## 3458/37/4

For discussion of other cellular automata.

### 3458/37/4

I suspect nobody has had much of a look at this as it very quickly delivers one of the holy grails of CA, which I'll get to at the bottom for those who are impatient. But really it is a case where it can be more fun to discover for yourself. So I'd recommend starting with one of the five viable orthogonal collisions between common c/2 spaceships which generate distinct asymmetric patterns. (Six more generate the same viable diagonally symmetric pattern which you can find easily enough.)
`x = 24, y = 416, rule = 3458/37/419.CB\$18.BA.C\$19.ABA\$19.3A\$20.A8\$.B\$C3A\$2.B2A\$C3A\$.B84\$20.C.C\$19.BA.AB\$20.ABA\$20.3A\$21.A8\$.CA\$.B3A\$2.C2A\$.B3A\$.CA84\$18.C.C\$17.BA.AB\$18.ABA\$18.3A\$19.A8\$.B\$C3A\$B.B2A\$.C2A85\$18.CB\$17.BA.C\$18.ABA\$18.3A\$19.A8\$.B\$C3A\$B.B2A\$.C2A85\$20.BC\$19.C.AB\$19.ABA\$19.3A\$20.A8\$.CA\$.B3A\$CAC2A\$2.B2A!`
I'm currently running the bottom one, beyond 35,000 iterations with a population over 9 million (live+dying) but please be encouraged to run one of the others and see what emerges. The growth rate is a bit quicker than 345/3/6 which has kept me focused for two years now (and which I hope I'm getting closer to writing up properly) but many of the patterns that are familiar from there and similar rules, also turn up in 3458/37/4, so the ones I'm highlighting below are one afternoon's worth of somewhat different discoveries.

A p250 switch engine which moves (2,2) per cycle:
`x = 12, y = 22, rule = 3458/37/49.2A\$9.3A\$6.3A.A\$6.2ACB\$7.BAC15\$.BA\$C2A\$.2A!`
A common enough diagonal p8 spaceship which moves (1,1) per cycle:
`x = 4, y = 4, rule = 3458/37/4.3A\$A2BA\$4A\$CA!`
A cyclically symmetric p4 oscillator:
`x = 7, y = 6, rule = 3458/37/44.3A\$3.3AB\$2.BC.C\$.C.CB\$B3A\$3A!`
Four "engines", the upper of each pair being technically a long period spaceship (p28 and p48), the second laying ubiquitous track which erodes at 6/10c until a noisy phase-dependent reblocking and the last leaving a trail of pairs of blocks p20:
`x = 36, y = 68, rule = 3458/37/432.C2A\$31.B.B2A\$31.C3A\$30.AB.A\$28.2A.A.A\$28.7A\$29.A3.B2A\$31.C3A\$32.B11\$32.B\$31.C3A\$7.CB.A.A.A.A.A.A.A.A.A.A.A2.B2A\$7.C.26A\$8.BC.A.A.A.A.A.A.A.A.A.A.A.A\$31.A.A\$31.B3A\$30.CA.B2A\$31.C3A\$32.B11\$32.B\$27.C.2AC3A\$2A.2A22.4A2.B2A\$6A3.BA.BC11.2A.A2.4A\$.A.C2A2.2ACA.2A9.3A2.3A.A\$.A.C2A2.2ACA.2A9.3A2.3A.A\$6A3.BA.BC11.2A.A2.4A\$2A.2A22.4A2.B2A\$27.C.2AC3A\$32.B12\$32.C2A\$31.B.B2A\$27.ABC.4A\$26.2A.2A.A\$26.2A.2A.A\$27.ABC.4A\$31.B.B2A\$32.C2A!`
Another track layer, but one which leaves behind a new viable seed pattern when it spontaneously transitions to a p8 spaceship:
`x = 23, y = 9, rule = 3458/37/419.B\$18.C3A\$.BC.A.A.A.A.A.A.A3.B2A\$C.20A\$CB.A.A.A.A.A.A.A.A.A\$16.C2.A\$18.C3A\$18.B.B2A\$19.C2A!`
A "delta" engine which is p28 immediately behind the engine and p560 by the time it starts producing the rakes of ships which produce a delta wing:
`x = 8, y = 8, rule = 3458/37/44.C2A\$.2A2.B2A\$.6A\$C2A.A\$4.A\$3.C3A\$3.B.B2A\$4.C2A!`
And the totally unexpected but very commonly produced holy grail:
`x = 8, y = 14, rule = 3458/37/4.2C\$B2.B\$C2AC\$.2A3\$4.3A\$4.3A\$5.A\$4.A.A\$4.AB2A\$2.CB.2A\$4.B\$4.C!`
And, no, I'm not giving a description. You really do have to at least run that one and be as surprised as I was.

ynotds

Posts: 31
Joined: August 23rd, 2010, 8:38 am
Location: Melbourne, Australia

### Re: 3458/37/4

Whoa. That... knightpuffer (?) is indeed impressive.

