## A spaceship in Langtons Ant!?

For discussion of other cellular automata.
gameoflifemaniac
Posts: 1028
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: A spaceship in Langtons Ant!?

A LOT of oscillators. Most of them are by me.

Code: Select all

x = 163, y = 147, rule = Langtons-Ant
119.A\$119.2A\$118.2A.A12.2A\$118.A2.2A2.A2.A2.A.2A.A\$117.2A.2A2.A2.A2.A
4.A.A12.2A\$114.3A3.A5.A.2A2.4A.A3.4A6.2A\$115.A3.2A.A6.2A.A.A.A3.A4.3A
2.2A.A\$116.3A2.A2.A2.4A3.A.2A.A2.A2.A.A.A3.A\$108.2A4.2A.A2.A2.A5.A3.A
.2A.A2.2A2.2A2.A2.A\$107.A2.A4.2A.4A2.5A.2A7.A5.3A3.A\$106.3A.2A2.2A.A.
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6A3.3A.A.A.A2.A2.A2.5A.2A\$107.2A5.5A3.A.A.A4.A2.A.A4.A.2A.5A.3A\$107.A
8.2A.A.A2.3A2.A.4A.3A.6A2.A.2A3.A\$108.A.3A3.A2.A3.2A.A.A.3A2.A2.A.A.A
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4.2A.2A4.A\$108.A3.A.4A4.2A.2A3.4A4.A3.A2.A.3A.2A.2A\$108.A2.11A.3A.3A
3.4A3.A.A4.4A3.A.A2.2A\$108.A.A.3A.3A7.A.3A2.2A.4A2.A.3A4.4A2.A.3A\$
108.A2.A2.A2.A.2A.A2.A.4A.A.5A2.2A.3A.A2.A2.3A3.A.A\$109.A2.A2.A2.3A.A
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5.HA4.I4.HA3.IG12.BI16.B24.A.3A.2A3.3A5.A3.A.2A2.A.A.3A7.4A3.A3.A\$57.
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107.A.A3.5A.A2.3A.2A.2A.A4.3A.A.A2.A3.A3.2A2.3A\$108.A.2A5.A2.6A2.A.A.
A.A.A2.A.2A2.3A.A3.5A\$111.A2.5A2.A.3A3.A.A5.2A.A.A4.2A.A3.A.A\$109.A2.
4A2.8A.A.A2.A.2A2.2A.A.A.A10.A\$110.A.2A3.A2.A.2A.2A.A7.A2.A.A4.A.3A.A
5.2A\$108.HA2.4A2.A.3A.A.2A.A10.5A.A.2A2.A.A4.2A\$17.AGE6.2A9.GA9.A10.A
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51.3A3.2A.A2.3A5.2A.A2.A.A3.2A2.A2.2A.A3.A3.A\$6.2G9.HIH16.EDG10.I9.I.
I49.A2.A4.A.2A7.A.A4.A2.A3.A4.A.5A2.A.A\$118.A2.A2.4A.2A.2A3.3A4.2A.A
2.3A.A.A.A\$70.2IB39.4A.A.2A.3A.5A4.A3.4A3.A.A.2A.A.A3.A.A\$71.DE39.A.A
.A10.2A.A.2A.A.A8.2A.2A.A2.2A2.3A\$70.2BC40.3A.A3.6A.A8.4A.3A.2A.2A3.A
.2A2.A\$114.3A2.A.2A2.6A.A.2A.A.3A.A4.2A4.6A\$118.A2.A3.5A3.3A2.A.A.A2.
4A.2A4.A\$115.2A.A8.2A2.3A.4A2.4A.A.5A\$3I111.A2.2A2.A6.3A2.4A.A.A5.2A
2.A.A.A\$3I80.H29.3A2.3A4.A2.2A2.2A.3A4.2A.A6.A\$83.A29.A.2A5.3A.4A2.A
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28.A.A2.A29.2A2.3A.2A4.A.2A.3A.A.2A.A2.2A2.3A\$35.A2.A14.E15.2A12.A2.
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67.G2.EA10.A2.A31.A.A.4A4.6A5.2A3.A.A\$83.3A29.A2.A.A4.2A2.A3.3A.A2.A
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2A.A.2A\$116.A2.A2.6A2.2A7.3A2.3A\$117.2A.A.A.4A3.A.A5.A4.3A\$47.I71.A2.
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37.IG23\$20.I\$16.C3.A3\$11.HA\$23.D3\$12.B\$23.AF\$103.2A\$102.AF2A\$15.A3.E
81.2A.A.A\$15.G84.A3.A.2A\$99.4A.3A.A\$99.5A.A2.2A\$100.A3.2A.2A.A\$101.3A
3.A2.2A4.2A\$102.A3.2A.2A.A2.A2.3A\$103.3A3.A2.2A2.A2.3A\$104.A3.2A.2A2.
A4.A.A\$105.3A3.3AHA2.A3.A\$106.A3.2A.2A2.2A2.A\$107.5A3.A3.A.A\$109.A2.
3A3.4A.10A\$112.4A2.A2.2A10.A\$107.A4.A.2A4.2A.A10.A\$107.A.A.5A3.2A.A7.
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.A2.A3.A3.A3.A.A\$109.A4.A2.2A4.2A6.3A\$108.A2.2A3.A.3A.4A2.A2.3A\$108.A
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4.A2.A.A.2A8.2A\$117.3A.A5.4A5.6A\$123.A12.A2.A.2A.A\$122.A2.A.3A5.3A3.
3A.A\$119.A2.3A2.2A6.A3.A.2A2.A\$119.A3.A2.A.2A7.4A2.3A\$119.A2.2A.A2.A
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3.A\$120.A.2A.A.2A\$126.A.A\$122.A.A3.A\$123.A3.2A\$124.3A!

Last edited by gameoflifemaniac on September 10th, 2017, 11:15 am, edited 1 time in total.
I was so socially awkward in the past and it will haunt me for my entire life.

