## Search found 508 matches

- January 14th, 2020, 2:57 am
- Forum: General Discussion
- Topic: Realizing still life constraints as a planar tiling
- Replies:
**110** - Views:
**52065**

### Re: Realizing still life constraints as a planar tiling

Another idea is to forget about the octagons entirely and use these 6 domino-like tiles, assuming the user is able to count. Screen Shot 2020-01-13 at 10.39.15 PM.png These must be placed so colors of squares and red boundaries meet. Each corner square contains a number of dots equal to the number o...

- January 13th, 2020, 5:46 pm
- Forum: General Discussion
- Topic: Realizing still life constraints as a planar tiling
- Replies:
**110** - Views:
**52065**

### Re: Realizing still life constraints as a planar tiling

In the original tiling, I put the focus on octagons centered at cell positions, and the other six tiles are just there to fit together diagonal neighbors. The horizontal and vertical neighbors are always touching. I realized, and maybe it's obvious to others, that the six diagonal tiles represent an...

- January 13th, 2020, 1:05 pm
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**4783** - Views:
**495628**

### Re: Random posts

Speaking of the WC Fields medal, shouldn't that be awarded for the best mathematics done in the bathroom (or WC)? Mathematician John Nash apparently reinvented the game of Hex when looking at hexagonal bathroom tiles. And of course, Archimedes charged out of the bathtub shouting Eureka! (though I th...

- January 11th, 2020, 1:04 pm
- Forum: The Sandbox
- Topic: cellular automata according to Max Planck
- Replies:
**226** - Views:
**15572**

- January 10th, 2020, 10:49 pm
- Forum: The Sandbox
- Topic: cellular automata according to Max Planck
- Replies:
**226** - Views:
**15572**

- January 10th, 2020, 2:01 pm
- Forum: The Sandbox
- Topic: cellular automata according to Max Planck
- Replies:
**226** - Views:
**15572**

- January 10th, 2020, 1:31 pm
- Forum: The Sandbox
- Topic: cellular automata according to Max Planck
- Replies:
**226** - Views:
**15572**

- January 10th, 2020, 11:47 am
- Forum: The Sandbox
- Topic: cellular automata according to Max Planck
- Replies:
**226** - Views:
**15572**

### Re: cellular automata according to Max Planck

- January 10th, 2020, 11:07 am
- Forum: The Sandbox
- Topic: cellular automata according to Max Planck
- Replies:
**226** - Views:
**15572**

### Re: cellular automata according to Max Planck

Sorry Moosey, but you simply do not know what you're talking about when you use words and terms from biology like "evolution", "population" and "generations". "Evolution" definition 4: A pattern of movements or maneuvers. ‘silk ribbons waving in fanciful evolutions’ applies here and is sometimes us...

- January 8th, 2020, 2:51 pm
- Forum: The Sandbox
- Topic: Famous Quotes
- Replies:
**251** - Views:
**73726**

### Re: Famous Quotes

Just rest assured that I've learned enough of mathematics to be able to enjoy it! To be blunt, the question is not whether you enjoy mathematics, but whether others enjoy your musings (and I won't speak for anyone else, but they do little for me). I appreciate that you show the courtesy of putting ...

- January 8th, 2020, 2:22 pm
- Forum: General Discussion
- Topic: Unproven conjectures
- Replies:
**87** - Views:
**43646**

### Re: Unproven conjectures

Finally, this stabilization works and it is unique: a b c d e f g h i o o . . o o . . . o o . . o o . . . o o . . o o . . . o o . . o o . . . o o . . . o o . . . o o . . o o . . . o o . . o o . . . o o . . o o . . . o o . . o o . . o o . . . o o . I made the analysis a lot harder than necessary. Ju...

- January 7th, 2020, 9:20 pm
- Forum: General Discussion
- Topic: Game of Life referenced in "intelligent design" paper
- Replies:
**32** - Views:
**5290**

### Re: Game of Life referenced in "intelligent design" paper

The only reason for me to register with such an obsolete electronic online community like this one was the topic of this very thread about intelligent design. Unfortunately, this is an unusual topic of very limited interest within this community, and I guess I bear some of the blame for bringing yo...

- January 7th, 2020, 9:17 pm
- Forum: The Sandbox
- Topic: Famous Quotes
- Replies:
**251** - Views:
**73726**

### Re: Famous Quotes

And to get an idea what my "deal" might be you'd better pay a visit to the Sandbox and have a look at my first thread entitled "cellular automata according to Max Planck". Yes, I saw it. You may have missed the point that a p23 oscillator is a new result of greater interest to most members of this ...

- January 7th, 2020, 7:05 pm
- Forum: The Sandbox
- Topic: Famous Quotes
- Replies:
**251** - Views:
**73726**

### Re: Famous Quotes

Clearly the author had no recognition of the fact that the first p23 and first new oscillator period in however-many-years is SUPER EXCITING. Aside from being a new period, my first thought was how is the period not a multiple of two? Now I see the two halves are out of phase. Nice use of a hassler...