I've been looking at the engines with the trails at 6c/10. You can combine them in many ways; I've found a clean rake and three puffers, which seem to grow forever.

`x = 35, y = 188, rule = 3458/37/410\$9.2AB\$9.2ACAC\$9.3AB\$12.A\$12.A.A.A.2A\$9.11A\$9.2AC6.2A\$9.7AC\$12.A.A.B\$12.A3.C\$9.3AB\$9.2ACAC\$9.2AB19\$11.2AC\$10.2AB.B\$11.3AC\$12.A.BA\$12.A.A.A.A.A.CB\$11.12A.C\$10.2AB6.A.A.BC\$11.6AB\$12.A.A.2AC\$12.A.BA\$11.3AC\$10.2AB\$11.3AC\$12.A.BA\$12.A.A.2AC\$11.6AB\$10.2AB6.A.A.BC\$11.12A.C\$12.A.A.A.A.A.CB\$12.A.BA\$11.3AC\$10.2AB.B\$11.2AC12\$11.2AB\$11.2ACAC\$11.3AB\$13.A.CB\$13.A.A.A.BC\$11.9A\$11.2AC5.B\$11.7AC\$13.A.A.AB\$13.A.CBA\$11.3AB\$11.2ACAC\$11.2AB12\$11.2AB\$11.2ACAC\$11.3AB\$14.A\$14.A.A.A.2A\$11.11A\$11.2AC6.A\$11.7AC\$14.A.A.B\$14.A3.C\$11.3AB\$11.2ACAC\$11.2AB20\$11.2AB\$11.2ACAC\$11.3AB\$14.A3.C\$14.A.A.B\$11.7AC\$11.2AC\$11.7AC\$14.A.A.B\$14.A3.C\$11.3AB\$11.2ACAC\$11.2AB21\$12.2AC\$11.2AB.B\$12.3AC\$13.A.BA\$13.A.A.A.A.A.2AC\$12.12AB\$11.2AB6.A.A2.C\$12.6AB\$13.A.A.2AC\$13.A.BA\$12.3AC\$11.2AB.B\$12.2AC!`
ebcube

Posts: 124
Joined: February 27th, 2010, 2:11 pm

### Re: 3458/37/4

ynotds wrote:A p250 switch engine which moves (2,2) per cycle

I like the little eye-catching P8 oscillator that's part of it:
`x = 3, y = 3, rule = 3458/37/4.C\$B2A\$3A!`
tod222

Posts: 14
Joined: August 23rd, 2010, 12:43 am

### Re: 3458/37/4

A Bug:
`x = 9, y = 10, rule = 3458/37/44.BC\$3.3A.2A\$4.2A.2A2\$4.2A.2A\$4.2A.2A\$2.2A\$2.2A\$2A\$2A!`

ssaamm

Posts: 125
Joined: June 4th, 2010, 9:43 pm

### Re: 3458/37/4

I have done a very similar rule that has a tiny p162 (I think) oscillator:
`x = 4, y = 4, rule = 345/367/3.2AB\$3A\$3A\$B!`
I Like My Heisenburps! (and others)

Extrementhusiast

Posts: 1719
Joined: June 16th, 2009, 11:24 pm
Location: USA

### A couple of distictively different puffers

Found these overnight in my saves from that fifth seed in the post above at 35,000 and 45,000. Both worth a look:
`x = 12, y = 8, rule = 3458/37/48.C2A\$7.B.B2A\$7.C3A\$.2A.A.A\$2AB6A\$.2A.A2.B2A\$5.C3A\$6.B!`
`x = 8, y = 10, rule = 3458/37/44.CA\$4.B3A\$.B3.C2A\$C7A\$.2ACA\$4.A\$3.C4A\$3.B.C2A\$4.B3A\$4.CA!`

ynotds

Posts: 31
Joined: August 23rd, 2010, 8:38 am
Location: Melbourne, Australia

### Re: 3458/37/4

Someone said knightship?

`x = 30, y = 32, rule = 3458/37/4\$17.2A\$17.2A\$18.2A5.3A\$18.2A5.2ACA\$25.3AB\$27.A3\$11.2A\$11.2A\$12.2A\$12.2A5.2C.3A\$18.B.2AC2A\$17.2ABA.3A\$18.4A\$19.A\$9.3A\$9.2ACA\$9.3AB\$11.A6\$3.2C.3A\$2.B.2AC2A\$.2ABA.3A\$2.4A\$3.A!`
ebcube

Posts: 124
Joined: February 27th, 2010, 2:11 pm

### Re: 3458/37/4

I like the knightship...