83bismuth38
Posts: 466
Joined: March 2nd, 2017, 4:23 pm
Location: Still sitting around in Sagittarius A...
Contact:

### Re: A spaceship in Langtons Ant!?

p20272?! waw...
EDIT:some... things:

Code: Select all

x = 45, y = 18, rule = Langtons-Ant
26.I\$25.AIA16.A\$23.2A.2A\$24.4A\$22.2A.E.A\$22.AGA.A\$23.A2.A\$24.2A3\$2.2A
\$AC.A\$AIA\$42.A\$40.2I\$40.2I2\$37.A!

Code: Select all

x = 8, y = 10, rule = B3/S23
3b2o\$3b2o\$2b3o\$4bobo\$2obobobo\$3bo2bo\$2bobo2bo\$2bo4bo\$2bo4bo\$2bo!
No football of any dui mauris said that.

83bismuth38
Posts: 466
Joined: March 2nd, 2017, 4:23 pm
Location: Still sitting around in Sagittarius A...
Contact:

### Re: A spaceship in Langtons Ant!?

BUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUMBT:

Code: Select all

x = 818, y = 727, rule = Langtons-Ant
782.A2.2A\$782.6A\$770.2A2.A3.2A.2A2.2A3.A\$769.A2.A2.3A3.3A.A2.3A\$768.A
4.A2.A6.A.A.A.2A\$763.2A2.2A.4A3.2A.4A3.3A.A\$762.4A2.3A2.A3.A4.2A2.2A
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2A.2A.2A2.A3.2A.2A2.2A2.A3.A.A.2A\$764.A4.4A.3A.A.A2.3A.5A.A5.A.A2.2A.
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2A\$180.A2.3A2.A.A\$179.3A3.A2.2A\$178.A2.3A2.A.A\$177.3A3.A2.2A\$176.A2.
3A2.A.A\$175.3A3.A2.2A\$174.A2.3A2.A.A\$173.3A3.A2.2A\$172.A2.3A2.A.A\$
171.3A3.A2.2A\$170.A2.3A2.A.A\$169.3A3.A2.2A\$168.A2.3A2.A.A\$167.3A3.A2.
2A\$166.A2.3A2.A.A\$165.3A3.A2.2A\$164.A2.3A2.A.A\$163.3A3.A2.2A\$162.A2.
3A2.A.A\$161.3A3.A2.2A\$160.A2.3A2.A.A\$159.3A3.A2.2A\$158.A2.3A2.A.A\$
157.3A3.A2.2A\$156.A2.3A2.A.A\$155.3A3.A2.2A\$154.A2.3A2.A.A\$153.3A3.A2.
2A\$152.A2.3A2.A.A\$151.3A3.A2.2A\$150.A2.3A2.A.A\$149.3A3.A2.2A\$148.A2.
3A2.A.A\$147.3A3.A2.2A\$146.A2.3A2.A.A\$145.3A3.A2.2A\$144.A2.3A2.A.A\$
143.3A3.A2.2A\$142.A2.3A2.A.A\$141.3A3.A2.2A\$140.A2.3A2.A.A\$139.3A3.A2.
2A\$138.A2.3A2.A.A\$137.3A3.A2.2A\$136.A2.3A2.A.A\$135.3A3.A2.2A\$134.A2.
3A2.A.A\$133.3A3.A2.2A\$132.A2.3A2.A.A\$131.3A3.A2.2A\$130.A2.3A2.A.A\$
129.3A3.A2.2A\$128.A2.3A2.A.A\$127.3A3.A2.2A\$126.A2.3A2.A.A\$125.3A3.A2.
2A\$124.A2.3A2.A.A\$123.3A3.A2.2A\$122.A2.3A2.A.A\$121.3A3.A2.2A\$120.A2.
3A2.A.A\$119.3A3.A2.2A\$118.A2.3A2.A.A\$117.3A3.A2.2A\$116.A2.3A2.A.A\$
115.3A3.A2.2A\$114.A2.3A2.A.A\$113.3A3.A2.2A\$112.A2.3A2.A.A\$111.3A3.A2.
2A\$110.A2.3A2.A.A\$109.3A3.A2.2A\$108.A2.3A2.A.A\$107.3A3.A2.2A\$106.A2.
3A2.A.A\$105.3A3.A2.2A\$104.A2.3A2.A.A\$103.3A3.A2.2A\$102.A2.3A2.A.A\$
101.3A3.A2.2A\$100.A2.3A2.A.A\$99.3A3.A2.2A\$98.A2.3A2.A.A\$97.3A3.A2.2A\$
96.A2.3A2.A.A\$95.3A3.A2.2A\$94.A2.3A2.A.A\$93.3A3.A2.2A\$92.A2.3A2.A.A\$
91.3A3.A2.2A\$90.A2.3A2.A.A\$89.3A3.A2.2A\$88.A2.3A2.A.A\$87.3A3.A2.2A\$
86.A2.3A2.A.A\$85.3A3.A2.2A\$84.A2.3A2.A.A\$83.3A3.A2.2A\$82.A2.3A2.A.A\$
81.3A3.A2.2A\$80.A2.3A2.A.A\$79.3A3.A2.2A\$78.A2.3A2.A.A\$77.3A3.A2.2A\$
76.A2.3A2.A.A\$75.3A3.A2.2A\$74.A2.3A2.A.A\$73.3A3.A2.2A\$72.A2.3A2.A.A\$
71.3A3.A2.2A\$70.A2.3A2.A.A\$69.3A3.A2.2A\$68.A2.3A2.A.A\$67.5A.A2.2A\$67.
3A2.A.A.A\$68.A.3A.2A\$68.A2.2A.A\$67.3A.3A\$67.AIA.2A\$68.2A!

Code: Select all

x = 8, y = 10, rule = B3/S23
3b2o\$3b2o\$2b3o\$4bobo\$2obobobo\$3bo2bo\$2bobo2bo\$2bo4bo\$2bo4bo\$2bo!
No football of any dui mauris said that.

fluffykitty
Posts: 653
Joined: June 14th, 2014, 5:03 pm
Contact:

### Re: A spaceship in Langtons Ant!?

Yeah, that happens with reversible Turmites.
I like making rules

gameoflifemaniac
Posts: 1028
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: A spaceship in Langtons Ant!?

