Registered: Apr 2006
Posts: 17

Hi

I go to high school in France and my school has now adopted the International Baccaleuarate (IB) . Part of my IB coursework involves writing a long research essay of 5000 words.

I find a new kind of science interesting and would like to write my essay on this topic. I do not know a lot about Cellular automata but my understanding is after reading the 2 chapters that Stephen Wolfram invented this research and invented cellular automata and proved a lot of very useful things about them.

I want to do my project on 3-D cellular automata because I think this is very fascinating. I do not have mathematica software but is there a way to download a test version for free ? My school has not a lot of money to buy software so i need to pay from my pocket money the software i need to use to write my essay.

we got a sheet of guidelines to follow. we need a thesis or hypothesis. i do not know what to investigate this far any ideas what I can do with 3-d cellular automata ?

does stephen wolfram visited france and held lectures here ?

thank you.

mohammed

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Registered: Aug 2003
Posts: 712

There is no free version of Mathematica, but there is a discount student version, including options to get one for a limited time. The details are here -

http://www.wolfram.com/products/stu...ents/index.html

There is also a piece of stand-alone software for investigating systems discussed in the book, called NKS Explorer. If you want to write your own programs, a full Mathematica is better. But if you just want to reproduce experiments described in the book, try them with different parameter values, and the like, NKS Explorer might be sufficient for you. It is laid out according to the chapters of the book, with system examples from most. You can find details on NKS Explorer here -

http://www.wolframscience.com/nksx/index.html

On the history of Cellular Automata, they were invented by John von Neumann decades ago. Wolfram studied them in the early 1980s and published a series of papers on them, long before the publication of A New Kind of Science. You can find historical details in this note -

http://www.wolframscience.com/nksonline/page-876b-text

As for visits to France, while he was there briefly last year he wasn't giving speeches. I don't know of any scheduled engagements there. I do know that there is a Cellular Automaton conference being given in the south of France later this year - specifically in September, at the University of Perpignan. You can find the details on this website -

http://acri2006.univ-perp.fr/

As for stuff about 3D CAs, the section of the book dealing with them starts on page 182. But frankly they can be fairly tough to work with, because they evolve in 3 spatial dimensions, and time makes a fourth - and it is relatively hard to get good visualizations of 4 dimensional objects. If you look at the whole history made by 2D CAs - treating each time step as one "slice" - you can get interesting 3D structures already, without going up to a 3D CA in the strict sense.

If you do decide to look at 3D CAs, try looking at the last step, or making animations of their growth. One other warning is that 3D CA simulations are computational quite intensive, and use lots of memory. Also, you are pretty much forced to look at somewhat simplified space of rules, like totalistic rules. Because the number of general CA rules even of 2 colors and range 1, with a full 3D neighborhood of up to 27 neighbors (9 above, 9 level with counting the center cell, and 9 below), has 2^27 entries in its rule table - that's 134 million cases - and 2^2^27 possible rules.

I'd recommend starting with 2D rules instead, and looking at the 3D structures they can make if you "stack" each time step on top of the next, most recent at the bottom and oldest at the top. You can read the section on those in NKS, starting on page 171. On the next page there is an example of the sort of pyramid structures those make.

I hope this helps.

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Registered: Apr 2006
Posts: 17

Thank you Mr Cawley for you opinion on my three dimensional cellular automaton inquiry.

It could be better for French students to download a student mathematica version in french.

What Thesis research plan is good for two dimensional cellular automata and their shape ?

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Registered: Aug 2003
Posts: 712

On possible projects for 2D CAs and the 3D shapes they generate, it depends on your level of experience, how much you think you can do, the scope of the project in terms of time, etc.

A few 2D CAs - Life e.g. - have been studied extensively. General surveys have been made of some simple classes like totalistic 2 color nearest neighbor, which you can find covered in the NKS book. There has been relatively little work on non-symmetric 2D CAs or rules with longer range. Even 3 color totalistics have received only a modest amount of study, focused again on specific rules or near variations (single changes to the rule table of a 3 color analog of Life e.g.). There has also been a significant amount of work on probabilistic 2D CAs e.g. the forest fire model (also used for epidemic modeling etc).

A beginners project would be to take a class like 2 color outer totalistic range 1 CAs, or 3 color totalistic range 1, and investigate the range of their typical behavior from simple, random, and sparse initial conditions. Simple meaning a single black cell (or black or grey - 2 or 1 - for the 3 color version). Random meaning all cells 0, 1 or 0,1,2 at random, perhaps varying the proportion that start in each. Sparse meaning place a modest number - up to 10, say - or 1s (or 1s, 2s) on a field of 0s, with various spacing and patterns.

Then generate the 3D shapes they make. Look at simplifying measures like the average density (portion of cells black) through time, as well. Pick one or two interesting rules to focus more detailed analysis on. Perhaps count the number of voids (regions of connected 0s) according to size, after say 100 steps. How much do such measures change for different sparse initial conditions?

That is plenty for a good pure NKS 2D CA project. If a more experienced person is interested in applied as well, a good problem would be to find assymmetric rules that result in shapes like those seen in "hoppering" (bismuth crystals e.g. - see page 993 of NKS). The rule would have to promote more rapid growth at the edges than in the interior, and might have some sort of additional assymmetry to generate their characteristic spirals.

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