Another knightship:
`x = 20, y = 18, rule = 3458/37/410.C\$7.CA.C\$6.B3A\$.3A2.4A\$.ABAC3.A8.3A\$2AB.2A8.C2.ABA\$.B.3A7.3A.3A\$2.C.C8.2A.2A\$14.CAC\$15.B3\$12.3A\$9.C2.ABA\$8.3A.3A\$8.2A.2A\$9.CAC\$10.B!`

Stable objects never get a chance to form behind this one.

I thought I could make more variants but haven't found any more yet.

EDIT:
Didn't look close enough the first time...
There is a single block that forms momentarily.
knightlife

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

### Re: 3458/37/4

Another knightship using different phases of the puffer:
`x = 14, y = 13, rule = 3458/37/47.A\$6.4A\$5.2AB.ABAC\$6.3A.ACAB\$7.7A\$11.2A2\$4.3A\$.C2.ABA\$3A.3A\$2A.2A\$.CAC\$2.B!`
knightlife

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

### Re: 3458/37/4

Knightship repeats every 64 generations (instead of 32):
`x = 21, y = 26, rule = 3458/37/46.A\$3.2CB2AB\$5.A.C2A\$.C2BA.3A\$BA2.CB.2A\$.2A\$.BC\$12.2A\$11.B3A\$11.AC2A.C\$10.2ACA.A\$11.A2CB.BAC\$11.2B3CA.2A\$14.2B4A\$17.3A2\$11.C\$8.CA.C\$7.B3A\$7.4A\$9.A8.3A\$15.C2.ABA\$14.3A.3A\$14.2A.2A\$15.CAC\$16.B!`
knightlife

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

### Re: 3458/37/4

This knightship has an extra-long tail:
`x = 21, y = 37, rule = 3458/37/4CBA2.C\$.2BAB3A\$.C2.A.2A\$3.AC.2A\$3.BA2.AB\$4.C2AC\$5.2A5\$8.A\$7.3A\$7.ABA\$5.2A2.ACB\$5.2A2.AC2A\$6.ABA.AB\$6.3A\$7.A2\$18.2A\$15.BC.3A\$14.3A.2A\$14.2ACA\$15.BAB\$16.A2\$10.C\$8.2BAB\$6.CAC.AC\$7.3AB\$7.2A\$16.C2A\$14.AB.2A\$14.2A.2A\$14.ABAC\$14.3A!`

The large spark is useful for making rakes (knightrakes?):
forward:
`x = 105, y = 116, rule = 3458/37/4CBA2.C\$.2BAB3A\$.C2.A.2A\$3.AC.2A\$3.BA2.AB\$4.C2AC\$5.2A5\$8.A\$7.3A\$7.ABA\$5.2A2.ACB\$5.2A2.AC2A\$6.ABA.AB\$6.3A\$7.A2\$18.2A\$15.BC.3A\$14.3A.2A\$14.2ACA\$15.BAB\$16.A2\$10.C\$8.2BAB\$6.CAC.AC\$7.3AB\$7.2A\$16.C2A\$14.AB.2A\$14.2A.2A\$14.ABAC\$14.3A35\$52.CBA2.C\$53.2BAB3A\$53.C2.A.2A\$55.AC.2A\$55.BA2.AB\$56.C2AC\$57.2A5\$60.A\$59.3A\$59.ABA\$57.2A2.ACB\$57.2A2.AC2A\$58.ABA.AB\$58.3A\$59.A2\$70.2A\$67.BC.3A\$66.3A.2A\$66.2ACA\$67.BAB\$68.A2\$62.C\$60.2BAB24.2A.A\$58.CAC.AC24.6A\$59.3AB27.A.2A8.C\$59.2A41.B\$68.C2A26.2A.2A.BC\$66.AB.2A26.3A.BA\$66.2A.2A26.2A.3A\$66.ABAC31.A\$66.3A\$86.BC\$85.C.2A\$85.C.2A7.C\$86.BC8.B\$91.2A.2A.BC\$91.3A.BA\$91.2A.3A\$95.A!`

more compact backrake:
`x = 73, y = 82, rule = 3458/37/43A\$ABA\$4A\$.A.B\$2.CBC\$.B\$.CB\$.BAC\$.AB\$.CBC7\$6.BA\$5.CBCBC.C\$5.B3.3AC\$4.CB3.4A\$6.2C3.3A\$8.C3.2A\$8.B3.2A12.2A\$6.B3A16.2A\$6.ACA\$7.B\$6.2C5\$15.2A\$15.3A\$16.A.3A\$17.AB2ACB\$17.AB2.A.C13.ABA.2A\$14.4A2BA.A.B11.ACA.3A\$14.BA2BA3BAC2A10.B3A.C2A\$13.C.CBA2.2A.3A13.5A\$14.B3A6.A11.2C3.2A\$14.CA18.AB2.C\$32.ABA.C\$32.3A.B.C\$33.A2.2AC\$35.C2A\$17.2A\$16.4ABA\$16.2AC.ACB\$16.4A.A.AC\$17.5AB2A\$19.2A.3A24.2A7.C\$49.2A5.CABAC\$40.C15.BCBCB\$38.2BAB14.CAB.C\$36.CAC.AC17.B\$37.3AB18.C\$37.2A20.B\$46.C2A9.C.C2A\$44.AB.2A11.3A\$44.2A.2A12.2A\$44.ABAC\$44.3A3\$70.C\$70.B\$65.2A.2A.BC\$65.3A.BA\$59.3A3.2A.3A\$58.AC2A7.A\$58.B3A\$59.A6\$62.3A.2C\$62.2AC2A.B\$62.3A.AB2A\$65.4A\$67.A!`

