## Search found 862 matches

- June 9th, 2022, 1:18 pm
- Forum: Other Cellular Automata
- Topic: Flow6
- Replies:
**33** - Views:
**10449**

### Re: Flow6

Can this modified Langton's ant unit cell be simplified? x = 74, y = 34, rule = Flow6 67.7A$67.A2.2A.A$60.7A.A2.A.A$60.A2.2A.2A.E.A.A$53.7A.A2.A3.A2.A.A$ 53.A2.2A.2A.E.A3.2A.A.A$46.7A.A2.A3.A2.A3.4A.A$46.A2.2A.2A.E.A3.2A.A 3.A4.A$39.7A.A2.A3.A2.A3.4A3.A4.A$39.A2.2A.2A.E.A3.2A.A3.A3.4A4.A$32. 4ABEA.A...

- June 8th, 2022, 2:46 pm
- Forum: Other Cellular Automata
- Topic: Trine
- Replies:
**20** - Views:
**2610**

### Re: Trine

Ed Pegg's counting Langton's ant : x = 111, y = 29, rule = Trine 4.C.BCA$2.AB.A2.B3.C$3.C.BC.BC.B$2.A.A2.A2.A$2.B2.CB2.C$2.C2.CB.B$3. 2A2.A$4.B2.C$4.C2.B$4.A2.A4$4.C.BCA6.C.BCA6.C.BCA6.C.BCA6.C.BCA6.C.BC A6.C.BCA6.C.BCA6.C.BCA6.C.BCA$.CAB.A2.B3.CAB.A2.B3.CAB.A2.B3.CAB.A2.B 3.CAB.A2.B3.CDB.A2.B3.CAB...

- May 30th, 2022, 12:30 pm
- Forum: Other Cellular Automata
- Topic: Trine
- Replies:
**20** - Views:
**2610**

### Re: Trine

Langton's ant unit cell (80×80 – position the unit cells so that their state-1 tips just overlap, without rotating or reflecting): x = 81, y = 81, rule = Trine 29.A21.A$29.C2.CBACBACBACBACBACBACB$29.B.A$28.A2.2BCABC$27.C2.CB.B3.A BCAB$26.B.BA2.A2.A6.C$7.ABCABCABCABCABCABCA2.BA3.CB.CBA2.A.ABCABCABCA ...

- May 29th, 2022, 12:27 am
- Forum: Patterns
- Topic: Smallest Known Oscillators to p106 (and Beyond)
- Replies:
**99** - Views:
**10064**

### Re: Smallest Known Oscillators to p106 (and Beyond)

New SKOP49 using the meatball in 188 cells: x = 81, y = 62, rule = B3/S23 11b4o$10bo4bo$8b3o4b2o$7bo6bobo$8bob2obo$8bo2bobo2bo$11bob2obo$8bobo6b o$8b2o4b3o12bo$9bo4bo15b2o$10b4o15b2o$4b2o$bo2bo2bo$obobob2o$bo2bo2bob o14b2o$4b2o2b2o13bo2bo$15b3o6b2o$13b2ob2o$15bo$27b2o$27bo14bo$28b3o12b o$30bo10b3o4$...

- May 4th, 2022, 1:54 am
- Forum: Other Cellular Automata
- Topic: Trine
- Replies:
**20** - Views:
**2610**

### Re: Trine

Thank you, very interesting! And what is the third pin on top the multiplicands? I guess it marks the beginning of the bit sequence? Indeed – I call such leads which indicate the positions of the arguments and trigger certain steps in the computation initiators . Here the initiator bit extracts one...

- April 28th, 2022, 12:42 am
- Forum: Other Cellular Automata
- Topic: Trine
- Replies:
**20** - Views:
**2610**

### Re: Trine

This works remarkably, almost unbelievably fast for a 32-bit multiplier! Do you have schematics? Is it a Wallace multiplier? Both this multiplier and its equivalent in Wireworld Modern (check that rule's thread for the pattern) merely implement the shift-and-add procedure for binary multiplication;...

- April 21st, 2022, 12:27 pm
- Forum: Other Cellular Automata
- Topic: Trine
- Replies:
**20** - Views:
**2610**

### Re: Trine

32-bit multiplier, working much the same way as the Wireworld Modern version: x = 312, y = 93, rule = Trine 67.CAB3.ABC3.BCA3.CAB3.ABC3.BCA3.CAB3.ABC3.BCA3.CAB3.ABC3.BCA3.CAB3.A BC3.BCA3.CAB3.ABC3.BCA3.CAB3.ABC3.BCA3.CAB3.ABC3.BCA3.CAB3.ABC3.BCA3. CAB3.ABC3.BCA3.CAB$66.B2.CABC2.ABCA2.BCAB2.CABC2.ABC...

