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[Nikov]

I can't tell if this is the most brilliant or the most useless thing I have ever encountered.

[Vector]

I can't tell if this is the most brilliant or the most useless thing I have ever encountered.

It's mathematics   Did you expect anything less?

[Oglokoog]

If you are still interested in doing said report on cellular automata, I have run across Rule 110. http://en.wikipedia.org/wiki/Rule_110
It is a cellular automata rule for a 1 dimensional automata which is proven to be turing complete. Or in other words, you can solve every mathematical problem using it (albiet inefficiently).

:O XKCD snuck it into a web comic without me even realizing it... http://xkcd.com/505/

As far as I can tell, it's not one-dimensional. That would be a row of cells. It has an x and y axis, which means it's two-dimensional. And I think even Game of Life is turing-complete.

[Shades]

As far as I can tell, it's not one-dimensional. That would be a row of cells. It has an x and y axis, which means it's two-dimensional. And I think even Game of Life is turing-complete.

It doesn't actually have a y axis, the images use the y axis to show progress through time.

Each row is a single snapshot of the rules universe and the row is only in a single dimension, that appears to be the logic of the naming convention anyway.

Game of Life is a two dimensional version and generally only one snapshot is shown at a time, but yes is also turing-complete.

[Oglokoog]

Oh. Sorry then.

[Starver]

Oh. Sorry then.

It's easy to confuse, as I've heard who knows how many people argue that the time (or at least 'tick') is a dimension that should be counted.  Thus (standard) Conway is 3D.  (Although I must admit I've never seen Conway-ticks 'stacked'...  And that gives me an idea...  Especially as I was messing about with DF's arena map last night... .

OTOH, as time in these constructs is unidirectional and thus there's a 'horizon' of effect[0] in one direction, there's plenty of arguments against counting it.

For one-dimensional including time cellular automation (i.e. point existence, ignoring ticks)...  Fibonacci series?  (Or does referring to two prior generations spoil the concept of cellular automata[1]?)  If not that, then something like the "if number is even, divide by two, if odd, multiply by three, until you reach 1" system might be considered.  (Although that particular version zooms up to infinity as soon as it hits a 3^n value, making me think I've forgotten something, e.g. that it's 3n+/-1, if odd.)

• But consider a Rule-110 variant where instead of referencing [X-1, X, X+1] for cell X's further iterations, you took [X+1,X+2,X+3] as the progenitor locations.  That's functionally the same in all respects, but with an apparent advancing horizon effect.  Minds greater than I have probably got that issue tied down, though.
[1] I'm tempted to say no, because two parallel (i.e. associated) infinite lines === one infinite line, on a purely 1:1 mapping.   (c.f. Infnity Hotel when it receives an infinite number of new visitors).  It's only when you get two perpendicular (i.e. independent) infinite lines that you need to call it a plane.  But, even

then[/] there's that "diagonalising of the a plane" (forgot its name, but if you're familiar with pixel ordering in JPEG encoding, that's what I'm talking about, except with infinite plane --> infinite line), though I still think in terms of aleph-null and aleph-prime, through force of habit...

[Oglokoog]

I don't consider time a dimension. That'S bullshit. You can measure the height of an object, you can measure it's length, but you can't measure its "time".

[Sean Mirrsen]

You only need to measure the amount of time the object has existed. You can do this precisely by being there when it appears (or is constructed - any given object has a point at which it begins existing as the defined object), or approximately by secondary means (like that measurement of something or other that was used to determine the age of fossils et al).

[Starver]

I don't consider time a dimension. That'S bullshit. You can measure the height of an object, you can measure it's length, but you can't measure its "time".

Like I said, it's arguable.  Personally I deal with time as "a different type of dimension" from any space ones[1].  But I've seen enough people 'discuss' this that I thought I'd (try, and fail) to summarise it.

Cheers for the bullshit bit, though.  Just trying to make you feel better about your misunderstanding.

@Sean: I always liked the "like a carrot with a man-shaped cross-section" analogy for seeing someone growing up...


[1] And, yet, my 'worldview' of the universe is more or less that it's a static entity, with 'our time' just a direction you can scan back and forth for someone somehow sitting outside of it looking upon it in whatever spare meta-time they happen to have at hand.  I variously analogue it to either a 'tapestry' (time in the direction of the warp, though, more precisely it's more something of a macramé given that each 'weft' of consequence travels diagonally in that direction also) or a multi-dimensional bubble (with the 'latitude' dimension representing the pole-to-pole/big-bang-to-big-crunch, or making it an infinite bell-shaped if it is a non-crunching universe).  Whichever way, consider it a cellular automation across as many dimensions as you like and spread across time for the ticks, with the possibility that some twists in the automata substrate mean that 'future' tick data affects 'past' ticks (if Hawking et al are correct) meaning that you either end up with 'flip flop' time loops or (ideally, in my philosophy) only cellular substrate configurations that generate self-consistent loops of information.  (i.e.the  "You go back and do only what you've already been back and done"-style time travel, regardless of intention... because you having done what you did with the intentions that you had (e.g.: to change history) was already a part of the history that set you up for going back...  But that's another arguable thing, and increasingly less to do with CA.)  Anyway, go figure.  And I write far too much.