Search found 14 matches

by quintopia
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 ...
by quintopia
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 ...
by quintopia
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 :D
by quintopia
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.)
by quintopia
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_...
by quintopia
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?
by quintopia
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...
by quintopia
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...
by quintopia
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...
by quintopia
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.
by quintopia
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.
by quintopia
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...
by quintopia
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...
by quintopia
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 ...