Code: Select all

```
x = 20, y = 9, rule = B3/S23
2b2o9bo$o3bo6bobobo$o5b2o3bo4bo$o3bo2b2o3b4obo$2b2o4b3o4bobo$10b3o3bob
2o$11bob2obobo$11b2o5bo$11b2o3b2o!
```

- May 19th, 2020, 7:24 am
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1275** - Views:
**587675**

A nice reduction to the second oscillator above:

Code: Select all

```
x = 20, y = 9, rule = B3/S23
2b2o9bo$o3bo6bobobo$o5b2o3bo4bo$o3bo2b2o3b4obo$2b2o4b3o4bobo$10b3o3bob
2o$11bob2obobo$11b2o5bo$11b2o3b2o!
```

- May 15th, 2020, 4:48 pm
- Forum: The Sandbox
- Topic: ConwayLife Skyscraper
- Replies:
**76** - Views:
**973**

Floor 27 contains nothing. The rooms are completely empty. There aren't even any rooms, actually, because that would require walls, and there's nothing on this floor. No ceiling. (the rest of the building continues upward approximately 100 meters off to the side) No floor, somehow: We're still debat...

- May 11th, 2020, 10:20 pm
- Forum: Patterns
- Topic: Thread For Your Useless Discoveries
- Replies:
**2379** - Views:
**955588**

This could be a possible starting point for 6xn block arrays if not for the fact that these two gliders intersect paths: x = 15, y = 23, rule = LifeHistory 12.A$4.2A6.A.A$4.A.A5.2A$5.A.A$6.A.A$.2E4.A.A$E.E5.A.A$2.E6.A.A$10.A. A$11.2A4$11.2A$10.A.A$2.E6.A.A$E.E5.A.A$.2E4.A.A$6.A.A$5.A.A$4.A.A5. 2A$4...

- May 7th, 2020, 5:58 pm
- Forum: The Sandbox
- Topic: I need help with a Script for the Fast Growing Hierarchy.
- Replies:
**5** - Views:
**248**

It would help if I knew which of those was the input and which was the subscript, but: You'd probably want to do something like, say, creating an iteration function thus: It(x,y,n+1) = It(f_y(x),y,n); It(x,y,0) = x And then construct the successor fgh as f_(y+1)(x) = It(x,y,x) Piggybacking: def FGH...

- May 7th, 2020, 5:44 pm
- Forum: The Sandbox
- Topic: Smallest still lifes with specific matches
- Replies:
**6** - Views:
**347**

Snake-with-feather improves xs4_126.

- May 7th, 2020, 5:36 pm
- Forum: Patterns
- Topic: Thread for your unsure discoveries
- Replies:
**1864** - Views:
**894697**

Sadly, passing a signal while the block is present causes an explosion.Jormungant wrote: ↑May 7th, 2020, 8:47 amand some unrelated block factory/glider gun & obstruction, which works in 2 directions!

Code: Select all

`x = 148, y = 69, rule = LifeHistory block-laying circuit that blocks transparent lanes in two directions`

- April 18th, 2020, 3:36 pm
- Forum: The Sandbox
- Topic: Smallest still lifes with specific islands
- Replies:
**28** - Views:
**2932**

If I made a DetLife variant that automatically detected forced supports, would anyone use it?

- April 15th, 2020, 6:11 pm
- Forum: The Sandbox
- Topic: Smallest still lifes with specific islands
- Replies:
**28** - Views:
**2932**

-4:A for awesome wrote: ↑April 15th, 2020, 11:25 amThe first one can be made slightly smaller:The other two are almost certainly minimal.Code: Select all

`x = 8, y = 7, rule = LifeHistory 6.2A$2A.2C2.A$A3.C.A$.A.C2.2A$2A.C.A$A2.C.A$2.2C.2A!`

Code: Select all

```
x = 10, y = 6, rule = LifeHistory
3.2C.2A.A$2A2.C.A.2A$2A.C2.A$3.C.2A$3.C$2.2C!
```

- April 11th, 2020, 4:25 pm
- Forum: Patterns
- Topic: Soup-based syntheses
- Replies:
**157** - Views:
**49196**

And the next question is, how to elaborate the casings and yield the version in DRH-oscillators.rle ? I've checked the enormous components_v4.rle; it says that the bi-block can be converted into a boat on block, which can lead to a table on block, a long-bookend on block, or a cap on block (all the...

