Search found 508 matches

by pcallahan
December 30th, 2019, 1:48 pm
Forum: General Discussion
Topic: Thread for basic questions
Replies: 1887
Views: 505130

Re: Thread for basic questions

This may be very basic for someone with better linear algebra skills than mine, at least if they extend to diophantine equations. How do you characterize the class of infinite still lifes such that every 3x3 window contains exactly 4 cells? We know that this pattern is a still life because a live ce...
by pcallahan
December 29th, 2019, 3:28 pm
Forum: General Discussion
Topic: Unproven conjectures
Replies: 87
Views: 43620

Re: Unproven conjectures

There would be no incremental way to build it one S-tetromino at a time -- it would have to be built up a full row at a time, at best, and if the rows are long enough there might not be room for enough gliders to get in and make the necessary adjustments. Is there a likely angle of attack for one o...
by pcallahan
December 29th, 2019, 1:07 am
Forum: General Discussion
Topic: Unproven conjectures
Replies: 87
Views: 43620

Re: Unproven conjectures

I may have found a counterexample: I think it's not hard to analyze. The initial pattern is a 2x9 rectangle that repeats periodically across the plane. Label the columns of one of these rectangles with letters a through i. The goal is to place a third row of cells to stabilize row 2. The cell in co...
by pcallahan
December 28th, 2019, 3:24 pm
Forum: General Discussion
Topic: Unproven conjectures
Replies: 87
Views: 43620

Re: Unproven conjectures

I may have found a counterexample: x = 90, y = 3, rule = B3/S23 b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b 2o2b2o3b2o$2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o 2b2o3b2o2b2o3b2o2b2o$3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o3b2o2b2o 3b2o2b2o3b2o2b2o3b2o2b2o3...
by pcallahan
December 26th, 2019, 3:42 am
Forum: The Sandbox
Topic: My Israeli Tea Party
Replies: 3
Views: 438

Re: My Israeli Tea Party

I believe this is way off topic and inappropriate in a number of ways.... Yes, definitely off topic. Maybe it can be moved to sandbox. For the record, I like simsim314. I do not like Netanyahu. I do not support the American Tea Party, though I read his description through Google translate and found...
by pcallahan
December 24th, 2019, 3:14 pm
Forum: The Sandbox
Topic: Low-tech universal computing
Replies: 22
Views: 3411

Re: Low-tech universal computing

Another option for rule 110 is to use tiles to represent the predictable regions that result from a line of on cells. This has the advantage of requiring fewer tile placements, but it does require an infinite tile set. The geometry is not really enforced by the tiles. The rule for placement is: The ...
by pcallahan
December 21st, 2019, 4:09 pm
Forum: The Sandbox
Topic: Low-tech universal computing
Replies: 22
Views: 3411

Low-tech universal computing

I'm putting this in sandbox since I don't think there is a great deal of interest other than me (but I may add similar ideas over time, since it's kind of an obsession). I have posted before about computing with tiles. I realized that an even simpler model that can be done as a kids' craft project u...
by pcallahan
December 21st, 2019, 12:52 pm
Forum: Patterns
Topic: Thread For Your Useless Discoveries
Replies: 2382
Views: 955851

Re: Thread For Your Useless Discoveries

Here's one that spontaneously forms the eater after about a million generations (I didn't tried to figure out exactly when). The input stream is complicated enough not to crystallize. It also throws off a few orthogonal spaceships towards the end. I think that if a spaceship stream from a c/2 puffer...
by pcallahan
December 20th, 2019, 6:55 pm
Forum: Patterns
Topic: Thread For Your Useless Discoveries
Replies: 2382
Views: 955851

Re: Thread For Your Useless Discoveries

Here's one of several previous times that that LWSS eater has come up. It was known long before that -- not sure who saw it first, or when. If I recall correctly, I first saw it over 25 years ago before I had really done much in Life. I was running experiments in XLife where I was trying to tunnel ...
by pcallahan
December 20th, 2019, 5:13 pm
Forum: Patterns
Topic: Thread For Your Useless Discoveries
Replies: 2382
Views: 955851

Re: Thread For Your Useless Discoveries

JP21 wrote:
December 20th, 2019, 10:16 am
8-cell lwss eater:

Code: Select all

x = 8, y = 13, rule = B3/S23
4b2o$2o2b2o$2o6$4b3o$4bo2bo$4bo$4bo$5bobo!
I've seen that before. I think I might have come up spontaneously when firing LWSSs at junk from the back of a p20 puffer.
by pcallahan
December 18th, 2019, 10:40 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4771
Views: 494575

Re: Random posts

I wrote: This is Wolfram rule 110 written as a regular expression: (🁣+🁤🁫+(🁤🁫(🁪)*🁫))* After having this regular expression for a couple of years, I realized the interesting part about making this a regular expression and not a DFA. The top level (+ expression) has no constraints on what fits together...
by pcallahan
December 18th, 2019, 3:16 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4771
Views: 494575

Re: Random posts

I was surprised because the fuse becomes momentarily asymmetric before returning to its stable state while burning On second thought, yes, it is strange because it actually changes the puffer period. You can see it in the pairing below. The gliders only hit the block sometimes. x = 65, y = 123, rul...
by pcallahan
December 18th, 2019, 1:31 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4771
Views: 494575

