Talk:Rule 110

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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)

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)

[edit] 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.

[edit] Argh

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All or part of this article may be confusing or unclear. Please help clarify the article. Suggestions may be on the talk page. (October 2007)

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

[edit] 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)