## Search found 1940 matches

- February 21st, 2020, 10:35 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**169** - Views:
**5739**

### Re: Ordinals in googology

So instead I'll work on a way to turn trees into ordinals... This notation, given I'm interpreting it correctly, has limit e_0. Proof: From the successorship and expansion rules we get that a-b must have value a+b. The tree (a+1)-0 is equivalent to a-a-a-a-... with w a's, so the value of (a+1)-0 is...

- February 21st, 2020, 10:17 pm
- Forum: Patterns
- Topic: Soup-based syntheses
- Replies:
**151** - Views:
**37510**

### Re: Soup-based syntheses

Soup for a double eureka variant with twits: x = 35, y = 71, rule = B3/S23 34bo$32b2o$33b2o18$8b2o6b2o$7bo2bo4bo2bo$8b2o6b2o5$o24bo$4o18b4o$3bo 18bo$3bo18bo3$3o20b3o4$3o20b3o3$3bo18bo$3bo18bo$4o18b4o$o24bo5$8b2o6b 2o$7bo2bo4bo2bo$8b2o6b2o18$33b2o$32b2o$34bo! Note that the related xp30_252y1252z04r4...

- February 16th, 2020, 3:03 pm
- Forum: The Sandbox
- Topic: Challenges
- Replies:
**252** - Views:
**61688**

### Re: Challenges

New number challenge I made up: You have a number x. You square it, sort the digits in non-descending order, and remove exactly one digit. The resulting number is 123456. What is the lexicographically smallest x? 1112. "Lexicographical" doesn't mean anything because the number of digits in x is for...

- February 16th, 2020, 2:57 pm
- Forum: The Sandbox
- Topic: Accumulation [GAME]
- Replies:
**78** - Views:
**529**

### Re: Accumulation [GAME]

+52

Hunting: 404 Not Found

testitemqlstudop: 333

PkmnQ: 247

Moosey: 163

BlinkerSpawn: 79

Gustone: 65

Hdjensofjfnen: 46

EV2: 41

Hunting: 404 Not Found

testitemqlstudop: 333

PkmnQ: 247

Moosey: 163

BlinkerSpawn: 79

Gustone: 65

Hdjensofjfnen: 46

EV2: 41

- February 14th, 2020, 12:20 am
- Forum: The Sandbox
- Topic: Accumulation [GAME]
- Replies:
**78** - Views:
**529**

### Re: Accumulation [GAME]

+27

Hunting: 202

Moosey: 78

testitemqlstudop: 54

BlinkerSpawn: 27

Hdjensofjfnen: 17

Hunting: 202

Moosey: 78

testitemqlstudop: 54

BlinkerSpawn: 27

Hdjensofjfnen: 17

- February 10th, 2020, 9:00 pm
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1245** - Views:
**550226**

### Re: Oscillator Discussion Thread

This suggests a maybe tractable route, although I don't know that the grin (or equivalent) and the spark can be inserted in such close proximity: x = 13, y = 15, rule = B3/S23 2b2o5bo$10bo$2ob3o4bo$2b2o5bo$2bo8bo$5b2o3bo$5bobobo$3bobob2o$4bo$10b o$9b3o$9b3o$8b2ob2o$9b3o$9b3o! Another generation bac...

- February 9th, 2020, 2:45 pm
- Forum: The Sandbox
- Topic: Smallest still lifes with specific islands
- Replies:
**10** - Views:
**383**

### Re: Smallest still lifes with specific islands

Hitting the 30+'s: xs7_134og: (39) x = 11, y = 9, rule = LifeHistory 2A3.2A$A.A2.A3.2A$2.A4.C2.A$2.2A2.2C.A$2A3.C3.2A$.A.2C2.2A$A2.C4.A$2A 3.A2.A.A$4.2A3.2A! xs7_13co: (27) x = 10, y = 10, rule = LifeHistory 8.2A$7.A.A$7.A$4.2C.2A$5.C2.A$2A.A2.C$.A.2A.2C$.A2.A2.C$2.A2.A$3.2A! xs7_1bs: (26) x = 10, y...

- January 26th, 2020, 11:28 am
- Forum: Patterns
- Topic: Soup search results
- Replies:
**2123** - Views:
**1236308**

### Re: Soup search results

A soup I found for an xs32 in 2018, still the only soup for it and there is no listed synthesis yet, the soup might be useful: soup Reduces to a small seed fairly easily: x = 19, y = 23, rule = B3/S23 o$b2o6bo$2o6b3o2$5b2o$5bob2o$5bob2ob2o$6b2o2b2o$11bo3$16bo$14b4o$13b2o 3bo$12bo3b2o$13b4o$14bo2$10...