- February 16th, 2022, 8:55 pm
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**3122** - Views:
**1086222**

- February 15th, 2022, 11:29 pm
- Forum: Other Cellular Automata
- Topic: Just Friends (B2-a/S12)
- Replies:
**44** - Views:
**18415**

### Re: Just Friends (B2-a/S12)

SKOP31 at 18 cells, adapted from the D2_+1 search:

Code: Select all

```
x = 11, y = 8, rule = B2-a/S12
6b2o2$2o3b5o$3bo$bo6b3o$bo5bo$8bo$8bo!
```

- January 20th, 2022, 12:46 pm
- Forum: The Sandbox
- Topic: Zarankiewicz's problem
- Replies:
**7** - Views:
**630**

### Re: Zarankiewicz's problem

The 105 solution on the first row is constructible from the Fano plane. I already knew that – I have also proved that it is the unique extremal matrix (where graph isomorphism determines uniqueness) for z(3,3, 15,15). The real challenge I'm facing now is to determine all non-isomorphic extremal mat...

- January 18th, 2022, 1:29 pm
- Forum: The Sandbox
- Topic: Zarankiewicz's problem
- Replies:
**7** - Views:
**630**

### Re: Zarankiewicz's problem

The values given by Guy in his 1967 and 1969 papers for z(2,2, 14,n) for n >= 24 are WRONG . x = 30, y = 76, rule = LifeHistory 26D$D3A3.2A16.D$DA2.2A3.2A14.D$DA9.5A9.D$DA14.5A4.D$D.A.A.A4.A4.A8.D$ D.A2.A6.A4.A3.A3.D$D.A6.A3.A4.A3.2A.D$D2.2A9.A4.A2.A2.D$D2.A.2A8.A2.A 6.D$D2.A6.A.A3.A6.2AD$D3.A2.A7.A...

- January 16th, 2022, 5:34 pm
- Forum: Patterns
- Topic: Synthesising Oscillators
- Replies:
**1447** - Views:
**1033020**

### Re: Synthesising Oscillators

Raucci's p217 in 160 gliders, with the final step from Dave Greene: x = 1300, y = 110, rule = B3/S23 1256bo$1255bo$1255b3o2$1265bobo$1265b2o$1266bo$757bo$755bobo245bo$ 756b2o246b2o$1003b2o$873bo$759bo112bo$759bobo110b3o$753bobo3b2o98b o20bo120bo117bo7b2o116bo7b2o$754b2o104bo18bobo118bobo115bobo5bobo...

- January 15th, 2022, 1:55 pm
- Forum: Other Cellular Automata
- Topic: Just Friends (B2-a/S12)
- Replies:
**44** - Views:
**18415**

### Re: Just Friends (B2-a/S12)

…right, I've just added it to Skopje – have you found any more new SKOPs in the meantime?creeperman7002 wrote: ↑October 8th, 2021, 5:55 pmp39, found by adding domino catalysts to the SKOP56:

- January 14th, 2022, 12:00 pm
- Forum: Patterns
- Topic: 21-bit still life syntheses
- Replies:
**45** - Views:
**4303**

### Re: 21-bit still life syntheses

Some soup-harvesting to solve three: #C xs21_4a96k4oz259701 x = 46, y = 54, rule = B3/S23 o$b2o$2o8$17bo$15bobo$16b2o14bo$33bo$31b3o$35bo$34bo$34b3o4$30bo$21bo 7bo5bobo$22bo6b3o3b2o$20b3o13bo19$6b2o$5bobo$7bo6$43b3o$43bo$44bo! #C xs21_ca2jaicz31252 x = 275, y = 40, rule = B3/S23 6bo122bo24bo$5bobo12...

- January 13th, 2022, 4:16 pm
- Forum: Patterns
- Topic: Smallest Known Oscillators to p106 (and Beyond)
- Replies:
**99** - Views:
**10064**

### Re: Smallest Known Oscillators to p106 (and Beyond)

A p8 variant of the above found by Kazyan on Discord achieves 108 cells for 128+8n to 240 and 103 for 248+8n. This both ties the fixed SKOP128 and displaces the p256 gun as the smallest SKOP256: x = 93, y = 68, rule = B3/S23 11b2o60b2o$11b2o60b2o3$11bo61bo$9bobo59bobo$7bo2b2o57bo2b2o$b2o5b2o53b 2o5b...

- January 13th, 2022, 9:48 am
- Forum: Patterns
- Topic: Synthesising Oscillators
- Replies:
**1447** - Views:
**1033020**

### Re: Synthesising Oscillators

The new SKOP102 in 30: x = 486, y = 122, rule = B3/S23 398bo$399b2o$398b2o4$105bobo$105b2o$106bo16$78bo$76bobo$77b2o344bo bo$424b2o$424bo4$85bo$83bobo$84b2o$80b2o115b2o100b2o116b2o$79bobo 114bobo99bobo114bo2bo$81bo113b3o99b3o$195b2o100b2o$196bobo99bobo 114b2obo$197bobo2b2o95bobo2b2o111bobo2b2o$198bo...