New oblique puffer!

Code: Select all

x = 2, y = 2, rule = Langtons-Ant
2I\$AG!
Can someone figore out the speed? It probably is (3,5)c/102.
EDIT:

Code: Select all

x = 7, y = 1, rule = Langtons-Ant
2B9A!
I was so socially awkward in the past and it will haunt me for my entire life.

Rhombic
Posts: 1064
Joined: June 1st, 2013, 5:41 pm

### Re: A spaceship in Langtons Ant!?

A variant of that oscillator idea gives a new family of adjustable period oscillators:

Code: Select all

x = 30, y = 2, rule = Langtons-Ant
2B20A.3A\$26.4A!
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

KittyTac
Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: A spaceship in Langtons Ant!?

Imagine if Langton's ant would be proven universal.

gameoflifemaniac
Posts: 1028
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: A spaceship in Langtons Ant!?

Oscillator collection:

Code: Select all

x = 1102, y = 59, rule = Langtons-Ant
A.A4.3A4.A.3A4.3A.3A4.3A.A.A4.3A.3A4.3A.3A4.3A.3A4.A.A.3A4.A.A.A.A4.A
.A.3A4.3A.3A4.3A.3A4.3A.A.A4.3A.3A4.3A.3A4.3A.3A4.3A.3A4.3A.3A4.A.3A.
3A4.A.A.3A4.A.A.3A4.A.3A.3A4.A.3A.A.A4.A.3A.3A4.A.A.A.3A4.A.3A.3A4.A.
3A.3A4.3A.3A.3A4.3A.3A.3A4.3A.A.A.3A4.3A.3A.3A4.3A.3A.3A4.3A.3A.A.A4.
3A.3A.3A4.3A.3A.3A4.3A.3A.3A4.A.A.3A.A.A4.A.A.3A.3A4.A.A.3A.3A4.A.A.
3A.3A4.A.A.3A.3A4.A.A.3A.A.A4.3A.3A.3A4.3A.A.A.3A7.3A.3A.3A6.3A.3A.A.
A8.3A.3A.3A6.A.A.3A.A.A10.A.A.3A.3A10.A.A.3A.A.A8.A.3A.A.A.3A11.A.3A.
3A.3A9.3A.3A.A.A.3A12.3A.3A.3A.3A11.3A.3A.3A.3A12.3A.3A.A.A.3A21.A.A.
3A.3A.3A40.A.3A.A.3A.3A64.A.A.A.A.A.3A82.3A.A.3A.3A.3A\$A.A4.A.A4.A.A
8.A.A.A6.A.A.A6.A.A.A6.A3.A6.A.A6.A.A.A.A4.A.A.A.A4.A.A.A.A4.A3.A6.A
3.A.A4.A3.A.A4.A3.A.A6.A3.A6.A.A6.A.A.A.A4.A.A.A6.A.A.A.A.A4.A.A3.A4.
A.A.A6.A3.A.A.A4.A3.A.A.A4.A3.A.A6.A.A.A.A.A4.A.A3.A6.A3.A3.A6.A.A.A.
A.A6.A3.A.A.A6.A.A.A.A.A6.A.A5.A6.A.A3.A8.A.A.A.A.A6.A.A3.A.A6.A3.A.A
8.A.A.A.A.A4.A.A.A.A.A.A4.A.A3.A.A.A4.A.A3.A3.A4.A.A.A3.A6.A.A3.A.A6.
A.A.A.A.A.A4.A3.A.A.A.A4.A3.A.A.A.A7.A3.A3.A.A6.A.A3.A.A.A8.A.A3.A3.A
6.A.A.A.A.A.A10.A.A3.A.A.A10.A.A.A.A.A.A8.A3.A.A.A.A.A11.A.A.A.A5.A
11.A3.A.A.A.A.A14.A.A.A.A.A.A.A13.A.A3.A5.A14.A.A.A.A.A.A.A21.A.A3.A.
A5.A40.A.A.A.A3.A.A66.A.A.A.A.A3.A82.A3.A3.A3.A.A\$3A4.3A4.A.3A4.3A.A.
A4.3A.3A4.3A.3A4.3A.3A4.3A.3A4.3A.A.A4.3A.3A4.3A.3A4.3A.3A4.3A.A.A4.
3A.3A4.3A.3A6.A.3A6.A.3A4.3A.3A4.3A.3A4.A.A.A.3A4.A.A.3A4.A.A.3A4.A.
3A.A.A4.A.3A.3A4.A.3A.3A4.A.3A.A.A4.A.3A.3A4.A3.A.3A4.3A.A.A.3A4.3A.
3A.A.A4.3A.3A.3A4.3A.3A.3A4.3A.3A.3A4.3A.3A.3A4.3A.3A.A.A4.3A3.A.3A4.
3A.3A.A.A4.3A.A.A.3A4.3A.3A.3A4.3A.3A.3A4.3A.3A.3A4.3A3.A.3A4.3A.3A.
3A4.3A.A.A.A.A4.3A.3A.3A7.3A.3A.3A6.3A.3A.3A8.3A3.A.3A6.A.A.A.A.3A10.
A.A.3A.3A10.A.A.3A.3A8.A3.A.3A.3A11.A.3A.3A.3A9.3A.3A.3A.A.A12.3A.3A.
A.A.3A11.3A.3A.3A.3A12.3A.3A.3A.3A21.3A.3A.3A.3A40.A.3A.A3.A.3A64.3A.
A.A.A.3A82.3A.A.3A.3A.3A\$2.A4.A.A4.A.A.A4.A3.A.A4.A5.A4.A3.A.A6.A.A8.
A.A.A6.A.A.A6.A3.A6.A.A.A6.A.A.A4.A.A.A.A4.A.A3.A4.A.A.A.A6.A.A8.A.A.
A4.A.A.A.A6.A.A.A4.A.A.A.A.A4.A.A.A6.A.A.A.A4.A.A3.A.A4.A.A5.A4.A3.A.
A.A4.A3.A.A.A4.A3.A.A.A4.A3.A.A6.A3.A.A.A.A4.A3.A3.A.A4.A5.A.A.A4.A5.
A.A6.A5.A.A.A4.A3.A.A3.A6.A.A.A.A.A6.A3.A.A.A6.A.A.A.A.A6.A.A.A3.A6.A
.A3.A.A6.A3.A.A8.A3.A.A.A6.A3.A.A.A6.A.A.A3.A6.A.A.A.A.A6.A3.A.A.A7.A
.A.A.A.A.A6.A.A.A5.A8.A.A3.A.A8.A.A.A.A3.A10.A.A.A3.A.A10.A.A.A.A3.A
8.A3.A3.A.A.A11.A.A.A3.A.A11.A3.A5.A.A.A12.A3.A.A.A.A.A.A13.A3.A3.A.A
16.A3.A3.A.A.A23.A3.A3.A.A42.A3.A.A3.A.A.A66.A.A.A.A.A86.A.A3.A3.A.A.
A\$2.A4.3A4.A.3A4.3A.3A4.3A3.A4.3A.3A4.3A.3A4.3A.3A6.A.3A6.A3.A6.A.3A
4.3A.3A4.3A.3A4.3A3.A4.3A.3A6.A.3A6.A.3A4.3A.3A4.3A.3A4.A.3A.3A4.A.A.
3A4.A.A.3A4.A.3A.3A4.A.3A3.A4.A.3A.3A4.A3.A.3A4.A.3A.3A4.A3.A.3A4.3A.
3A.3A4.3A.3A.3A4.3A3.A.3A4.3A.3A.3A4.3A.3A.3A4.3A.3A3.A4.3A.3A.3A4.3A
3.A.3A4.3A.3A.3A6.A.3A3.A6.A.3A.3A6.A.3A.3A6.A.3A.3A6.A3.A.3A6.A.3A3.
A4.3A.3A.3A4.3A3.A.3A7.3A.3A.3A6.3A.3A3.A8.3A3.A.3A6.A.A.3A3.A10.A.A.
3A.3A10.A.A.3A3.A8.A3.A3.A.3A11.A.3A.3A.3A9.3A.3A3.A.3A12.3A.3A.3A.3A
11.3A.3A.3A.3A12.3A.3A3.A.3A23.A.3A.3A.3A40.A.3A.A3.A.3A66.A.A.A.A.3A
82.3A.A.3A.3A.3A3\$B\$HA6.AF26.IG20.IE10.A21.CI\$15.DB54.GI52.F9.I2.C40.
EA258.B\$8.D17.AIC18.2D31.2A21.D54.D9.AFB8.GA95.AB13.A40.F2.B56.I44.2A
CGA28.2A14.D25.BA43.C2.I44.A\$114.ECA8.F20.CG55.A10.2A22.2A10.ACIA22.A
13.2E56.ABA26.B13.I45.B30.F13.F91.HA\$36.B153.F24.F190.I4.C162.B37.F
12.A40.F6.H\$8.B7.F19.F55.B171.H52.A43.ACI119.F13.A17.B11.B13.2CA12.A
39.D26.ACI\$7.ABA6.D31.I9.2BA255.EC130.I2.E46.DB13.2A25.A14.2B33.F\$26.
B20.AI20.CG22.B223.A181.A12.B15.H26.A\$24.HA44.A9.AGCA30.ABH532.A.A
C21.ACG\$37.F141.CG554.F4.F25.2A46.I4.I32.B\$180.A209.BA374.C\$25.AGI8.D
23.A\$49.F8.DH10.A2.A18.BA22.B274.H\$15.2A30.D23.EC18.AB21.F\$15.CG\$890.
E26.I2\$25.AEC8.E\$36.GA\$92.2A86.D\$69.2B2A18.F2.F85.A\$180.A\$180.B\$24.B
2AB8.C\$36.2A1026.E36.E\$37.C\$92.A\$92.A\$91.DB3\$37.F\$37.A\$38.F6\$36.A\$37.
IG5\$965.E44.I2\$36.AECA!
I could not find any p12 oscillator. Are there any?
I was so socially awkward in the past and it will haunt me for my entire life.

