## Search found 14 matches

- April 22nd, 2011, 5:54 am
- Forum: General Discussion
- Topic: Natural Information Entropy of CGoL
- Replies:
**16** - Views:
**6594**

### Re: Natural Information Entropy of CGoL

Well, the wiki made a point of distinguishing the two. I got the impression, that Garden of Edens were the set of patterns that did not have predecessors, but Orphans were the set of patterns such that any pattern containing it as a subpattern had no predecessor. It is not immediately obvious to me ...

- April 22nd, 2011, 3:21 am
- Forum: Patterns
- Topic: New type of wickstretcher?
- Replies:
**6** - Views:
**3140**

### Re: New type of wickstretcher?

I do not understand what it is you are describing. What do you mean by wick? Maybe you should invent your wickbeam first and then I can watch the pattern and understand what it is. However, this did make me think of something that would be interesting: a wick composed of stable static elements that ...

- April 22nd, 2011, 3:13 am
- Forum: Patterns
- Topic: Smaller moving sawtooth
- Replies:
**4** - Views:
**3522**

### Re: Smaller moving sawtooth

If the wiki is up to date...yes.

If not...someone should fix that

If not...someone should fix that

- April 21st, 2011, 11:01 pm
- Forum: General Discussion
- Topic: Natural Information Entropy of CGoL
- Replies:
**16** - Views:
**6594**

### Re: Natural Information Entropy of CGoL

It turns out that what I mean when I said Gardens of Eden was Orphans. I would assume that all the 11x11 known GoEs are also Orphans, and that the 11x11 area has been completely searched? (I saw 14 12x12 GoEs on the wiki, but that gives a worse bound.)

- April 11th, 2011, 1:25 am
- Forum: Other Cellular Automata
- Topic: Smallest slowest spaceship?
- Replies:
**27** - Views:
**16826**

### Re: Smallest slowest spaceship?

Substitute "a c/4 orthogonal spaceship" for every occurrence of LWSS and it should make more sense. I'm sorry but I'm still having problems understanding your argument. After substitution you get: "the glider's travel is always less than or equal to the c/4 ortogonal spaceship's travel time." In L_...

- April 9th, 2011, 6:26 pm
- Forum: General Discussion
- Topic: Natural Information Entropy of CGoL
- Replies:
**16** - Views:
**6594**

### Re: Natural Information Entropy of CGoL

oh okay, got it. is 11x11 the largest area searched for GoEs so far?

- April 9th, 2011, 5:48 am
- Forum: Other Cellular Automata
- Topic: Smallest slowest spaceship?
- Replies:
**27** - Views:
**16826**

### Re: Smallest slowest spaceship?

quintopia: I'm having trouble following your argument. Is it an argument for L_1 or for L_inf? Or is it a mixture of both? You wrote: "Thus, the glider's travel is always less than or equal to the LWSS's travel time." In L_inf it's "less than" and in L_1 it's "equal". Exactly what do you mean by "a...

- April 9th, 2011, 5:41 am
- Forum: General Discussion
- Topic: Natural Information Entropy of CGoL
- Replies:
**16** - Views:
**6594**

### Re: Natural Information Entropy of CGoL

And here's my counterargument: Although that cell can't store more log_2(2^121-5) bits of information with respect to its contribution toward any particular 11x11 square it is in, it may be storing some small amount of information with respect to a polyplet not contained in that square, for instance...

- April 8th, 2011, 7:55 pm
- Forum: Other Cellular Automata
- Topic: Smallest slowest spaceship?
- Replies:
**27** - Views:
**16826**

### Re: Smallest slowest spaceship?

I think the only worthwhile choice is between L_inf and L_1. Which should it be? Here is an argument for L_1: Suppose you want to see how long it takes a ship to get from (0,0) to (x,x). It will take a glider 2x generations, but it will take a LWSS 4x generations. How about from (0,0) to (x,0)? If y...

- April 8th, 2011, 7:35 pm
- Forum: General Discussion
- Topic: Natural Information Entropy of CGoL
- Replies:
**16** - Views:
**6594**

### Re: Natural Information Entropy of CGoL

No, the bound is still too low given what we know. You can't use 121 as your denominator if we're going to use polyonimoes/polyplets. However, if you are using (without saying) mu as the base your logarithm, then yes, that would be correct.

- April 5th, 2011, 6:05 am
- Forum: Other Cellular Automata
- Topic: Smallest slowest spaceship?
- Replies:
**27** - Views:
**16826**

### Re: Smallest slowest spaceship?

We could speak of a /sequence/ of smallest slowest spaceships, however. Namely, the sequence of ships which are slower than all smaller ships.

- April 5th, 2011, 5:15 am
- Forum: General Discussion
- Topic: Natural Information Entropy of CGoL
- Replies:
**16** - Views:
**6594**

### Re: Natural Information Entropy of CGoL

Rather than basing your calculations around polyominoes, it may be a good idea to use polyplets, as they are more natural in the Moore neighborhood. Good point. This will the log base higher, obviously. I should look up the bounds on the growth rate of the polyplet sequence. The limit as the side-l...

- April 4th, 2011, 7:11 pm
- Forum: Patterns
- Topic: super breeders?
- Replies:
**42** - Views:
**30387**

### Re: super breeders?

As a possible solution to the Gemini UCC-based SSS breeder, try making an SS breeder that produces its string of blocks to the NE. The UCC is in the SW. Its Y-axis elbow moves upwards at twice (or more) the rate that the X elbow moves rightwards, but neither has to move faster than the rate at which...

- April 4th, 2011, 4:56 pm
- Forum: General Discussion
- Topic: Natural Information Entropy of CGoL
- Replies:
**16** - Views:
**6594**

### Natural Information Entropy of CGoL

I've just finished reading Susskind's The Black Hole War in which the maximum information entropy of any volume of space is computed (a bound which is met by black holes). So this got me to thinking about what exactly the information entropy of GoL might be. It's obvious that n cells are capable of ...