Re: Random posts

Surprised this holds together I'm not sure what you mean by "holds together" but chaotic c/2 puffers rarely self-destruct (unless my memory fails me). The engine and helpers get out of the way too fast for the exhaust to catch up. (Eh, never mind I was thinking it would be easy to replace the HWSS ...
by pcallahan
December 16th, 2019, 8:31 pm
Forum: Patterns
Topic: Methuselah-ish Symmetric Soups
Replies: 3
Views: 1942

Re: Methuselah-ish Symmetric Soups

Update: Proof of concept. This won't set any records I'm sure, but here's one that takes about 1.3 million steps to kill the engine and stays active past generation 1.7 million as the remaining gliders collide. x = 30, y = 16, rule = B3/S23 7bobo$6bo$7bo2bo$9b3o7$3o2$bo$b2o25b2o$2b2o24bo$o2b2o! (Wi...
by pcallahan
December 16th, 2019, 3:03 pm
Forum: General Discussion
Topic: Game of Life referenced in "intelligent design" paper
Replies: 32
Views: 5278

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

It's the small neighborhood in the GOL rules. That's what makes the search space for interesting patterns hilly, without which hill climbing algorithms such as our spaceship search programs, or natural selection, wouldn't work. Dembski is quite right that if fitness was a random function of genotyp...
by pcallahan
December 16th, 2019, 1:54 pm
Forum: Patterns
Topic: Methuselah-ish Symmetric Soups
Replies: 3
Views: 1942

Re: Methuselah-ish Symmetric Soups

I wonder what's the smallest starting state that results in a diagonal puffer (<c/4) with receding gliders. I assume it eventually turns into some pairing of Corderman engines. That could form the basis of many similar large-period methuselahs depending on what the gliders were colliding with. Has a...
by pcallahan
December 15th, 2019, 1:49 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4771
Views: 494575

Re: Random posts

I just realized that instead of working on tile-based computers I should work on rubber-stamp computers. I may extend that to a serious post, but I'll leave it for now.
by pcallahan
December 15th, 2019, 1:03 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4771
Views: 494575

Re: Random posts

Implemented Margolus Critters Since I haven't seen much interest in Critters, I'll repeat this pattern here. It converts incoming gliders (critters) from a periodic stream into copies of bits in a loop and then counts them with a binary ripple counter. #C [[ RLE input o$bo$bo$o! ]] #C [[ PASTET EVE...
by pcallahan
December 15th, 2019, 1:09 am
Forum: The Sandbox
Topic: Random posts
Replies: 4771
Views: 494575

Re: Random posts

Mostly to test unicode. This is Wolfram rule 110 written as a regular expression: (🁣+🁤🁫+(🁤🁫(🁪)*🁫))* Interpret the row of "dominoes" as two rows of cells that are on or off. Then just keep applying it from one row to the next, making sure that each pair of adjacent rows satisfies the regular expressi...
by pcallahan
December 14th, 2019, 7:49 pm
Forum: Patterns
Topic: Thread For Your Useless Discoveries
Replies: 2382
Views: 955851

Re: Thread For Your Useless Discoveries

This ties with the smallest known predecessor or any gun: Unfortunately, there is no obvious way to push it below 21. I found only three clusters of size 7 that can produce an unstabilized queen bee (leaving 3 for the block) and they're all basically the same. x = 23, y = 22, rule = B3/S23 2o8b2o8b...
by pcallahan
December 14th, 2019, 4:40 pm
Forum: General Discussion
Topic: A Broader Audience for Cellular Automata
Replies: 65
Views: 36275

Re: A Broader Audience for Cellular Automata

Sorry this went unanswered so long. Conversely, I think some of the ideas about livestreaming, lessons, and challenges for students are much more appealing. There was a comparison to chess at some point in the thread, and a comment about chess being far less interesting than CGOL. While that's obvio...
by pcallahan
December 14th, 2019, 4:26 pm
Forum: Patterns
Topic: Thread For Your Useless Discoveries
Replies: 2382
Views: 955851

Re: Thread For Your Useless Discoveries

That wasn't the synth he was referring to Correct. I just meant that in the most general sense, we have a lot of ways to make Gosper glider guns. Figuring out how to compact a predecessor into a box does not help; it's just a puzzle. A Gosper gun stabilized with an eater could hypothetically show u...
by pcallahan
December 14th, 2019, 3:44 pm
Forum: General Discussion
Topic: Game of Life referenced in "intelligent design" paper
Replies: 32
Views: 5278

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

Three more thoughts. First, I think I have a Gosper glider gun with "ASC" about 4 using 26 cells in a 36x3 boxes. (The "complexity" is reduced by 81.) If I could reduce the cell count further, I might be able to get it to go negative. This is not important at all, but it's a puzzle. I would argue th...
by pcallahan
December 14th, 2019, 1:31 pm
Forum: Patterns
Topic: Thread For Your Useless Discoveries
Replies: 2382
Views: 955851

Re: Thread For Your Useless Discoveries

This qualifies as useless, since we already have plenty of syntheses for Gosper's p30 glider gun but I've been obsessed with the puzzle for a couple of days of finding a minimal predecessor in terms of bounding box and cell count. Maybe somebody else can improve this. I see this as a partial order o...
by pcallahan
December 13th, 2019, 4:51 pm
Forum: General Discussion
Topic: Game of Life referenced in "intelligent design" paper
Replies: 32
Views: 5278

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

It's a little hard for me to to understand how that "implication" can survive even a few minutes of playing around with cellular automata, where chaos routinely gets transformed by (what seem to me to be) "naturalistic processes", into highly structured patterns ... in an incredible variety of diff...