wildmyron
Posts: 1397
Joined: August 9th, 2013, 12:45 am

### Re: A spaceship in Langtons Ant!?

gameoflifemaniac wrote:I could not find any p12 oscillator. Are there any?
p12:

Code: Select all

x = 4, y = 2, rule = Langtons-Ant
2AB\$2.BA!
This small collection completes the divisible by 4 periods up to 100
p52, p80, p84, p92, p100

Code: Select all

x = 83, y = 7, rule = Langtons-Ant
2A2.2A18.3A16.2A15.A3.2A15.AE\$2.2D20.2AEA13.3AB15.2A.I2.C13.A.A\$2A2.
2A16.A3.C17.D36.G\$22.2A16.2A\$20.A.2A17.2A\$20.3A\$21.A!
And a small collection of oscillators with periods not divisible by 4.
p18, p22, p34, p50, p54, p58, p74, p90

Code: Select all

x = 144, y = 7, rule = Langtons-Ant
DF18.2D19.C19.A20.E17.B2AB16.2A.B16.DB\$HB18.2B18.A21.A18.AG17.D2.D16.
2AHBA\$41.AC18.2A18.A.A17.2A19.D\$41.2GA16.D2.B17.2AE58.BD\$60.A.B17.2A.
EA\$60.4A16.A\$61.A.F!
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

gameoflifemaniac
Posts: 1028
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: A spaceship in Langtons Ant!?

P2!

Code: Select all

x = 2, y = 2, rule = Langtons-Ant
BF\$HD!
I was so socially awkward in the past and it will haunt me for my entire life.

thorsilver
Posts: 13
Joined: March 31st, 2018, 9:43 pm
Location: Glasgow, Scotland

### Re: A spaceship in Langtons Ant!?

KittyTac wrote:Imagine if Langton's ant would be proven universal.
Langton's Ant was proven universal back in 2000: http://www.dim.uchile.cl/~anmoreir/ofic ... on_dam.pdf

kthxbye
Posts: 6
Joined: January 30th, 2019, 9:31 am

### Re: A spaceship in Langtons Ant!?

English not my native.