It was fun to engineer those rakes but I'm sure smaller versions with just a few of engines exist, more on the order of this p8 oscillator "knightpuffer":
`x = 17, y = 20, rule = 3458/37/48.B\$7.CAC\$6.2A.A\$4.3A.2AC\$4.B3A.B\$5.C\$11.CBC2A\$11.B2.B2A\$11.C2ABA\$12.4A2\$.CA.C\$B3A\$4A\$2.A8.3A\$8.C2.ABA\$7.3A.3A\$7.2A.2A\$8.CAC\$9.B!`

I found a knightpuffer that creates other knightpuffers but it also makes a ton of debris.
I am trying to find a clean one (knightpuffer knightrake!) .

EDIT:
Correction made... forward rake is truly forward (I think)
Last edited by knightlife on December 31st, 2010, 8:56 pm, edited 1 time in total.
knightlife

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

### Re: 3458/37/4

Found this small, clean, two engine "knightrake":
`x = 21, y = 25, rule = 3458/37/411.A\$7.2ACB3A\$6.2AB2.2BA\$7.3A.3A\$9.BC.C4\$18.3A\$15.C2.ABA\$.3A10.3A.3A\$.ABAC9.2A.2A\$2AB.2A9.CAC\$.B.3A10.B\$2.C.C5\$12.3A\$9.C2.ABA\$8.3A.3A\$8.2A.2A\$9.CAC\$10.B!`

Discovered while trying to clean up a much larger rake.
knightlife

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

### Re: 3458/37/4

Nice double backrake uses just two knight engines:
`x = 20, y = 19, rule = 3458/37/411.B\$10.CAC\$9.2A.A\$7.3A.2AC\$.3A3.B3A.B\$.ABAC3.C\$2AB.2A8.CBC2A\$.B.3A8.B2.B2A\$2.C.C9.C2ABA\$15.4A4\$12.3A\$9.C2.ABA\$8.3A.3A\$8.2A.2A\$9.CAC\$10.B!`
knightlife

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

### Re: 3458/37/4

Two engine double K-rake (forward and backward):
`x = 18, y = 18, rule = 3458/37/49.4A\$9.AB2ACB\$8.2AB2.A.C\$9.A2BA.A.B\$9.2A3BAC2A\$12.2A.3A\$16.A3\$.CA\$B3A\$4A\$2.A8.3A\$8.C2.ABA\$7.3A.3A\$7.2A.2A\$8.CAC\$9.B!`
knightlife

