIE$EI2A.A.A2.A.A.2AIE$E2A.A.6A.A.2A
E$IA.A.2A4I2A.A.AI$IA2.2AIE2.EI2A2.AI$I4AIE4.EI4AI$IA2.AI6.IA2.AI$IA
2.AI6.IA2.AI$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 = 0345/2/10
3.2EI3A4I2E$2.EI10AIE$.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$2A
2.AI6.IA2.2A$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.
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Re: Free Star (0345/2/10)

Postby A for awesome » December 3rd, 2014, 2:09 pm

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$3A17.3A$.A
19.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)

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

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce
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