- January 8th, 2020, 7:34 pm
- Forum: Patterns
- Topic: Synthesising Oscillators
- Replies:
**1003** - Views:
**741133**

### Re: Synthesising Oscillators

Syntheses involving a catalyst Saves a glider: x = 40, y = 32, rule = B3/S23 34bo4bo$32b2o3b2o$33b2o3b2o3$20b2o$17b2o2bo$18b3o$16bo$9bo6b3o$7bobo9b o$8b2o8bobo$18bo2bo$19bobo$20bo3$8b2o$7bobo$9bo$36b2o$3b2o30b2o$2bobo 10bo21bo$4bo10b2o3bo$14bobo2b2o10b2o$19bobo9bobo$31bo$23b2o$22b2o$b2o 21bo$obo$2b...

- January 7th, 2020, 6:20 pm
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1245** - Views:
**550226**

### Re: Oscillator Discussion Thread

A small p12, also with a 1-2-3-4 in it. I think 12 is the lowest known number of rotor cells in a true-period p12. x = 20, y = 15, rule = B3/S23 12b2o$4bo2bo2bo2bo2bo$2b3o2b4obo3b3o$bo3b2o4bo7bo$bo2bo3b2o4b4obo$2obo 2b2ob2o2bo4bo$2bob2obo3bo2b4o$2bo2bo2b3ob2o$3bobobo2bo4bo$2b2obob2obob 4o$5bo2bobo$...

- December 12th, 2019, 4:34 pm
- Forum: Patterns
- Topic: 19-bit still life syntheses
- Replies:
**99** - Views:
**6361**

### Re: 19-bit still life syntheses

That higher-clearance insertion has now helped solve xs19_03p68oz39c32 and about eight relatives. I've been trying to make a component sequence to do this other transformation, as well. So far, no luck, but it's getting closer: x = 128, y = 13, rule = B3/S23 85bo2bo$89bo$84b6o$85bobo$4bo5b2o32bo39b...

- December 5th, 2019, 4:00 pm
- Forum: The Sandbox
- Topic: Challenges
- Replies:
**252** - Views:
**61688**

### Re: Challenges

I interpreted the rules as allowing two expressions, each of which could use at most one of each symbol, is that not the case?

- December 5th, 2019, 3:39 pm
- Forum: The Sandbox
- Topic: Challenges
- Replies:
**252** - Views:
**61688**

### Re: Challenges

A difficult number-puzzle: go from 16 to 25 in two moves, using only the number two, the operations +, *, ^, /, and -, (only one operator per use) and adding together all digits once (per use). Not all of these must (or in this case can) be used. Either subtract two or multiply by two, then raise t...

- December 5th, 2019, 3:31 pm
- Forum: The Sandbox
- Topic: Guess the sequence [GAME]
- Replies:
**16** - Views:
**1739**

### Re: Guess the sequence [GAME]

a(n) = digits of 9n in ascending ordertestitemqlstudop wrote: ↑July 31st, 2019, 11:18 pmDo as the title.

#0:Code: Select all

`9 18 27 36 45 45 36 27 18 9 99 18 117 126 135 144 135 126 117 18 189 189 27 126 225 234 234 225 126`

- November 29th, 2019, 5:10 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**169** - Views:
**5739**

### Re: Ordinals in googology

Can anyone explain me ordinals significantly bigger than the BHO? In many commonly used ordinal notations, W_1 acts as a fixed point of psi_0. We can then define psi_1 which creates expressions with W_1, and define W_2 as a fixed point of psi_1. Many strong notations, such as Pi and Pair Sequence S...

- November 28th, 2019, 5:53 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**169** - Views:
**5739**

### Re: Ordinals in googology

Can anyone explain me ordinals significantly bigger than the BHO? In many commonly used ordinal notations, W_1 acts as a fixed point of psi_0. We can then define psi_1 which creates expressions with W_1, and define W_2 as a fixed point of psi_1. Many strong notations, such as Pi and Pair Sequence S...