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

### Re: 3458/37/4

Finally, a clean K-puffer K-rake:
`x = 167, y = 123, rule = 3458/37/451.2A\$51.2A2\$72.2A\$72.2A\$71.2A\$71.2A2\$38.2A\$38.4A\$40.2A4\$30.2A\$30.4A\$32.2A29.2A\$63.2A2\$84.2A\$22.2A60.2A\$22.4A57.2A\$6.BC16.2A57.2A\$6.2A\$5.A2BA41.2A\$5.4A41.4A\$14.2A18.BC16.2A\$14.4A16.2A\$16.2A15.A2BA44.BC\$2.2A29.4A43.C.2A\$2.2A38.2A18.BC12.2A.AB.2A7.C\$CB.A38.4A16.2A12.4A.BC8.B\$2.A41.2A15.A2BA8.A.2A2.A6.2A.2A.BC\$2.3AB24.2A29.4A6.3A2BA.3A5.3A.BA\$3.AC2A23.2A39.2A.ABA2CA6.2A.3A\$3.BAB22.CB.A42.2A.BAB10.A\$4.A25.A47.A\$30.3AB24.2A\$31.AC2A23.2A\$31.BAB22.CB.A\$32.A25.A\$58.3AB\$59.AC2A\$59.BAB27.C.C\$60.A28.3AB\$87.2A.2B\$86.2AB3A\$87.2A.A5\$87.2A\$87.2A\$91.A\$90.4A35.3A\$89.2AB.ABAC31.CBABC\$90.3A.ACAB28.C7.C\$91.7A28.C.CB2AC.CB\$95.2A30.BC2A.B2A.A\$131.3A.2A\$122.2C8.B.4A\$107.2A15.B7.CBA.BC\$107.2A12.C.2C5.ABC2.C\$106.2A12.AB.BA4.3A2.B\$106.2A12.2A.2A4.3ACABC\$120.AB.BA4.ABC.B\$121.C.2C7.BC\$124.B\$122.2C9\$119.2A19.CBA\$119.2A19.2A.2A\$118.2A20.5A\$118.2A22.A3\$140.B\$139.C3A3.C\$139.A.2B3.AB\$137.3A.2AB.3A\$137.2A.A2.C.B4A\$138.A2.A2.C4.3A\$137.3A.2AB2.3AC2A\$137.3ABA.A.A.A.3A\$140.3ACACB\$144.BA12.2A\$131.2A25.2A\$131.2A24.2A\$130.2A20.B4.2A\$130.2A19.CBC\$149.2C2.B4.A\$154.BC5A\$151.C.C2.2A2BA\$150.B2A.3A2.B2A\$137.2A11.2A.B.A.C3A\$135.C.2A13.C3A2.B\$136.2A16.A4.A\$136.2A15.3A2.4A\$153.3A2.AB2ACB\$157.2AB2.A.C\$149.3A6.A2BA.A.B\$149.ABAC5.2A3BAC2A\$136.C11.2AB.2A7.2A.3A\$133.CA.C12.B.3A11.A\$132.B3A14.C.C\$132.4A\$134.A8.3A\$140.C2.ABA\$139.3A.3A\$139.2A.2A16.3A\$140.CAC14.C2.ABA\$141.B14.3A.3A\$156.2A.2A\$157.CAC\$158.B!`

Well, it's a puffer factory that uses five knight engines to make a rake that outputs knightpuffers cleanly.
All output is completely stable, which took a while longer to achieve.
It is still before midnight on the last day of the year 2010, which was my other goal.
knightlife

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

### Re: 3458/37/4

This small trail engine based puffer creates the (2,2)c/250 switch engine spaceship:

`x = 265, y = 88, rule = 3458/37/4\$217.C\$216.B2A\$216.3A4\$224.A\$223.3A\$223.AB2A\$222.2AB.B\$223.A.BC\$216.BCBA.3A2C\$215.C.A.AB.2A2CB\$214.2B.B2CA2.A.AB\$215.CA2CA.2A.A\$175.2A40.2B6A2.C\$173.B3A45.3A.BAB\$135.2A35.2A2C2A46.A.4A\$135.2A35.3A.B2C45.2A.2A\$134.C2.C35.3A49.A2.2A\$135.2A38.C48.2A2.2A\$135.2A38.2BC45.2AC2A\$104.C2A68.A48.B3A\$104.3A68.CBC47.2A\$100.BC2A.B2A68.B\$99.C.C5A25.2A11.BC\$94.A4.C3.A28.2A11.2CB\$93.4A.A.A2.AB40.B2.BC\$61.BC29.B2.8AC41.C.C.C\$60.3AB28.C2A2.CA2.2A42.CB50.2A.2A35.2A.2A\$60.2AB3.CB24.B.A.BA49.BC36.2A10.2A.2A23.2A10.2A.2A\$61.ABA.ABC24.3A2.AB45.4A37.2A38.2A\$62.4A2.B24.AB2AC46.ABA\$65.3AC3.2A19.4A47.3A59.2A38.2A\$65.3AC2.B2AB131.2A38.2A\$18.2A40.2C8.2ACAC2.CBAC\$16.B3A40.2A8.4A2.C.A.AB\$16.A2CB34.2A.5A9.2A4.2A.A25.2A21.2AC10.2A\$4.B10.2AC32.2A2.2A2B.B2A11.C.C.CB.2A24.2A13.2A6.3A9.4AB\$2.3AC9.2AB32.2A4.5A12.CB4.3A39.2A5.2AB10.2A2C2A\$.2AB2.AC16.2A30.2A71.2AC9.3AC2A14.2A6.AB\$2.6A16.2A116.3AB15.2A.AC.C.2AC\$3.A.A.2A50.2A97.A4.3A.C.3A.AB\$3.A.AC2A49.B2AB64.A14.C14.4A3.2A.A.AB2ABCA\$2.6A49.2A2C2A62.3A11.CBA14.A2BA4.ABCBC3.BC2A18.2A38.2A\$.2AB2.B51.B2AB57.C5.ABA11.3AC13.AB.C6.AB5.3A18.2A38.2A\$2.3AC53.2A16.B7.C15.2A14.CB5.2A.C12.2AB12.A.AB\$4.B25.2A43.3AC6.C15.2A13.2A6.AC15.A13.2A.A11.2C45.2A38.2A\$30.2A43.2A2.2A.2C2.2A28.3A6.2A24.C2.2ABA21.2ABC34.2A38.2A\$38.3A30.B4.A.2A.2A2.4A26.2AC.2A3.B2A28.3A21.2ACA\$38.3AC28.CBAB.CB.A.2ACAB2C2A27.6A.CA.A29.A22.3A.2A\$38.C2.2A28.2CA2.3A2.C2A2C2B29.A.B2A.C.3A54.ABA41.2A\$41.2A27.ABC2A.2AB3A2CBA30.3A.AC4.2A21.C32.ABA41.2A\$40.3A27.2A.A3.B.A.AC.B32.2A3.B.2A21.2AB32.3A\$37.C.2A29.4AC2.C.5A34.2AB2A.2A20.2AB16.2A38.2A38.2A\$40.BC28.A.A2.C.2A3.C2A32.BA.2C2A.A21.2A16.2A38.2A10.2A.2A23.2A10.2A\$39.C31.3A2.2A.AB4A32.C2.BA2.AC91.2A.2A35.2A\$71.5AB.A.CA30.C.C3.B.A2.A.B\$72.2A.7A29.BAC4.C5A.CAC\$76.A2.3A30.3ACBA4.2B.B.AB23.2A\$112.2A.BC3A.AB2A.3A23.2A\$116.A.A.2A.A2.A\$116.CB2.2C.2A.2A113.A\$116.2AC2AB2A.AB2A111.3A9.C\$117.3A.A.A2CBA27.2A82.2ABA7.BCAB\$117.3A2.CBAB2A27.2A42.A40.2A8.A2B\$198.B3A37.A2.A7.4A\$155.2A40.C.B2A37.2A2BA9.CAC\$155.2A40.CB.2A37.A3BA9.B.B\$196.B2.A37.BA2.ACA8.CA.C\$196.2C.2A35.2AC2A.B10.2BC\$196.B2.2A36.B4ACA\$196.3A39.A.A.2A\$197.2AC39.2A2BA\$240.4A\$241.A8\$236.3A\$236.B2A\$237.C!`

