Search found 508 matches

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

Re: cellular automata according to Max Planck

Moosey wrote:
January 11th, 2020, 12:38 pm
do you not understand that you have failed to post the correct evolution (i.e. phases) of the glider?
对牛弹琴 (and with that I will leave this thread).
by pcallahan
January 10th, 2020, 10:49 pm
Forum: The Sandbox
Topic: cellular automata according to Max Planck
Replies: 226
Views: 15572

Re: cellular automata according to Max Planck

Hubi1857 wrote:
January 10th, 2020, 10:09 pm
You force me to struggle all the time against your ignorance.
Actually, nobody forces you to do anything.
by pcallahan
January 10th, 2020, 2:01 pm
Forum: The Sandbox
Topic: cellular automata according to Max Planck
Replies: 226
Views: 15572

Re: cellular automata according to Max Planck

Hubi1857 wrote:
January 10th, 2020, 1:35 pm
I see. Your problem is the Sandbox!
While mine is whatever you might call "common sense"...
Common sense says you don't show up in a forum on arithmetic and write "2+2=5" unless the intent is humor or shock value. Are you a performance artist?
by pcallahan
January 10th, 2020, 1:31 pm
Forum: The Sandbox
Topic: cellular automata according to Max Planck
Replies: 226
Views: 15572

Re: cellular automata according to Max Planck

Hubi1857 wrote:
January 10th, 2020, 12:07 pm
Even when I do nothing worse but playing here in the Sandbox...
Even in the sandbox, it would enhance your credibility if you could get the simplest moving pattern right. My problem? Like you said, it's the sandbox. Anything goes.
by pcallahan
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

Hubi1857 wrote:
January 10th, 2020, 11:33 am
pcallahan wrote:
January 10th, 2020, 11:07 am

Words usually have more than one meaning and there is no reason to think Moosey was using the term from biology.
Frankly, I simpy do not know what Moosey thinks and I definitely haven't got the slightest idea what your problem is, Mr. Callahan!
Well, are you going to fix your mistake?
by pcallahan
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...
by pcallahan
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 ...
by pcallahan
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...
by pcallahan
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...
by pcallahan
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 ...
by pcallahan
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...
by pcallahan
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...
by pcallahan
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...
by pcallahan
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...
by pcallahan
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...
by pcallahan
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....
by pcallahan
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?

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