# Talk:Rule 110

## Citations Needed

Could someone add a citation for: "Class 4 behavior," i'm sure there's some in NKS. It would be very useful. New299 13:37, 15 June 2007 (UTC)

Citations to some sort of news source are also needed for the history section. --Jordo ex (talk) 15:51, 9 March 2011 (UTC)

## Pictures need explanation

The pictures don't make any sense to me. What are the pictures of? Are they plots? If they're plots, then what are the axes? What does black represetn, what does white represent?--ASL 00:02, 25 June 2006 (UTC)

I believe the Y axis is time (generations, iterations of the rule), proceeding downwards. Black/White are 0 and 1. The table at the top of the article explains how each particular pattern proceeds into a subsequent pattern. (Each cell's state in the next generation is dependent on its own state, and that of its two neighbors). —Hobart 19:55, 2 July 2006 (UTC)
this is correct, except you got white and black back to front. black is one, not white Mathmo 02:39, 16 August 2006 (UTC)
The pictures are of the rule 110 cellular automaton. In a one-dimensional cellular automaton, time usually goes downwards, in other words, each row is calculated based on the row just above it. Each cell (a cell being one of those squares, often represented as a single pixel) in a row being calculated is either white or black depending on the whiteness or blackness of the cells in the row above it (which is the visual way of representing the row that existed one moment before it). In this particular case, each cell depends only on the one just above it, the one just above and to the right of it, and the one just above and to the left of it, and is black if the three above it are black+black+white, black+white+black, white+black+black, white+black+white or white+white+black. Order is important, that is to say, white+white+black is not the same as black+white+white. The above rule (that is to say, the next cell being black when those particular cells are black) is called 'elementary rule 110'. You can read more about cellular automata at the cellular automata page. - green_meklar 22:41, 28 December 2006 (UTC)

The large images at the bottom of the article (well, actually most of the article) aren't that easy to follow. How do they interconnect? What the heck do they even do/show? The colored inlays are damned hard to read, even when watching the high-res versions. /193.11.202.125 14:15, 20 January 2007 (UTC)

## only proven universal computationer?

how can rule 110 be only proven rule capable of universal computation: reflections over left right yields rule 124, while switching 1s with zeros yields 145 & 131 as all posible. Saganatsu 23:50, 30 April 2007 (UTC)

Shouldn't there be links to rule 181 and 30? I unfortunally do not know how one create an "see also" section.

## Argh

I think the reasoning behind these tags is self-evident... <eleland/talkedits> 22:39, 24 October 2007 (UTC)

## The 2,3 machine is the simplest universal turing machine

Can someone please update? See http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html --cslarsen 12:48, 25 October 2007 (UTC)

I read Smith's proof, downloadable as http://www.wolframscience.com/prizes/tm23/TM23Proof.pdf. Smith shows how to emulate an arbitrary Turing machine A with a machine B that reads a sequence of increasing initial conditions assembled by a machine C. The n-th initial condition allows B to emulate A for n steps. Since A is arbitrary and C is nonuniversal, Smith infers that B is universal. But by taking B to be a linear bounded automaton these conditions are easily met, and it is well known that linear bounded automata are not universal. Smith's argument therefore fails on account of an elementary fallacy of automata theory. --Vaughan Pratt 08:25, 29 October 2007 (UTC)

But are touring machines in fact simpler than cellular automata? I believe it may be possible that rule 110 is simpler than the 2,3 machine. I have taken out the part about the 2,3 machine being simpler until someone can show me a citation proving me wrong. Exploto (talk) 00:26, 15 January 2009 (UTC)

## Why called Rule 110?

All is explained at the root article Cellular_automaton. That you ask the question is very significant. It seems to me that this page on "rule 110 CA" (and the corresponding one on "rule 30 CA") were created as "children" of the main page Cellular automaton. It is clear that at the very least link-back is needed. I will try to do this as soon as possible. --Михал Орела (talk) 08:35, 22 December 2008 (UTC)

## Suggested name change

See Talk:Rule 30#Suggested name change--RDBury (talk) 16:22, 15 May 2009 (UTC)

## Description of Class 4 Behaviour

The article describes class 4 behaviour as "neither completely random nor completely repetitive." However, given that cellular automata are totally deterministic systems, no cellular automaton can be random. Furthermore, since the evolution of a cellular automaton is computed by repeatedly applying the same rules, all cellular automata are, in some sense, completely repetitive. I understand the spirit of the description, but it doesn't seem precise enough. How about describing class 4 behaviour as "neither completely chaotic nor completely stable?" Does someone who knows more about the topic think that this is an accurate description? —Preceding unsigned comment added by 64.229.83.176 (talk) 02:50, 23 October 2010 (UTC)

The thing about Rule 110 is that it's been proven to be Turing complete and capable of universal computation. I/O? I haven't reviewed its use in A New Kind of Science (which is free to download)... but rather than treat it generally as a cellular automata, I'd make sure any changes in this article primarily reflect it's categorization and use in the book's context, and its notability due to the Turing proof as well.—Machine Elf 1735 (talk) 03:39, 23 October 2010 (UTC)

## Is pattern number 2 really a "spaceship"

Having implemented Rule 110 on a 1280 X 1024 monitor screen (that is, to much greater detail than is shown here) I can see the second pattern moving as described, BUT it doesn't seem to comply strictly with the definition of spaceship. To me, it seems more of a "comet" rather than a "spaceship"; in that whilst there is movement, there is no single particular shape that is repeated. For example, in generations (is that the right word?) 600 to 690 (or thereabouts), in the area of interest there is no change at all. Old_Wombat (talk) 09:54, 10 May 2011 (UTC)

OK, I've done a few more 110-runs with quasi-random data which has cleared up a lot. There are both comets and spaceships and the example given of pattern 2 is correct but rather poor. I can supply a better one, and I've even coloured it! Old_Wombat (talk) 08:13, 11 May 2011 (UTC)

## "Among the 64 possible unique elementary cellular automata"

The '64 possible unique' probably needs explaining. I presume the value 64 is derived from:

256 (total rules) / 2 (for 0/1 <-> 1/0 inversion) / 2 (x-axis symmetry) = 64 —Preceding unsigned comment added by 86.137.138.80 (talk) 11:43, 20 May 2011 (UTC)