Speeds found so far:

(1,1)c/8 [diagonal c/8]
(2,2)c/250 [diagonal c/125]
(8,6)c/32 [knight (4,3)c/16]
orthogonal c/2 ("basic" spaceships)
ebcube

Posts: 124
Joined: February 27th, 2010, 2:11 pm

### Re: 3458/37/4

Nice one, ebcube.

This quadratic has a similar form, releasing K-puffers symmetrically backward:
`x = 61, y = 47, rule = 3458/37/453.B\$52.3C\$54.B\$50.2A.2A\$49.3ACBC\$49.B.2C\$33.A.2A12.A3C.C\$31.6AC9.C3A3B\$28.C.3A2.A.2A8.A\$28.4AB.C2.2A8.6A.2C\$26.2A.A.C4.2A9.4ABA.B\$25.3ACB2.BC2.2AC10.4AB2A\$.2AC11.BC9.2A.C.C19.A.2A\$2AB.B4.2A.A.A.2A13.CB3.2AB\$.3AC3.CB9A12.C4.AB.C\$5.A.A4.A.A.AB4A4.C.2C7.3A\$3.8A.A2.C3A.2AC.3A2.B6.A.AB15.A\$2.2AB2.A.A.BA.A2.C2.A.2B.2A2.C5.C2A.C13.3AB\$3.2AC4.6AB2A.A.C4AC.CB4.B.A15.2AC2A.C\$12.A.A3.5A2.3A.C6.B16.3A2.AB\$13.C.B2.AC.2A4.CB6.C20.2A.AC\$14.B2C.C2AC5.C28.3A\$19.2A6.C29.AC2\$19.2A6.C29.AC\$14.B2C.C2AC5.C28.3A\$13.C.B2.AC.2A4.CB6.C20.2A.AC\$12.A.A3.5A2.3A.C6.B16.3A2.AB\$3.2AC4.6AB2A.A.C4AC.CB4.B.A15.2AC2A.C\$2.2AB2.A.A.BA.A2.C2.A.2B.2A2.C5.C2A.C13.3AB\$3.8A.A2.C3A.2AC.3A2.B6.A.AB15.A\$5.A.A4.A.A.AB4A4.C.2C7.3A\$.3AC3.CB9A12.C4.AB.C\$2AB.B4.2A.A.A.2A13.CB3.2AB\$.2AC11.BC9.2A.C.C19.A.2A\$25.3ACB2.BC2.2AC10.4AB2A\$26.2A.A.C4.2A9.4ABA.B\$28.4AB.C2.2A8.6A.2C\$28.C.3A2.A.2A8.A\$31.6AC9.C3A3B\$33.A.2A12.A3C.C\$49.B.2C\$49.3ACBC\$50.2A.2A\$54.B\$52.3C\$53.B!`

