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Anyone on here also interested in cellular automatas? I think they can be considered related to fractals, in many ways. Look at this for example:

http://en.wikipedia.org/wiki/Rule_110_cellular_automaton

Also, i'd love to know what is going on here...

http://www.youtube.com/watch?v=Dh9EglZJvZs

This is a math that Marko Rodin has discovered /developed which is a modulo 9 group math but zero is not used, the counting numerals 1 2 3 4 5 6 7 8 9 are.

Now i wonder if any one would care to see if the Axioms of set FS apply to this group math. one thing I have learned already is that the numeral for 0 should not be included in the counting stages because it represents the region that is being iterated. Similarly infinity numeral/symbol should not be included as it represents the  iteration process state  not a stage in the iteration. Nullity and infinity I have briefly discussed as two new operators in computational maths and the numerals 0 and infinity may better be representations of these operators in geometrical space. That is to say that the iterations that nullify a geometrical space in any given region at any given fractal scale we have in the past mystically or in ignorance represented by 0, and similarly the iterations that are continuing, and never ending we have latterly represented by infinity for any fractal scale on any region in geometrical space.

Bearing this in mind the automata rules may be studied to see if they form a group math on stages in the iterations or in the operator rule/ algorithm structure.


Learn and enjoy

http://www.youtube.com/watch?v=nVYfXQcIcMA&feature=player_profilepage

I am the owner of the book:
A New Kind of Science
from Stephen Wolfram

Which can be seen as one off the best books on cellular automata.

Disadvatage:
The book has 1197 pages.
The message of the book is: Every thing in the Universe is constructed by simple cellular automata. Even the Universe itself!
How this is done in detail, Stephen Wolfram didn't tell.
But if one can work out the details Stephen Wolfram will be the first one who has dicovered it.
Steven Wolfram also has developed Mathematica. So many of the examples in the book are written for the Mathemtica tool.
(From this point of view the book is a comercial for Mathematica)

Postitiv:
The book contains a lot of information on cellular automata and their possible relation to other kinds of science.
A lot of fascinating pictures (black and white only)
The book is easy to read on the surface, but terrible if one goes into details (May be different if one is a Mathematica fan)
If one has enough time an energie buy this book and start reading.


Her is an link to an internet page that contains Java-Applets that simulate cellular automata.
http://www.collidoscope.com/modernca/ (http://www.collidoscope.com/modernca/)

Very interesting Hermann and thanks for the post. I will look into it when i get time. The Turing machine always comes to mind when i think of cellular automata, but i do not understand that or them at this stage.

My comment would be that as a mechanism for constructing a universe i would expect these to be applicable to the planck length level and to describe geometrical or spaciometric quanta relationships for extension and rotation of space. I would expect them to illuminate Lie Group Algebras and to explain quantum chromo dynamic properties. I would expect them to do this simply.

On this page of the forum one can find a presentation of Steven Wolfram on You Tube.

http://www.fractalforums.com/non-fractal-related-chit-chat/a-formula-for-everything/ (http://www.fractalforums.com/non-fractal-related-chit-chat/a-formula-for-everything/)

He is already searching for the structure of the Universe.

Wow Hermann, really neat!

I have just started using spacetime.us myself and there is a free version of a mathematica type programme called mathMaxima which i have not explored yet.

Would you be surprised if i said i found it hard to know what he was going on about?

I recognise this is how others view what i write and so am making the point that we play with what interests us and maybe someone else may start to recognise what we are playing with. If not we are still having fun!

Computation to me is simply rearrangement of spaciometric relations and relativity (of spaciometric structures). Biologically this is called a conformation. Computation starts with geometrical or spaciometric forms functions(roles), structures, relationships, boundaries, attributes, relativity and motion: and ends with  a simple vortex motion to define input and output for any system divinable in them. Computation exists independent of awareness because computation is the source of awareness in that sense of rearrangement of chemical and microbiological forms.

To simplify it i have elicited 2 fundamental motions which derive from the one fundamental action of the vortex: spaciometric rotation,and spaciometric extension: specifically (for a reference) rotation and extension.

Computation for me derives from these two motions and thus from the vorticular motion of the fundamental motion field.

Now i am quite comfortable with writing that knowing that it is strange and not at all plain despite the simplicity and plainess of some of the words. And that is the problem:Words are such a poor substitute for what i am experiencing. Thus i do not know what Stephen Wolfram is experiencing when he says "the computational universe".

I do see a bit more what he is after when he want to make knowledge "computable": but this buzz word does not translate to me well, because what he wants to do is actually quite complex!

You know i asked wolfram Alpha about the lottery: it said "it does not compute!" currently. :dink: 

http://www.youtube.com/watch?v=60P7717-XOQ&feature=player_embedded

I have now inserted the presentation of Stephen Wolfram again, cause it is close related to cellular automata.

As one can see at the end of his presentation, Stehpen Wolfram has four main projects:

• Mathematica
• Wolfram Alpha
• A New Kind of Science
• Physics

The Book: A New Kind of Sicence can be read online through the following link.
http://www.wolframscience.com/ (http://www.wolframscience.com/)

In this presentation I heared the first time of his physics project.
I think he tries to construct a computable universe based on cellular automata.