There exist another thread about LA, but I more appreciate this one. I have noticed some (maybe) interesting things, here they are:

1) If we place 2 ants with same direction and coordinats (x1,y1) and (x2,y2) on infinite grid (all cells one-colored), so they:

1.1) may meet in one cell and destroy each other;
1.2) create an oscillator;
1.3) at least one of them build highway.

If distance between two ants very long, they obviosly always build two non-crossing patterns and finally two highways. But there also exist some infinite, but bounded area, so if we define a=|x1-x2|, b=|y1-y2|, k,m - integers, k>=0, m>=0, there are:

a) finite number of (1.1) for some a=2k, b=2m;
b) infinite number of (1.2) for some a=2k, b=2m+1 (or a=2k+1, b=2m);
c) infinite number of (1.3) for any a=2k+1, b=2m+1 (and also for some a=2k, b=2m or a=2k, b=2m+1 or a=2k+1, b=2m).

Also if we define p1 as periodicity of (1.2) for a=2k, b=2m+1 (and p2 for a=2k+1, b=2m), n - natural, n>=2, so:

a) gcd(p1,2^n)>=4;
b) gcd(p2,2^n)=4;

2) Shortest way to build two different highways.

Code: Select all

x = 6, y = 2, rule = Langtons-Ant
E2.E\$2.E2.E!
Also if we numerate a1(0,0), a2(2,1), a3(3,0), a4(5,1), so:

a) a3 build standard highway (2,2)c/104;
b) a1 and a4 build highway (3,5)c/102;
c) a2 decorates their work with (6,10)c/688.

3) Cherry on the cake - absolute oscillator (which about I was asking here).

Code: Select all

x = 218, y = 3, rule = Langtons-Ant
B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.
B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.
B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.
B2.B2.B2.B2\$.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B
2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B
2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B2.B
2.B2.B2.B2.B2.B2.B2.B2.B!
kthxbye wrote:Take any oscillator. Choose any generation (we need at least one). Clone it n times on infinite grid with two conditions: 1) each copy shifted by the same distance from previous (we need at least one way); 2) for any natural n those groups of copies is also oscillators with P_k(n) (polynomial) periodicity. If it satisfies given conditinions we may define it as absolute oscillator.
For LA we can redefine it as simple (or single) block of colony. Also:

a) it's periodicity 4(8n+3);
b) first triangle finised after ~6n steps, second after ~12n steps;
c) after 2(8n+3) ants repeat all what they do symmetrically in backward order;
d) each ant moves in area bounded by square with side n+5;
e) real area where it moves (equivalently number of cells in area bounded by square which ant visit at least once) equal 5(n+3);
f) whole colony moves in area bounded by rectangle with length 3(n+1) and width 2(n+2);
g) real area 3n(n+5)+2.

If we define T1(n,k) as number of white cells colored to black at the whole period by upper ant in k-th block of colony length n blocks (and T2(n,k) for lower ant), so:

a) T1(n,k)=T2(n,k)=0, n<k
b) T1(n,k)=4(5n+1), k=1 or k=n;
c) T1(n,k)=2(11n+1), 1<k<n;
d) T2(n,k)=4(3n+2), k=1 or k=n;
e) T2(n,k)=10(n+1), 1<k<n;
f) T1(n,k)+T2(n,k)=4(8n+3), n>=k.

If we define q(n,k) as number of black cells at k-th generation of colony length n blocks, q1(n,k)=q(n+1,k)-q(n,k), so:

a) q(n,k)=q(4(8n+3)±k);
b) q2(n,k)=q1(n+1,k)-q1(n,k)=0, 6n+9>=k;
c) q3(n,k)=q2(n+1,k+6)-q2(n,k)=0, 12n+4>=k;
d) q4(n,k)=q3(n+1,k+12)-q3(n,k)=0, 20n-4>=k;
e) q5(n,k)=q4(n+1,k+20)-q4(n,k)=0, 26n+15>=k;
f) sum(k=1..4(8n+3)) q1(n,k) = 8(77n+31);
g) sum(k=1..4(8n+3)) q(n,k) = 4(77n^2-3(5n-6)).

kthxbye
Posts: 6
Joined: January 30th, 2019, 9:31 am

### Re: A spaceship in Langtons Ant!?

Small and not very interesting addenum.

Oscillators which produce and use still life for their working.

Code: Select all

x = 47, y = 58, rule = Langtons-Ant
B24.B50\$B7\$46.B!
Specific one (look at it with slow speed).

Code: Select all

x = 28, y = 5, rule = Langtons-Ant
B4\$27.B!

kthxbye
Posts: 6
Joined: January 30th, 2019, 9:31 am

### Re: A spaceship in Langtons Ant!?

Not completely absolute oscillator, but family of oscillators which has similar properties. Here you can see 7 basic blocks.

Code: Select all

x = 26, y = 15, rule = Langtons-Ant
25.H2\$21.H2.F2\$17.H2.F2\$13.H2.F2\$9.H2.F2\$5.H2.F2\$.H2.F2\$F!
Each time when we add symmetrically 2n blocks, it always oscillates with p(n)=8(4n+21*floor(n/2)+53).

Code: Select all

x = 154, y = 79, rule = Langtons-Ant
153.H2\$149.H2.F2\$145.H2.F2\$141.H2.F2\$137.H2.F2\$133.H2.F2\$129.H2.F2\$
125.H2.F2\$121.H2.F2\$117.H2.F2\$113.H2.F2\$109.H2.F2\$105.H2.F2\$101.H2.F
2\$97.H2.F2\$93.H2.F2\$89.H2.F2\$85.H2.F2\$81.H2.F2\$77.H2.F2\$73.H2.F2\$69.H
2.F2\$65.H2.F2\$61.H2.F2\$57.H2.F2\$53.H2.F2\$49.H2.F2\$45.H2.F2\$41.H2.F2\$
37.H2.F2\$33.H2.F2\$29.H2.F2\$25.H2.F2\$21.H2.F2\$17.H2.F2\$13.H2.F2\$9.H2.F
2\$5.H2.F2\$.H2.F2\$F!
For example, when n=0 we have only basic 7 blocks = 14 ants and p(n)=8*53=424. If n=16, we have 7+2*16 = 39 blocks = 78 ants and p(n)=2280.

gameoflifemaniac
Posts: 1028
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: A spaceship in Langtons Ant!?