`x = 453, y = 111, rule = 3458/37/496.C\$87.B7.3A\$85.3AC3.6A\$84.2AB3.A.2A2.C2.CB\$85.4ABABA.CB3.3A\$86.A.ABA.AB2.CB.2A\$86.A.3AC.AC.2A.A.A\$85.5A3.B.B.A.2AB\$84.2AB2.AB3ACACA2.AC\$85.2AC.3A.B.B2ABC2\$85.2AC.3A.B.B2ABC\$84.2AB2.AB3ACACA2.AC\$85.5A3.B.B.A.2AB\$86.A.3AC.AC.2A.A.A\$86.A.ABA.AB2.CB.2A\$85.4ABABA.CB3.3A\$84.2AB3.A.2A2.C2.CB\$85.3AC3.6A\$87.B7.3A\$96.C2\$2.AC\$3AB\$2AC2.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.2A\$81A\$2.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A\$2.A.CB\$3AB\$2ACAC\$2AB2\$110.C\$101.B7.3A\$99.3AC3.6A\$98.2AB3.A.2A2.C2.CB\$99.4ABABA.CB3.3A\$100.A.ABA.AB2.CB.2A\$100.A.3AC.AC.2A.A.A\$99.5A3.B.B.A.2AB\$98.2AB2.AB3ACACA2.AC\$99.2AC.3A.B.B2ABC\$256.A194.2A\$99.2AC.3A.B.B2ABC132.B6.A.3A191.B3A\$98.2AB2.AB3ACACA2.AC128.3AC3.B2ABABA191.A2CB\$99.5A3.B.B.A.2AB127.2AB2.2BC.2A.A126.A65.2AC\$100.A.3AC.AC.2A.A.A128.4AC.C.BA5.2BC110.B6.A.3A53.AC8.A.2AC\$100.A.ABA.AB2.CB.2A131.2BA.BAC5.2AC109.3AC3.B2ABABA51.3AB7.3A.B\$99.4ABABA.CB3.3A130.BABC2A.C2.2C.A.C107.2AB2.2BC.2A.A53.2AC.B6.4A\$98.2AB3.A.2A2.C2.CB129.6A.2A.B2.B.2A109.4AC.C.BA5.2BC47.4AC4.2A.A\$99.3AC3.6A131.2AB.A.A.2AC.CAB.BC111.2BA.BAC5.2AC51.A4.B2A.A\$101.B7.3A132.2AC2.C3A3.BC114.BABC2A.C2.2C.A.C50.AC3AC2AC2A\$110.C259.6A.2A.B2.B.2A48.3ABC2A3.3A\$244.2AC2.C3A3.BC111.2AB.A.A.2AC.CAB.BC48.2AC4A\$243.2AB.A.A.2AC.CAB.BC109.2AC2.C3A3.BC51.2AB\$244.6A.2A.B2.B.2A\$246.BABC2A.C2.2C.A.C108.2AC2.C3A3.BC51.2AB\$246.2BA.BAC5.2AC108.2AB.A.A.2AC.CAB.BC48.2AC4A\$244.4AC.C.BA5.2BC108.6A.2A.B2.B.2A48.3ABC2A3.3A\$243.2AB2.2BC.2A.A116.BABC2A.C2.2C.A.C50.AC3AC2AC2A\$244.3AC3.B2ABABA114.2BA.BAC5.2AC51.A4.B2A.A\$246.B6.A.3A112.4AC.C.BA5.2BC47.4AC4.2A.A\$256.A112.2AB2.2BC.2A.A53.2AC.B6.4A\$370.3AC3.B2ABABA51.3AB7.3A.B\$372.B6.A.3A53.AC8.A.2AC\$382.A65.2AC\$449.A2CB\$449.B3A\$451.2A22\$178.3A\$168.AC5.AB.3A\$166.3AB4.C2ACACB\$166.2AC.A2C2.2A.BA\$166.3A2B4.CBA4.2C\$168.A2CB.CB6.2B\$168.ACAC.2A7.A\$166.7A.2A.C2.C.2B\$166.2AC.A.A.BA3.BC.C\$166.2AB4.3A3.C2\$166.2AB4.3A3.C\$166.2AC.A.A.BA3.BC.C\$166.7A.2A.C2.C.2B\$168.ACAC.2A7.A\$168.A2CB.CB6.2B\$166.3A2B4.CBA4.2C\$166.2AC.A2C2.2A.BA\$166.3AB4.C2ACACB\$168.AC5.AB.3A\$178.3A!`

