ConwayLife.com

Since the Fibonacci sequence (which approximates the golden ratio) can be found within Pascal's triangle, it is also possible to find the sequences that approximate the silver ratio (Pell, ...) and higher metallic means within it or similar arithmetic devices? Likewise for the Tribonacci sequence a...

dvgrn wrote:

On Mon Jan 17, 2000, Stephen Silver wrote: long-lost theorem

Thanks. This definitely seems like it should be on LifeWiki. Would it be appropriate to use your post as a citation?

Can I have a trusted flag, please? There's a theorem about phoenixes that I want to add a citation for.

Can someone please link the proof of non-existence of p3 phoenixes? I can't find it anywhere.

Relevant thread: http://www.conwaylife.com/forums/viewtopic.php?f=11&t=3599 Most of the work was already done in this video: https://www.youtube.com/watch?v=NaL_Cb42WyY The whole video is actually a pretty neat proof of pi/4 = 1 - 1/3 + 1/5 - ... and I recommend watching it. But the specific result ...

A cell with maximum heat would be surrounded by infinitely many cells. This 'maximum heat' number is finite, but I do not yet know its value. A 511x511 block of cells yields the number 6.0267726589419..., but that's not even close to a good estimate. I have settled on using 7 when engineering day a...

With the modification to the script I detailed earlier, everything seems to be working exactly as it should. Here's the modified version: -- initAsyncUniverse - initialise a part of the universe to run asynchronous CA rules -- see http://conwaylife.com/forums/viewtopic.php?p=61953#p61953 -- Author: ...

I don't know. The script is giving me errors. The first one was from one of the comments, so I deleted all the comments, and now I'm getting an error from the "local g = golly()" thing. How are you trying to run that script, exactly? That one is in Lua, but Golly ordinarily figures out automaticall...

Does this match the behaviour you were hoping for? I don't know. The script is giving me errors. The first one was from one of the comments, so I deleted all the comments, and now I'm getting an error from the "local g = golly()" thing. But, just from looking at the script, I'm unsure about this pa...

x = 13, y = 13, rule = B3/S23 obob2o2bo$o2bo3bo2bo$2bo2bob2obobo$bo4b2obobo$bobobob2o$5b2o3bobo$bobo 3bob2obo$2b2o5b2o$o2b3o3b2o$o4bo2bo$3bobobo2b2o$4bo$6b2o3bo! I know that this thread is -ded- but hey, we need more games like this. x = 15, y = 17, rule = B3/S23 3b2obo3bo2bo$bo6bo3bo$2b2ob3o3b3o$2...

I asked for this before, but it got misunderstood, so I'm gonna try again. I want a way to take a normal life-like rule, say B3678/S01245 (just an example) and run it so instead of the cells all updating simultaneously, they update in a specific asynchronous fashion. The way cells should update is a...

I had this idea for a Margolus version of WireWorld, but I can't figure out how to use the conversion script. Help? @RULE MWW @TABLE n_states:3 neighborhood:Margolus symmetries:rotate4reflect # 0: empty # 1: off # 2: on var a={0,1,2} var b={1,2} var c={b} var d={b} var e={b} # 0 or 1 wires: nothing ...

Some misc. stuff in Brainspawn6: x = 12, y = 37, rule = Brainspawn6 .B2.B$.4A$.B2.B$.B2.B$.4A$.B2.B6$2.A$.A.A$A3.A3.A$.A.A3.A.A$2.A3.A3.A $7.A.A$8.A3$5.A$AB2.A.A$AB2.A.A$5.A7$AB$AB2$9.2A$5.4A.2A$5.6A$6.4A! Ahem. Beehives eat small photons quickly: x = 12, y = 4, rule = Brainspawn 10.A$AB.AB4.A.A$AB...

dvgrn wrote:We won't know for absolutely sure until somebody bothers to set up Vacuum-Minus-Eight in JLS and set a search going. It won't take long to run such a search.

Ok, how do I run that search in WLS? EDIT Nvm, the answer is here:
http://conwaylife.com/forums/viewtopic.php?f=9&t=1575

How do we know we haven't hit a GoE already? Has anyone at least found a predecessor?

It would be an oscillator if you could construct a rule it works in. Unfortunately, that doesn't appear to be possible, even with extended neighborhoods. See, when the dot hits one of the circles, it gets eaten. This means that the circle goes back into a steady state and has no reason to emit a do...

dvgrn wrote: Isn't there already a script somewhere that makes a report of all non-totalistic neighborhoods that are actually used by a given pattern? I have a very vague memory of maybe seeing something like that.

There is such a script here, however it only handles semi-totalistic rules.

Speaking of rules that create large blobs, has anyone made any attempts so far at an interesting non-totalistic Day and Night variant? (preferably, one that preserves invertability?) I have recently experimented with Day & Night variants. B3-c4k678/S34-k5c678 has 2 gliders; a common octomino and a ...

c/6 and 3c/14 orthogonal:

If I may suggest a more pronouncable (and memorable) name, how about Geneticow? (A genetic cow? A cross between a genet and a cow?)

Mazeon (123/3/3) Similar to Maze, but the clouds take an eon to settle. Gert (2368/357/3) The r-pentomino and t-tetromino are (or technically, evolve into) spaceships. Named for Generations + r + t. A kickback: x = 13, y = 35, rule = 2368/357/3 A$2A$A28$8.3A$7.A2BA$7.AB2.BA$9.A2BA$9.A2BA! A one-tim...

Check out what xp0_blinker evolves into:

Traffic lights beat beehive, I'm winning. :P

Starting a new post since that last one was getting long. The first thing I tried with Brainspawn was having a Brain cell be born from 6 Life cells. @RULE Brainspawn6 @TABLE n_states:3 neighborhood:Moore symmetries:permute var a={0,2} var b={a} var c={a} var d={a} var e={a} var f={0,1} var g={f} var...