- November 25th, 2019, 4:29 pm
- Forum: Patterns
- Topic: 19-bit still life syntheses
- Replies:
**99** - Views:
**6361**

### Re: 19-bit still life syntheses

A slightly more expensive method from the other side: x = 23, y = 24, rule = B3/S23 15bo$14bo$14b3o2$13bo$14bo$12b3o2$19bo$17b2o$18b2o$4bo$5b2o$4b2o3$19b 2o$15b2o2bo$14bo2bobo2bo$15bobo2b3o$6b2o8bob2o$2o5b2o8bo2bo$b2o3bo11bo bo$o18bo! One fewer glider and much more clearance: x = 23, y = 20, rule =...

- November 22nd, 2019, 5:14 pm
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1245** - Views:
**550226**

### Re: Oscillator Discussion Thread

Indeed, four cells off the P49: That version was supposed to have a smaller footprint; if it's population you want reduced, you'll want this version: x = 18, y = 16, rule = B3/S23 8b2o$8bo$10bob2o$2b2o5b2obo$bo2bob2o4bo$o2b2obob4ob2o$b2o5bo2bobobo$3b 4o2bo2b2obo$3bobo4bo2bob2o$4bo5b4o2bo$b3o6bo3b3o...

- November 21st, 2019, 10:46 am
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1245** - Views:
**550226**

### Re: Oscillator Discussion Thread

More clearance in the back at the cost of some top clearance:

Code: Select all

```
x = 18, y = 15, rule = B3/S23
8b2o$6b3obobo$5bo4b2obo$5bob2o4bo$2o2b2obob4ob2o$o2bo5bo2bobobo$b2ob4o
2bo2b2obo$2bobobo4bo2bob2o$2bo2bo5b4o2bo$3b2o6bo3b3o$11b4o2bo$14bob2o$
11b2obobo$11b2obobo$15bo!
```

- November 15th, 2019, 10:37 pm
- Forum: The Sandbox
- Topic: Challenges
- Replies:
**252** - Views:
**61688**

### Re: Challenges

Find a gun with the smallest bouding diamond width perpendicular to the glider stream Simkin's p120 is gonna be pretty hard to beat at only 29hd: x = 52, y = 24, rule = LifeHistory D20.2A5.D$.D6.4B2.B.3B.BABA5.D$2.D5.4B.8BA9B$3.D3.2A5B2A16B$4.D2.2A5B 2A16BD$5.D2.B.22B.D$6.D3.B2A21BD$7.D3.2A7B2.13BD...

- November 14th, 2019, 11:02 pm
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1245** - Views:
**550226**

### Re: Oscillator Discussion Thread

EDIT 2: Nothing special, just a couple new (as of 2014, at least) billiard tables (and one p5 non-billiard table): x = 114, y = 61, rule = B3/S23 6bo7bo43bobo45bobobo2$4bobo5bobo41bo49bo2$6bo7bo41bobobo45bobo2$6bo7bo 41bo5bo47bo2$4bobobo3bobobo41bobo45bobo14$13b2o$8b2o3bo45b2o$8bo5bo45b o51bo$10bo2...

- November 14th, 2019, 10:37 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**169** - Views:
**5739**

- November 12th, 2019, 12:12 am
- Forum: The Sandbox
- Topic: Thread for Non-CA Academic Questions
- Replies:
**315** - Views:
**76693**

- November 10th, 2019, 11:55 am
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1245** - Views:
**550226**

### Re: Oscillator Discussion Thread

Edit 3: Here's another "Trivial p6", just for amusement. Right is new. x = 24, y = 14, rule = LifeHistory 11.A.2A$.2A6.2A3.A$A2.A9.A4.A$.2A2.2A4.A5.A.A2.2A$3.2A2.A4.A4.A2.A2.A $.2A3.A3.A.3A.2A.2A.A$A2.2A2.6A4.A4.2A$A.A3.3A6.2A2.A.A$.A.2A.A7.2A.A 4.2A$3.A2.A.A2.4A2.A.2A.A$3.A.A4.A4.A.A.A2.A$2.2A.A.2...

- November 9th, 2019, 9:34 pm
- Forum: Patterns
- Topic: 19-bit still life syntheses
- Replies:
**99** - Views:
**6361**

### Re: 19-bit still life syntheses

Found with Chris's script. Seems pretty elementary as a transformation. x = 33, y = 35, rule = B3/S23 bo$2bo$3o5$28bo$27bo$27b3o11$25bo$24bo$24b3o3$12bo$10bobo$11b2o4bo$17b obo$17b2o10bo2bo$27b6o$26bo$27b2obo$25bobob2o$25b2o! Two seconds in Seeds of Destruction: x = 23, y = 33, rule = B3/S23 21bo$2...