Here's a stamp collection of all small oscillators discovered by me (p12 by wildmyron).

Code: Select all

x = 1666, y = 66, rule = Langtons-Ant
3A6.A.A6.3A6.A.3A6.A.3A6.A.A.A6.A.3A6.A.3A6.3A.3A6.3A.3A6.3A.A.A6.3A.
3A6.3A.3A6.3A.3A6.3A.3A6.3A.A.A6.3A.3A6.3A.3A6.A.A.3A6.A.A.A.A6.A.A.
3A6.3A.3A6.3A.3A6.3A.3A6.3A.A.A6.3A.3A6.3A.3A6.3A.3A6.3A.3A6.3A.3A6.
3A.3A6.3A.3A6.3A.3A6.3A.3A6.A.3A.3A6.A.3A.A.A6.A.3A.3A6.A.A.3A6.A.A.
3A6.A.3A.3A6.A.3A.A.A6.A.3A.3A6.A.3A.3A6.A.3A.3A6.A.A.A.3A6.A.3A.3A5.
A.3A.3A6.A.3A.3A6.A.3A.A.A6.A.3A.3A6.A.3A.3A5.A.3A.3A7.A.3A.3A6.3A.3A
.3A6.3A.3A.A.A6.3A.A.A.3A6.3A.3A.3A6.3A.3A.A.A6.3A.3A.3A6.3A.3A.A.A6.
3A.3A.3A6.3A.3A.A.A6.3A.A.A.3A6.3A.A.A.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.
3A6.A.A.3A.A.A6.A.A.A.3A6.A.A.3A.3A6.A.A.3A.3A6.A.A.A.A.3A6.A.A.3A.A.
A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.A.3A16.3A.A.
3A15.3A.3A.3A11.3A.3A.3A9.3A.3A.3A6.3A.A.3A6.A.3A.3A.3A6.A.3A.3A.A.A
12.3A.3A.3A.A.A20.3A.A.A.A.3A16.3A.3A.3A.3A12.3A.3A.3A.3A15.3A.3A.3A.
3A14.3A.3A.A.A.3A17.A.A.A.A.A.3A20.A.A.3A.3A.3A25.3A.3A.3A.3A27.3A.3A
.3A.3A49.3A.3A.3A.3A\$2.A6.A.A6.A.A6.A.A.A6.A3.A6.A.A.A6.A.A8.A.A.A8.A
.A.A8.A3.A8.A.A.A8.A.A10.A.A.A8.A.A.A8.A3.A8.A.A.A8.A.A10.A.A.A6.A.A.
A.A6.A.A.A.A6.A.A.A.A6.A5.A6.A3.A8.A3.A.A6.A3.A.A6.A3.A.A8.A3.A8.A.A
10.A.A.A6.A.A.A.A6.A.A.A.A6.A.A3.A6.A.A.A8.A.A.A.A6.A.A.A.A.A6.A.A.A.
A.A6.A.A.A.A.A6.A.A3.A6.A.A.A8.A3.A3.A6.A3.A.A.A6.A3.A.A.A6.A3.A3.A6.
A3.A.A8.A.A.A.A.A6.A.A5.A5.A.A3.A8.A.A3.A.A6.A.A3.A.A6.A3.A3.A6.A3.A.
A7.A.A.A3.A7.A.A.A.A10.A.A.A.A.A8.A3.A.A.A8.A.A.A.A.A8.A.A3.A.A8.A.A.
A.A.A8.A.A.A.A.A8.A.A.A.A.A8.A.A.A.A10.A.A.A.A.A8.A.A.A.A.A8.A.A.A.A.
A8.A.A3.A.A8.A.A.A3.A8.A.A.A.A8.A.A.A.A.A.A6.A.A.A.A8.A.A3.A3.A6.A.A
3.A.A8.A.A.A.A.A.A6.A.A.A.A.A.A6.A3.A3.A8.A3.A.A.A.A6.A5.A.A.A6.A3.A
3.A.A6.A3.A3.A.A8.A.A3.A18.A.A.A19.A.A.A3.A11.A.A.A3.A11.A.A3.A3.A6.A
.A.A.A8.A.A5.A.A.A6.A.A5.A.A.A14.A3.A.A3.A.A22.A.A.A.A3.A18.A.A.A.A.A
.A.A14.A3.A.A5.A17.A.A3.A5.A16.A.A.A.A.A.A.A17.A.A.A.A.A.A.A20.A.A3.A
.A5.A25.A3.A.A.A3.A.A27.A5.A3.A.A.A49.A.A.A3.A.A.A.A\$3A6.3A6.3A6.A.A.
A6.A.3A6.A.3A6.A.3A6.A.3A6.3A.A.A6.3A.3A6.3A.3A6.3A.3A6.3A.3A6.3A.A.A
6.3A.3A6.3A.3A6.3A.3A6.3A.3A6.3A.A.A6.3A.3A6.3A.3A6.3A.3A6.3A.3A6.3A.
A.A6.3A.3A6.3A.3A8.A.3A8.A.3A8.A.3A6.3A.A.A6.3A.3A6.3A.3A6.3A.3A6.3A.
3A6.A.A.A.A.A6.A.A.A.3A6.A.A.A.3A6.A.A.3A6.A.A.3A6.A.3A.3A6.A.3A.3A6.
A.3A.3A6.A.3A.3A6.A.3A.3A6.A.3A.3A6.A.3A.3A5.A.3A.3A6.A.3A.A.A6.A.3A.
3A6.A3.A.3A6.A3.A.3A5.A.3A.3A7.A.3A.3A6.3A.A.A.3A6.3A.3A.3A6.3A.3A.A.
A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.A.A.3A6.3A.3A
.A.A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.A.A.3A6.3A.A.3A6.3A.
3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.A.A6.3A.3A.A.A6.
3A.3A.A.A6.3A.3A.3A8.A.A.3A18.A.A.3A17.A.3A.3A11.3A.3A.3A9.3A3.A.3A6.
3A.A.3A6.A.3A.3A.A.A6.A.3A.3A.3A12.3A.3A.3A.3A20.3A.3A.A.3A16.3A.3A.A
.A.3A12.3A.3A.3A.3A15.3A.3A.3A.3A14.3A.3A.3A.3A17.3A.A.3A.A.A20.3A.3A
.3A.3A25.3A.3A.3A.3A27.3A.3A.3A.3A49.3A.3A.3A.3A\$A10.A6.A.A6.A.A.A6.A
.A8.A3.A6.A.A.A6.A.A.A6.A3.A.A6.A3.A8.A5.A6.A3.A.A6.A3.A.A8.A.A.A8.A.
A10.A3.A8.A.A.A8.A.A.A8.A.A.A8.A3.A8.A.A.A8.A.A10.A.A.A6.A.A.A.A6.A.A
3.A6.A.A.A.A8.A.A10.A.A.A8.A.A.A6.A.A.A.A6.A.A.A.A8.A.A10.A.A.A8.A.A.