- April 10th, 2020, 10:58 am
- Forum: Patterns
- Topic: Small Spaceship Syntheses
- Replies:
**438** - Views:
**343669**

Shows promise for a significant reduction: x = 10, y = 10, rule = B3/S23 5bo2b2o$5b5o$5b4o$3b2o$2bo2b3o$b2obo2bo$5o$b2o5bo$bo4b2o$8bo! EDIT: Proof-of-concept work: x = 24, y = 24, rule = Life 19bo$13bo4bo$13bobo2b3o$13b2o3$15bo$15bobo3bo$15b2o4bobo$9b2o10b2o$10b o$9bo$8bo9b2o$7bo10bobo$6bob3o7bo$5bo...

- April 8th, 2020, 9:21 am
- Forum: Patterns
- Topic: Spaceship Discussion Thread
- Replies:
**1054** - Views:
**545394**

Is it possible to make a 2c/6o spaceship using the following frontend? x = 22, y = 9, rule = B3/S23 3bo14bo$2bobo12bobo$bo3bo10bo3bo$2b3o12b3o2$bo3b2o9bo3b2o$2o3bo9b2o3b 2o$2o4b3o5bo$o7bo! I would be inclined to answer "no". The rest of the ship would have to stay directly behind the HF predecessor...

- April 6th, 2020, 10:08 pm
- Forum: Patterns
- Topic: Small Spaceship Syntheses
- Replies:
**438** - Views:
**343669**

I suspect that further developments will unfold if a 4g equivalent to the upper activation of the loaf-bend-tail area is found, Such that it doesn't plume out so far towards the sufficiently-long boat fuses. If we can get more clearance there, my suggestion from the Discord that we insert two domin...

- April 4th, 2020, 3:51 pm
- Forum: Patterns
- Topic: Small Spaceship Syntheses
- Replies:
**438** - Views:
**343669**

Possible cheaper eater activation?

Code: Select all

```
x = 13, y = 16, rule = B3/S23
8bo$o3b2obobo$o4bobo2bo$b2o2bo2b2o$2o4b2o$o7b2o$3b2o3bo$4bo4b3o$bo2bob
o5bo$2bo2b2o4bo$b2o7bo$9bo$8bo$7bo$6bo$5bo!
```

- April 2nd, 2020, 9:57 am
- Forum: Patterns
- Topic: Small Spaceship Syntheses
- Replies:
**438** - Views:
**343669**

Some trivial touch-ups: x = 76, y = 76, rule = B3/S23 60bo$60bobo$60b2o3$39bo$38bo$38b3o3$36bo$36bobo5bo$36b2o5bo$16bo26b3o 28bo$17b2o54bo$16b2o30bo24b3o$27bo19bo$25b2o20b3o$26b2o$6bo14bo$7bo11b obo$5b3o12b2o$38b2o$37bobo$2bobo31bobo3b2o$3b2o30bobo4b2o5bobo$3bo13b 2o15bobo12b2o7bo$10bo5bo2bo13bobo14...

- March 24th, 2020, 11:49 am
- Forum: The Sandbox
- Topic: Game Of Life Comics
- Replies:
**75** - Views:
**21338**

x = 48, y = 101, rule = B3/S23 4b2o$4bo2bo$4bo3bo$6b3o$2b2o6b4o$2bob2o4b4o$bo4bo6b3o$2b4o4b2o3bo$o9b 2o$bo3bo$6b3o2b2o2bo$2b2o7bo4bo$13bob2o$10b2o6bo$11b2ob3obo$10b2o3bo2b o$10bobo2b2o$10bo2bobobo$10b3o6bo$11bobobo3bo$14b2obobo$11bo6b3o2$11bo 9bo$11bo3bo6bo$12bo5b5o$12b3o$16b2o$13b3o2bo$11bob3obo$1...