- January 13th, 2022, 9:30 am
- Forum: Patterns
- Topic: Thread for your unsure discoveries
- Replies:
**2537** - Views:
**1361728**

### Re: Thread for your unsure discoveries

Just to clarify, the specific p4 variant that Jormungant suggested seems to be shorter but wider than the p4 in the p52 gun -- maybe it could find a use somewhere (but not in the p52). I would like to see how low in population the p4 and p8 versions can go – they may be useful for Skopje. I have no...

- January 13th, 2022, 7:19 am
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**3122** - Views:
**1086222**

### Re: Oscillator Discussion Thread

While implementing an upgrade to Skopje I noticed that Jason's p156 is no longer SKOP156, that title now held by a p6 loop (92 -> 86): x = 46, y = 59, rule = B3/S23 9bo$4b2o3b3o$2obo8bo$2o2bo2bo3b2o$5bobo$6bo7b2o$14b2o$5b2o$5b2o7bo $13b2o$13bobo7$12bo$11bobo$11bobo$12bo$16b2o$16bobo$18bo$18b2o10$ 26...

- January 12th, 2022, 5:51 pm
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**3122** - Views:
**1086222**

### Re: Oscillator Discussion Thread

To summarise: x = 232, y = 132, rule = B3/S23 2b3o30b3o2$o5bo2b2o18b2o2bo5bo$o4b2o4bo16bo4b2o4bo$o11bo14bo11bo$11b2o 14b2o3$5b2o26b2o$5bo28bo$6b3o22b3o$8bo22bo25$2b3o30b2o14b2o30b2o14b2o 30b2o14b2o30b2o14b2o30b3o$36bo14bo32bo14bo32bo14bo32bo14bo$o5bo2b2o18b 2o4bo16bo4b2o18b2o4bo16bo4b2o18b2o4bo16bo4...

- January 12th, 2022, 4:23 pm
- Forum: Patterns
- Topic: Smallest Known Oscillators to p106 (and Beyond)
- Replies:
**99** - Views:
**10064**

### Re: Smallest Known Oscillators to p106 (and Beyond)

All 6n periods can now be realised with strictly less than 100 cells ; the following construction based on here achieves 66+6n in 96, 132+12n in 86 and 264+24n in 83 (p102 shown): x = 58, y = 71, rule = B3/S23 9bo$4b2o3b3o$2obo8bo$2o2bo2bo3b2o$5bobo$6bo7b2o$14b2o$5b2o$5b2o7bo $13b2o$13bobo7$12bo$11...

- January 12th, 2022, 2:22 pm
- Forum: Patterns
- Topic: Synthesising Oscillators
- Replies:
**1447** - Views:
**1033020**

### Re: Synthesising Oscillators

Strontium in 14 gliders: x = 97, y = 62, rule = B3/S23 76bo$77b2o$76b2o2$96bo$94b2o$95b2o3$78b2o$79bo$39bo39bobo$39b2o39b 2o$38bobo$43b3o$43bo44bobo$44bo43b2o$89bo$85bo$84bo$84b3o2$81b2o$ 81bobo$81bo10$91bo$89b2o$90b2o3$85b2o$77bo7bobo$77b2o6bo$76bobo3$ 6bo$5bo$5b3o$obo$b2o38b2o37b2o$bo38bobo36bobo$...

- January 12th, 2022, 2:00 pm
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**3122** - Views:
**1086222**

### Re: Oscillator Discussion Thread

- January 12th, 2022, 6:32 am
- Forum: Patterns
- Topic: Synthesising Oscillators
- Replies:
**1447** - Views:
**1033020**

### Re: Synthesising Oscillators

New SKOP96 in 24 gliders (trivially implying the gun itself can be made in 20, by removing the snake): x = 274, y = 82, rule = B3/S23 257bo$255bobo$256b2o$260bo$62b2o119b2o59b2o14bobo$63bo120bo60bo14b2o$b o61bobo118bobo58bobo$b2o61b2o119b2o59b2o$obo$5b3o$5bo15bobo3bobo53bobo 3bobo112bo50bo9bobo4b2o$...

- January 8th, 2022, 1:25 am
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**3122** - Views:
**1086222**

### Re: Oscillator Discussion Thread

I believe there's one new SKOP in the form of a 45-cell SKOP32 (beating out the 48-cell previous record holder), though I am unaware of any SKOPs found between the 66-cell SKOP62 and the 45-cell SKOP32. I saw the (your) new SKOP32 while browsing the thread prior to my post asking if there were any ...

- January 7th, 2022, 6:35 am
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**3122** - Views:
**1086222**

### Re: Oscillator Discussion Thread

Have any new SKOPs been found since the last time I posted here?