A6.A.A.A.A.A6.A.A.A3.A6.A.A.A.A.A6.A.A.A8.A.A.A.A6.A.A3.A8.A.A5.A6.A.
A3.A.A6.A3.A.A8.A3.A.A.A6.A3.A.A.A6.A3.A.A7.A3.A.A.A6.A.A.A.A.A6.A.A.
A3.A6.A3.A.A8.A3.A.A.A5.A3.A.A9.A3.A.A.A6.A3.A.A.A.A6.A3.A5.A6.A5.A.A
.A6.A3.A.A.A.A6.A3.A.A3.A6.A3.A.A.A.A6.A5.A3.A6.A5.A.A.A8.A.A.A3.A8.A
3.A.A.A8.A3.A.A.A8.A.A.A.A.A8.A3.A.A10.A3.A.A.A8.A.A.A3.A8.A.A.A.A8.A
3.A.A10.A3.A.A.A8.A3.A.A.A8.A.A.A3.A8.A3.A.A.A8.A.A.A.A.A6.A.A.A3.A.A
6.A.A.A.A.A.A6.A.A.A.A.A.A8.A.A.A20.A.A.A.A17.A3.A.A13.A.A3.A.A.A9.A.
A3.A.A10.A.A.A.A6.A3.A.A3.A.A6.A3.A.A5.A12.A5.A.A.A3.A20.A5.A.A.A18.A
3.A.A.A.A.A.A14.A3.A3.A.A19.A3.A3.A.A18.A3.A3.A.A.A19.A.A3.A.A.A22.A
3.A3.A.A29.A3.A.A.A.A.A27.A.A.A3.A3.A.A49.A.A.A.A.A.A.A.A\$3A8.A6.3A6.
A.3A6.A.3A6.A3.A6.A.3A6.A.3A6.3A.3A6.3A.3A6.3A3.A6.3A.3A6.3A.3A6.3A.
3A6.3A.3A6.3A3.A6.3A.3A6.3A.3A8.A.3A8.A3.A8.A.3A6.3A.3A6.3A.3A6.3A.3A
6.3A3.A6.3A.3A8.A.3A8.A.3A8.A.3A6.3A.3A6.3A.3A6.3A.3A6.3A.3A6.3A.3A6.
A.3A.3A6.A.3A3.A6.A.3A.3A6.A.A.3A6.A.A.3A6.A.3A.3A6.A.3A3.A6.A.3A.3A
6.A.3A.3A6.A.3A.3A6.A3.A.3A6.A.3A.3A5.A.3A.3A6.A.3A.3A6.A.3A3.A6.A3.A
.3A6.A3.A.3A5.A.3A.3A7.A.3A.3A6.3A.3A.3A6.3A.3A3.A6.3A3.A.3A6.3A.3A.
3A6.3A.3A3.A6.3A.3A.3A6.3A.3A3.A6.3A.3A.3A6.3A.3A3.A6.3A3.A.3A6.3A3.A
.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A8.A.3A3.A8.A.A.3A8.A.3A.3A8.A.3A.3A
8.A3.A.3A8.A.3A3.A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A6.3A.3A.3A
8.A.A.3A18.A.A.3A17.A.3A.3A11.3A.3A.3A9.3A3.A.3A6.3A.A.3A6.A.3A.3A.3A
6.A.3A.3A3.A12.3A.3A.3A3.A20.3A3.A.A.3A16.3A.3A.3A.3A12.3A.3A.3A.3A
15.3A.3A.3A.3A14.3A.3A3.A.3A19.A.A3.A.3A22.A.3A.3A.3A25.3A.3A.3A.3A
10.G39.A31.A26.2D42.DH88.A110.A\$28.D21.CA45.CE24.GC24.EA24.CE12.F10.A
2D.A10.2G.A26.BF14.C14.A57.DF27.G14.A15.A.B30.D.A82.A34.A65.B16.B36.D
B162.F90.H\$50.E98.E25.CE12.B11.BA38.FA25.C36.CG12.B13.H12.B24.B.A10.F
25.2B12.DF12.2D.A10.GE13.GE100.D13.ABDA13.A14.G12.HB12.AFDA13.E12.AB
14.H32.B18.F17.C47.DHA32.B49.A33.A34.2A81.H82.A91.B\$19.B260.F51.HF11.
2F22.A.D153.A43.B27.GE29.A44.DA130.AFB17.A13.B52.2E149.A31.D\$18.ABA
156.A154.F12.B24.A153.HB29.E56.I61.A30.A49.I.A14.C17.E16.A16.2F65.A
34.D13.G71.D45.A16.D14.AC17.F47.D18.A40.2F\$83.EG25.HB24.D25.2BA359.A
180.A85.G33.A35.AB12.E100.C15.GE17.F81.F16.GE40.2H44.A\$98.A23.A92.ABD
10.AB11.B11.D39.A11.F484.C84.C116.A100.A82.DH20.D36.G15.D18.F\$62.B35.
2B23.CE24.HBA37.FA38.B11.A12.AF37.B11.H77.FBA108.D381.I69.H230.FB19.B
25.F10.A.F37.DF37.2E38.2A40.A27.BA26.F566.F190.D16.D120.A26.F57.2B\$
184.B2.B\$215.2A12.FA140.DF196.FH337.A537.B4.B\$62.DA125.DFA36.AF141.A
D75.B78.D12.2E25.C11.FA11.2B366.DFA620.AFB30.2F\$111.I25.B75.2A25.AH
39.I\$109.G26.AB24.FA77.FA36.G39.F537.A.A798.C\$213.GE27.B37.E37.AHA
146.D302.A.D84.CG800.G\$61.EG126.A277.BD301.H886.I\$61.IC20.B2AB102.CI
277.B1189.E2\$111.A51.2B140.FA1286.H\$110.DF25.B24.2D130.A1298.BD\$136.A
157.D1299.F\$85.F50.B51.A103.H12.D\$84.ABA102.H\$162.2A25.F\$110.AECA49.H
B23.A2\$136.A\$136.H\$85.BF\$84.HD51.F2\$188.B\$189.H\$189.F\$190.D\$136.2D\$
137.2B3\$188.AF3\$189.D5\$189.F\$188.A2\$189.D!
I will still work on it and continuously extend the collection.
Last edited by gameoflifemaniac on April 6th, 2020, 2:49 pm, edited 3 times in total.
I was so socially awkward in the past and it will haunt me for my entire life.

