What do we Iearn from looking at these patterns?
Is this a "magic eye" or "lava lamp" application that requires hallucinogens to really appreciate? <img src=/S/nuts.gif border=0 alt=nuts width=15 height=15>
What do we Iearn from looking at these patterns?
Is this a "magic eye" or "lava lamp" application that requires hallucinogens to really appreciate? <img src=/S/nuts.gif border=0 alt=nuts width=15 height=15>
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<img src=/S/nun.gif border=0 alt=nun width=20 height=20> Sister Dory
Our Lady of Perpetual Help, Holstein Falls, Wisconsin, USA
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Good question ! Wolfram's book is enormous, but the key points that he makes about this very simple class of cellular automata include:
1. Rules like 30, despite their extreme simplicity, generate "intrinsic randomness", requiring no seeding with noise from a complex environment outside. (the random integer number generator in Mathematica is, in fact, based on rule 30).
2. Rules like 110 (you may need a pretty deep Excel spreadsheet to see this properly) generate behaviour at the highest level of complexity that exists. It turns out that the patterns created by rule 110 can be used as computations (to find the square of a number, generate the sequence of primes, etc.) A significant part of Wolfram's book is a demonstration that the patterns of Rule 110 can in fact be used to emulate a universal (arbitrarily programmable) computational system, capable of handling computations as sophisticated as any that can be run on any other computing system.
Rule 110, incidentally creates a highly complex interface between more or less regular patterns on the bulk of the left hand side, and highly structured patterns on the right hand side that are hard to reduce to any obvious regularity. To see this happening you need to extend your spreadsheet pretty deep, write a custom application, use Mathematica, or look at the pictures to which the http://www.wolframscience.com/preview page provides links.
On the broader issues of where the randomness in Nature comes from, and how easily the highest levels of complexity arise from the simplest rules, there is an interesting articles on Wolfram and his project on www.Forbes.com Rule 30 is discussed on page 5 of the article at http://www.forbes.com/asap/2000/1127/162_5.html
Good luck !
Not sure if people have seen the Business Week, New York Times, or Wired articles on "A new kind of Science" by Stephen Wolfram http://www.wolframscience.com. The examples in the book are all written in Mathematica, but it turns out that you can play around quite easily in Excel with the main cellular automata he describes, and the visual effects can be quite compelling.
I have attached a sample spreadsheet, but it's quite easy to do it manually.
The trick is:
1. to place a "Wolfram rule number" (Integer in range 0-255, try 110 for a start) in the top left A1 cell of the spreadsheet.
2. to fill a good-sized block of cells with copies of a formula of the form:
=MOD(INT($A$1/(2^(AboveLeft*4+Above*2+AboveRight))),2)
where the three "Aboveetc" are the addresses of a) the cell immediately above the current cell [img]/forums/images/smilies/cool.gif[/img] the two neighbours of this latter.
3. Place the number 1 anywhere on the line of cells immediately above your block of cellular automata formulae.
This sets up a cascade of recalculations and a pattern of 0 and 1 digits emerges.
To improve the look and ease of use:
1. Surround your block of cellular automaton formulae with a border
2. Use conditional formatting of pattern and font colour to replace the 1 and 0 digits with blocks of different colour
3. Resize the height of rows and width of columns to make it all into a compact square grid.
You can then experiment with changing the Wolfram number at top left (110 gives complexity, 30 gives randomness, 126 gives a kind of Sierpinski fractal stucture etc.)
You can also add/delete "1" from any cell immediately above your grid to watch the interaction of different cellular cascades.
Wolfram argues that these kinds of simple rules provide a more powerful way of modelling nature than do traditional mathematical formulae ...
Based on my experience at the office today I can state that the highest levels of complexity (and randomness) are generated by the simplest MINDS, as well. You should see the inventory spreadsheet down in Receiving! Talk about random.
Seriously, thanks for the overview. I just put a hold on Wolfram's book at my local library. Looks very interesting.
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<img src=/S/nun.gif border=0 alt=nun width=20 height=20> Sister Dory
Our Lady of Perpetual Help, Holstein Falls, Wisconsin, USA
I'm glad you find it interesting, I certainly do.
Good luck with the inventory spreadsheet :-) Perhaps it take more complex mental work to come up with simplicity. Wolfram's book, incidentally, argues that complexity comes more or less free, and that the main work of natural selection and evolution is actually to keeps things manageably simple, rather than make them more complex ...
all best.