- January 7th, 2020, 2:34 pm
- Forum: The Sandbox
- Topic: Are non-computerized mathematical "recreations" dead?
- Replies:
**5** - Views:
**1933**

### Are non-computerized mathematical "recreations" dead?

Sandbox for my rant, but I would be interested in hearing opinions, particularly from those who never knew a world where programmable computers were not ubiquitous and cheap. First, to be clear, I think there will always be an interest in "puzzle math", competitive problem solving of the sort seen i...

- January 6th, 2020, 10:21 pm
- Forum: General Discussion
- Topic: Thread for basic questions
- Replies:
**1891** - Views:
**505488**

### Re: Thread for basic questions

Each subset should also add up to a fixed sum, and the total needs to be 4. So for instance, we may have: a + b = 1 (a and b are horizontally periodic) d + e = 1 (d and e are horizontally periodic) c + f + i = 2 (c, f, and i are vertically periodic) g + h = 0 (so both are always 0 and periodic by d...

- January 5th, 2020, 11:17 pm
- Forum: The Sandbox
- Topic: Low-tech universal computing
- Replies:
**22** - Views:
**3418**

### Re: Low-tech universal computing

This is not universal computing, but it is a low-tech solution to constructing random instances of a class of still life patterns that tile the plane with 3x3 neighborhoods containing exactly 4 live cells. Screen Shot 2020-01-05 at 9.06.54 PM.png The idea illustrated above is to use paper strips. Th...

- January 3rd, 2020, 5:36 pm
- Forum: General Discussion
- Topic: Thread for basic questions
- Replies:
**1891** - Views:
**505488**

### Re: Thread for basic questions

the a/b pattern forces horizontal stripes and the c/d pattern forces conflicting vertical stripes. So any perceived aperiodicity is the union of striped patterns. I think I finally have this nailed down, though I don't have a formal proof. Every still life composed of 4-cell neighborhoods is a unio...

- January 3rd, 2020, 2:19 pm
- Forum: General Discussion
- Topic: Seeds of Destruction: A Puzzle Game
- Replies:
**40** - Views:
**82726**

### Re: Seeds of Destruction: A Puzzle Game

... I hope someone who has actually written a working Java program in the last decade can take over from this point -- I'm not in familiar territory here. I have, though I don't think that fact is especially helpful. Just searching on the error string, I found this bug report, which looks relevant....

- January 3rd, 2020, 12:30 pm
- Forum: Patterns
- Topic: Refactoring DRH's cyclotron with stable components?
- Replies:
**51** - Views:
**25671**

### Re: Refactoring DRH's cyclotron with stable components?

It works for me. My only real requirement was that no excess gliders are produced in a catalyzed reaction, and this qualifies.Entity Valkyrie 2 wrote: ↑January 3rd, 2020, 6:02 amI'm not sure if my P369 would qualify, but it only consists of blocks, eater 1s and 31.4s.

- January 2nd, 2020, 3:09 pm
- Forum: General Discussion
- Topic: Thread for basic questions
- Replies:
**1891** - Views:
**505488**

### Re: Thread for basic questions

I've only been able to find answers to the original question that are aperiodic in 1 direction, such as the following: Another idea that may provide a big simplification. Take this 4x4 neighborhood: a ? ? b ? ? ? ? ? ? ? ? c ? ? d From the original neighborhood constraints, it is easy to derive the...

- January 1st, 2020, 3:40 pm
- Forum: General Discussion
- Topic: Thread for basic questions
- Replies:
**1891** - Views:
**505488**

### Re: Thread for basic questions

I've only been able to find answers to the original question that are aperiodic in 1 direction, such as the following: The idea of sliding (spatially) period-3 columns up or down by a cell can be applied to create both aperiodic rows and columns in the same pattern, as this example shows (the surro...

- December 31st, 2019, 6:23 pm
- Forum: General Discussion
- Topic: Thread for basic questions
- Replies:
**1891** - Views:
**505488**

### Re: Thread for basic questions

I've only been able to find answers to the original question that are aperiodic in 1 direction, such as the following: x = 24, y = 20, rule = B1235678/S3 3bo2bo2bo5bo5bo$b11ob5ob5o$o11bo5bo$o2bo2bo2bo2bo2bo2bo2bo$b11ob5ob5o$ o11bo5bo$o2bo2bo2bo2bo2bo2bo2bo$b11ob5ob5o$o11bo5bo$o2bo2bo2bo2bo2bo2b o2b...

- December 31st, 2019, 4:52 pm
- Forum: General Discussion
- Topic: Thread for basic questions
- Replies:
**1891** - Views:
**505488**

### Re: Thread for basic questions

Note that if the question had about the set of patterns in which 3x3 neighborhoods have even parity (a superset of the 4-cell neighborhood still lifes) then there would be a pure solution in terms of linear equations on GF(2). Are all of these solutions periodic? If so, then all the still lifes are....

- December 31st, 2019, 1:11 pm
- Forum: General Discussion
- Topic: Thread for basic questions
- Replies:
**1891** - Views:
**505488**

### Re: Thread for basic questions

And it needs an infinite amount of (wasted) energy to actively ignore the existence of the imaginary numbers. I'm not quite sure what you're getting at, but linear algebra is often sufficient to prove the non-existence of solutions in cases like this. It's true that if you find a solution, it might...