yujh
Posts: 994
Joined: February 27th, 2020, 11:23 pm
Location: China
Contact:

### Langtons Ant.new.osc

HaHa!

Code: Select all

checking for oscillation...
P176376

Code: Select all

x = 72, y = 99, rule = Langtons-Ant
10.2A\$2A6.2A2.2A6.2A4.8A2.2A4.2A\$2A6.2A2.2A6.2A4.8A2.2A4.2A\$2A6.2A2.
2A6.2A8.2A4.2A4.2A\$2A6.2A2.2A6.2A8.2A4.2A4.2A\$2A6.2A2.2A6.2A8.2A4.2A
4.2A\$3A4.3A2.2A6.2A8.2A4.2A4.2A\$.3A2.3A3.2A6.2A8.2A4.8A\$2.6A4.2A6.2A
8.2A4.8A\$3.4A5.2A6.2A8.2A4.2A4.2A\$4.2A6.2A6.2A8.2A4.2A4.2A\$4.2A6.2A6.
2A2.2A4.2A4.2A4.2A\$4.2A6.3A4.3A2.3A2.3A4.2A4.2A\$4.2A7.8A4.6A5.2A4.2A\$
4.2A8.6A6.4A6.2A4.2A84\$70.2E!
B34kz5e7c8/S23-a4ityz5k!!!
Mission: find a rule with 2-5ob,7-15d,3-5o ships and 4 sparky hp osc.
B2ikn35j6i/S23-a8
B2ck3ar4ac5e6c7/S1e2-an3ejnr4air5iy6c7c8

Hunting
Posts: 2971
Joined: September 11th, 2017, 2:54 am

### Re: A spaceship in Langtons Ant!?

This is less trivial:

Code: Select all

x = 68, y = 41, rule = Langtons-Ant
22.2A\$21.A2.A\$18.3A4.A26.4A\$17.A8.A18.8A2.13A\$16.A10.A17.A.3A.A.2A.A
5.A4.A\$15.A12.A16.A2.A2.A.2A.4A.2A.4A\$14.A14.A15.A.A.A.A4.3A.3A4.A\$
13.A16.A14.A.3A.A.2A.2A.4A.4A\$12.A18.A13.A.3A.A.2A.A5.A4.A\$11.A20.A
12.23A\$10.A22.A\$9.A24.A\$8.A26.A\$7.A28.A\$6.A30.A\$5.A32.A\$4.A34.A\$3.A
36.C\$2.A37.A\$.A17.A2.A18.A\$A18.A2.A18.A\$A18.A2.A17.A\$.A37.A\$.E36.A\$2.
A34.A\$3.A32.A\$4.A30.A\$5.A28.A\$6.A26.A\$7.A24.A\$8.A22.A\$9.A20.A\$10.A18.
A\$11.A16.A\$12.A14.A\$13.A12.A\$14.A10.A\$15.A8.A\$16.A4.3A\$17.A2.A\$18.2A!
MLP will live on forever, so does John Horton Conway.
Moosey wrote:
February 5th, 2019, 7:51 pm
“New knightship tagalong!”
“Quick, hide it!”
My TODO list

LeapLife - DirtyLife - LispLife

I could make a rule in ten seconds flat

gameoflifemaniac
Posts: 1028
Joined: January 22nd, 2017, 11:17 am
Location: There too

### Re: A spaceship in Langtons Ant!?

Is there any p6 osc?
I was so socially awkward in the past and it will haunt me for my entire life.

LuxiusGOL
Posts: 65
Joined: April 6th, 2020, 4:28 pm

### Re: A spaceship in Langtons Ant!?

This 2c/544 (or c/272) spaceship in a Turmite rule

Code: Select all

x = 8, y = 7, rule = Turmite_180121020081
3.2A\$2A.DA\$DA2.A\$.4A.2A\$6.2A\$4.2A\$4.2A!
L'Omnipotent Luxius

logarithmic rake

Code: Select all

x = 18, y = 22, rule = 456n8/268/3
3\$10.BA\$11.BA\$12.BA\$13.BA\$6.BA6.BA\$5.BA.BA4.BA\$5.A.2A.BA.BA\$6.BA.BA.B
A\$5.2A.BA\$.B2.BA.BA\$4.A.BA\$5.BA\$4.BA\$B2.BA\$A2BA\$.2A!