The initial trail can changed in length by a multiple of 10, longer or shorter (this one is 70 cells shorter):
`x = 383, y = 111, rule = 3458/37/426.C\$17.B7.3A\$15.3AC3.6A\$14.2AB3.A.2A2.C2.CB\$15.4ABABA.CB3.3A\$16.A.ABA.AB2.CB.2A\$16.A.3AC.AC.2A.A.A\$15.5A3.B.B.A.2AB\$14.2AB2.AB3ACACA2.AC\$15.2AC.3A.B.B2ABC2\$15.2AC.3A.B.B2ABC\$14.2AB2.AB3ACACA2.AC\$15.5A3.B.B.A.2AB\$16.A.3AC.AC.2A.A.A\$16.A.ABA.AB2.CB.2A\$15.4ABABA.CB3.3A\$14.2AB3.A.2A2.C2.CB\$15.3AC3.6A\$17.B7.3A\$26.C2\$2.AC\$3AB\$2AC2.A.A.2A\$11A\$2.A.A.A.A\$2.A.CB\$3AB\$2ACAC\$2AB2\$40.C\$31.B7.3A\$29.3AC3.6A\$28.2AB3.A.2A2.C2.CB\$29.4ABABA.CB3.3A\$30.A.ABA.AB2.CB.2A\$30.A.3AC.AC.2A.A.A\$29.5A3.B.B.A.2AB\$28.2AB2.AB3ACACA2.AC\$29.2AC.3A.B.B2ABC\$186.A194.2A\$29.2AC.3A.B.B2ABC132.B6.A.3A191.B3A\$28.2AB2.AB3ACACA2.AC128.3AC3.B2ABABA191.A2CB\$29.5A3.B.B.A.2AB127.2AB2.2BC.2A.A126.A65.2AC\$30.A.3AC.AC.2A.A.A128.4AC.C.BA5.2BC110.B6.A.3A53.AC8.A.2AC\$30.A.ABA.AB2.CB.2A131.2BA.BAC5.2AC109.3AC3.B2ABABA51.3AB7.3A.B\$29.4ABABA.CB3.3A130.BABC2A.C2.2C.A.C107.2AB2.2BC.2A.A53.2AC.B6.4A\$28.2AB3.A.2A2.C2.CB129.6A.2A.B2.B.2A109.4AC.C.BA5.2BC47.4AC4.2A.A\$29.3AC3.6A131.2AB.A.A.2AC.CAB.BC111.2BA.BAC5.2AC51.A4.B2A.A\$31.B7.3A132.2AC2.C3A3.BC114.BABC2A.C2.2C.A.C50.AC3AC2AC2A\$40.C259.6A.2A.B2.B.2A48.3ABC2A3.3A\$174.2AC2.C3A3.BC111.2AB.A.A.2AC.CAB.BC48.2AC4A\$173.2AB.A.A.2AC.CAB.BC109.2AC2.C3A3.BC51.2AB\$174.6A.2A.B2.B.2A\$176.BABC2A.C2.2C.A.C108.2AC2.C3A3.BC51.2AB\$176.2BA.BAC5.2AC108.2AB.A.A.2AC.CAB.BC48.2AC4A\$174.4AC.C.BA5.2BC108.6A.2A.B2.B.2A48.3ABC2A3.3A\$173.2AB2.2BC.2A.A116.BABC2A.C2.2C.A.C50.AC3AC2AC2A\$174.3AC3.B2ABABA114.2BA.BAC5.2AC51.A4.B2A.A\$176.B6.A.3A112.4AC.C.BA5.2BC47.4AC4.2A.A\$186.A112.2AB2.2BC.2A.A53.2AC.B6.4A\$300.3AC3.B2ABABA51.3AB7.3A.B\$302.B6.A.3A53.AC8.A.2AC\$312.A65.2AC\$379.A2CB\$379.B3A\$381.2A22\$108.3A\$98.AC5.AB.3A\$96.3AB4.C2ACACB\$96.2AC.A2C2.2A.BA\$96.3A2B4.CBA4.2C\$98.A2CB.CB6.2B\$98.ACAC.2A7.A\$96.7A.2A.C2.C.2B\$96.2AC.A.A.BA3.BC.C\$96.2AB4.3A3.C2\$96.2AB4.3A3.C\$96.2AC.A.A.BA3.BC.C\$96.7A.2A.C2.C.2B\$98.ACAC.2A7.A\$98.A2CB.CB6.2B\$96.3A2B4.CBA4.2C\$96.2AC.A2C2.2A.BA\$96.3AB4.C2ACACB\$98.AC5.AB.3A\$108.3A!`
knightlife

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

### Re: 3458/37/4

knighlife, your "clean K-puffer K-rake" particularly appeals to me.

I just found that a slight rule change also turns the original K-puffer engine into a K-ship:
`x = 14, y = 13, rule = 345/378/4C5\$11.A\$10.3A\$10.ABA\$11.A\$10.B.2A\$10.BC2A\$9.C.3A\$10.C!`
but aren't rushing to explore the obvious adjacent possibilities. No such luck as yet with the true (4,2)c/10 puffer block trail which is still turning up occasionally in various WMPVN rules.

ynotds

Posts: 31
Joined: August 23rd, 2010, 8:38 am
Location: Melbourne, Australia

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