## Free Star (0345/2/10)

For discussion of other cellular automata.
Alexey_Nigin
Posts: 323
Joined: August 4th, 2014, 12:33 pm
Location: Ann Arbor, MI
Contact:

### 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:

Code: Select all

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

Code: Select all

x = 5, y = 5, rule = 0345/2/10
4.A2$A$.A$2.A! Code: Select all x = 5, y = 5, rule = 0345/2/10 .BA$C.A$D3A$E.A.I$.FGH! Code: Select all x = 4, y = 4, rule = 0345/2/10 GHA$D2AH$F2AC$CD.B!
A c/2 spaceship:

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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": Code: Select all 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:

Code: Select all

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

Code: Select all

x = 15, y = 6, rule = 0345/2/10
14.A2$IHGFEDCBA$IHGFEDCBA2$13.A! You might also want to visit this thread. There you can find a similar (but a bit more explosive) rule. There are 10 types of people in the world: those who understand binary and those who don't. A for awesome Posts: 1942 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: ### Re: Free Star (0345/2/10) Some "tractor beams": Code: Select all x = 92, y = 23, rule = 0345/2/10 CD.I$.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: Code: Select all 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: Code: Select all 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

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

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

An interesting gun produces rare 2c/3 spaceships:

Code: Select all

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):

Code: Select all

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.

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

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

This is a very cool rule. Here's a pretty frightening puffer/breeder of ever-increasing complexity.

Code: Select all

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!

bprentice
Posts: 629
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

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

Oscillators like this one:

Code: Select all

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:

viewtopic.php?f=11&t=1015&p=7395#p7395

Brian Prentice

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

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

Luke Bradford wrote:This is a very cool rule.
Thank you!

Here is a nice gun:

Code: Select all

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:

Code: Select all

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

Code: Select all

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!
There are 10 types of people in the world: those who understand binary and those who don't.

A for awesome
Posts: 1942
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

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

Interesting wickstretcher for which there is probably a better end stabilization:

Code: Select all

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) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce flipper77 Posts: 197 Joined: October 24th, 2010, 3:25 am Location: Spokane, WA ### Re: Free Star (0345/2/10) A for awesome wrote:Interesting wickstretcher for which there is probably a better end stabilization: Code: Select all 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:

Code: Select all

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!  c0b0p0 Posts: 645 Joined: February 26th, 2014, 4:48 pm ### 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). Code: Select all 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.

Code: Select all

x = 7, y = 5, rule = 0345/2/10
3.A$2.3A$.2A.2A$2A.A.2A$.5A!


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

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

Here's a cool growing rake/spacefiller:

Code: Select all

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! Alexey_Nigin Posts: 323 Joined: August 4th, 2014, 12:33 pm Location: Ann Arbor, MI Contact: ### Re: Free Star (0345/2/10) c0b0p0 wrote: Alexey_Nigin wrote:Here is a nice gun: Here is a smaller c/2 ship gun. Code: Select all 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. There are 10 types of people in the world: those who understand binary and those who don't. bprentice Posts: 629 Joined: September 10th, 2009, 6:20 pm Location: Coos Bay, Oregon ### Re: Free Star (0345/2/10) I'm surprised at the lack of interest in this rule. Some more guns: Code: Select all 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!


Code: Select all

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!


Code: Select all

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!


Code: Select all

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!  Code: Select all 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:

Code: Select all

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!


Code: Select all

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!  Code: Select all 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!  Brian Prentice bprentice Posts: 629 Joined: September 10th, 2009, 6:20 pm Location: Coos Bay, Oregon ### Re: Free Star (0345/2/10) A few more guns: Code: Select all 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!  Code: Select all 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$48.A!  Code: Select all x = 89, y = 14, rule = 0345/2/10 5.IHGFEDCBA$.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!


Code: Select all

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!


Code: Select all

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!  Code: Select all 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!


Code: Select all

x = 5, y = 6, rule = 0345/2/10
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 bprentice Posts: 629 Joined: September 10th, 2009, 6:20 pm Location: Coos Bay, Oregon ### Re: Free Star (0345/2/10) Five more guns: Code: Select all 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!


Code: Select all

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!


Code: Select all

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!


Code: Select all

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!  Code: Select all 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!

Brian Prentice

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

### 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!

Code: Select all

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$214.A! Its period is about 10M generations, although I have not calculated the exact value yet. There are 10 types of people in the world: those who understand binary and those who don't. bprentice Posts: 629 Joined: September 10th, 2009, 6:20 pm Location: Coos Bay, Oregon ### Re: Free Star (0345/2/10) Alexey_Nigin wrote:I have constructed a really high-period gun. Well done! oscar.py reports a period of 13,214,880 for your gun. Brian Prentice Last edited by bprentice on November 29th, 2014, 9:57 am, edited 2 times in total. c0b0p0 Posts: 645 Joined: February 26th, 2014, 4:48 pm ### Re: Free Star (0345/2/10) Here is a 7-cell gun. Code: Select all x = 3, y = 4, rule = 0345/2/10 2.G$C2A$.2A$2.A!

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

### 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):

Code: Select all

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:

Code: Select all

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!  bprentice Posts: 629 Joined: September 10th, 2009, 6:20 pm Location: Coos Bay, Oregon ### Re: Free Star (0345/2/10) The variety of guns that can be constructed with this rule is fascinating. Some more examples: Code: Select all 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!


Code: Select all

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!  Code: Select all 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$16.HFA!  Code: Select all x = 14, y = 75, rule = 0345/2/10 HDIA$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!  Code: Select all 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!


Code: Select all

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. Code: Select all 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. A for awesome Posts: 1942 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: ### Re: Free Star (0345/2/10) Wow. Code: Select all 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:

Code: Select all

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:

Code: Select all

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)

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

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

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

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

Variable period gun for any even period 12 or more:

Code: Select all

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 Code: Select all 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!


towerator
Posts: 328
Joined: September 2nd, 2013, 3:03 pm

### 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"

Code: Select all

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! Code: Select all  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!

flipper77
Posts: 197
Joined: October 24th, 2010, 3:25 am
Location: Spokane, WA

### 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:

Code: Select all

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: Code: Select all 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.

A for awesome
Posts: 1942
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

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

Tiny breeder:

Code: Select all

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:

Code: Select all

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