- March 24th, 2020, 11:39 am
- Forum: Patterns
- Topic: Small Spaceship Syntheses
- Replies:
**438** - Views:
**343669**

A workable replacement for the canoe-activation potentially buildable from a snake:

Code: Select all

```
x = 11, y = 17, rule = B3/S23
bobo$2bo2$b2o$2b3o$5b3o3$4b2ob2o$b2o2b2obo$obo$2bo2$8bobo$7bob2o$7bo$
6b2o!
```

- March 22nd, 2020, 10:17 am
- Forum: Patterns
- Topic: Small Spaceship Syntheses
- Replies:
**438** - Views:
**343669**

Final step for 56P6H1V0! Over on the Discord, Kazyan found the key step of "activating" the pythons and with a bit of help with the cleanup from others I was able to put together this final step: rle The base still-life is pretty huge but I suspect its synthesis should be fairly easy in comparison ...

- March 8th, 2020, 9:55 am
- Forum: Patterns
- Topic: Synthesising Oscillators
- Replies:
**1045** - Views:
**765985**

R2D2 in 86 gliders (If I counted correctly): ... Very nice! Cleanup in key step can be reduced by two: rle That long canoe looked unnecessary, and it is: x = 51, y = 51, rule = B3/S23 2bo$obo$b2o7$19bo$20b2o$19b2o3$15bobo$16b2o$16bo5bo$23b2o17bo$22b2o16b 2o$41b2o$15bobo$16b2o$16bo4$31b2o$31bobo$33b...

- March 6th, 2020, 4:28 pm
- Forum: The Sandbox
- Topic: Challenges
- Replies:
**277** - Views:
**73562**

Just give the inverse Ackermann sequence some silly name.Moosey wrote: ↑March 6th, 2020, 9:37 amChallenge: come up with a sequence like Gijswijt's sequence with

1) an even harder name to spell and pronounce

2) a slower growth rate

- March 6th, 2020, 4:26 pm
- Forum: The Sandbox
- Topic: Thread for Non-CA Academic Questions
- Replies:
**329** - Views:
**89136**

It looks like a "model" is essentially a set large enough that logical axioms and formulae can be interpreted and manipulated as subsets of said set.

Someone better-trained in set theory than myself will have to refine that.

Someone better-trained in set theory than myself will have to refine that.

- February 28th, 2020, 11:57 pm
- Forum: The Sandbox
- Topic: Thread for Non-CA Academic Questions
- Replies:
**329** - Views:
**89136**

The base of natural logarithm e has many characteristics/defnitions, e.g. e₁=lim(x→∞)(1+1/x)^x e₂=∑(n=0 to ∞)(1/n!) e₃ is the unique solution x for ∫(t=1 to x)(1/t)dt = 1 e₄ is the unique number a such that f(x)=a^x is equal to its own derivative and has unit tangent slope at (0,f(0)) How to prove ...

- February 28th, 2020, 11:31 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**185** - Views:
**17027**

But can anyone give me a simple understanding of Mahlos like this? All I need is a better understanding of clubsets Specifically, the part with the "closed" part Not the unbounded part According to the Wikipedia definition, club sets can be thought of as being indexable by ordinals: In fact a club ...

- February 23rd, 2020, 2:51 pm
- Forum: Patterns
- Topic: POTY 2019 Voting
- Replies:
**47** - Views:
**6794**

(vote) Not entirely sure, but this one might also be invalid since the numbers need to have two digits (i.e. #01 instead of #1) I get the need for consistency, but unless you have some sort of script that's pulling the contents of these posts and tallying I don't see what difference it would make.

- February 23rd, 2020, 9:49 am
- Forum: Patterns
- Topic: POTY 2019 Voting
- Replies:
**47** - Views:
**6794**

#01 *

#02 ***

#04 *

#05 **

#06 **

#07 **

#08 ***

#12 *

#15 *

#19 *

#21 ***

#25 *

#02 ***

#04 *

#05 **

#06 **

#07 **

#08 ***

#12 *

#15 *

#19 *

#21 ***

#25 *

- February 21st, 2020, 10:35 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**185** - Views:
**17027**

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...