I think most of the readers are familiar with Wolfram Alpha.
The people who are not here is the link:
http://www.wolframalpha.com/ (http://www.wolframalpha.com/)
I think Alpha will accept Mathematica code.
People who are familiar with mathematica can use this kind of code for asking questions.

One can also ask Alpha for specific cellular automata.
Example try: cellular automata rule 30
http://www.wolframalpha.com/input/?i=cellular+automata+rule+30 (http://www.wolframalpha.com/input/?i=cellular+automata+rule+30)

For those who like cellular automatas I suggest the SoupAutomat:

http://www.frank-buss.de/automaton/SoupAutomat/

Bon appétit !

(For starters, the plural is 'cellular automata'; the singular is 'cellular automaton'.)

By far the best cellular automaton simulator is Golly:

golly.sourceforge.net (http://golly.sourceforge.net)

As far as I know, it is the only cellular automaton simulator that supports the multi-state HashLife algorithm. Furthermore, it can easily manage universes with googols of cells in them -- that's more cells than atoms in the observable universe!


If you want a book on cellular automata, I recommend Andrew Adamatzky's Game of Life cellular automata, especially because I wrote Chapter 25.  :)


One of the most interesting things that you can do in cellular automata is von Neumann self-replication, where a machine reads a tape of instructions and copies itself indefinitely. I am in the process of co-authoring a paper concerned with efficient self-replication in von Neumann's original cellular automaton.

Just to add a clarifying point, a disambiguation if you will: compute, and process or manipulate i see as essentially the same  action. Well possibly compute refers more to the intention to act on the environment, but essentially the same thing: to act on the space in and around a focus region.

Wow you guys have been busy! So i am going to have a little look and play too. Computation, data processing, information processing are all notions i expect to be involved with this, but there is one further element and that is action on the environment "holding" the data creating a feedback loop.

So some "The Matrix" speak is appropriate here: i am finding how deep the rabbit hole goes! any way the main thing is that this is about "recursion" which is a late Latin way of saying iteration, which "recursively" is a Latin way of saying do it again(injunctive) or doing it again(verb). I long ago combined the two notions under the one that is to iterate. This was principally because a kind of obfuscation had grown up around the word recursion which was totally unnecessary.

I found the word "iter" has among its cognates the word circuit as in a road one journeys around. That is good enough for me.

So computability theory is all about iteration, which is what i want to hear. Circular automata, as one might as well call them, or better still circuitous automata are about "iterating" an environment around a given path/circuit ( in this case called a rule), and dumping the result st the end of each iteration while using the result as the new environment to "iterate" around the path!

Heres a picture: pick up a box; run round a 400m track doing something to it, lets say ripping any flat side which is not already ripped, or ripping a side that is ripped at an angle of 1 radian to the last rip. Stop to take a picture. Do this  again with the same box.Etc...

Ok so you are going to end up extremely fit and carrying a curious pile of shredded paper/card.

The path the action and the staged outcomes, plus the effect on the operator are what i am highlighting here. Cellular automata belong to this class of behaviours if you like, and have a real world counterpart in growth, change, entropy, systematic developments, regional variation, weather forecasting,long term stock market behaviours in rigid market structures etc. In fact anything you want to describe in terms of "iteration" around a fixed path of behaviour.

"iteration" here is used as a noun describing a process of iterating. The process of iterating is of course the path, so the physical path is a symbolic or physical representation of the process, its start and stage points and its finish point. This then becomes a self referring analogy which highlights the fractal products of iteration,its region and thus boundaries and its self referencing structure.

Cellular automata have the characteristic triangular shape because the fractal is linearly expanding  at each iteration.

More complex rules will need to explore 2d and 3d variations.

I have just read some customer reviews for Steven Wolframs book A New KInd of Science on Amazone.
At the moment there are 339 reviews at all.
Very interesting to read them.

105 reviews gave the book only one star. (mayority of commends)
86   reviews gave the book five stars.
The book gets an average of three stars.

Reading through the reviews enhances some of my impressions.

• The book is not a general book on cellular automata
• The proof that primitve cellular automata of the Wolfram kind are applicable to all kind of sicence is missing.
• The book covers the kind of cellular automata that Stepen Wolfram has explored.
• Stepen Wolfram has spent much time and energy on exploring cellular automatas.

A big thank you to bib, Calcyman and jehovajah for their informaition.
I would like to have more time to test the software and to have a look on another book on cellular automata.
The book from Andrew Adamatzky Game of Life cellular automata sounds interesting.
Has it a focus on the Game of life cellular automatas?

So as i continue my research i come upon some old friends  (http://en.wikipedia.org/wiki/Foundations_of_mathematics) from my youth. God i love this stuff!

What devious and supercilious ponces we mathematicians are! And i include myself as always. By this statement i hope to impress the humanity of mathematics, the social group activity of mathematicians, and the grandiose madness within mathematicians. And yet, What "beautiful minds!"

I suspect that my take on mathematics was formulated at this juncture in my life when i came upon Hilbert's Programme and realised mathematics was a human endeavour, a game ,an agonia for some and a pleasurable pastime for others.

Why all this scribbling? Why all this gobbledegook, and jargon?.

Fortunately i met some real live mathematicians who were humans, and i met my first programme card computers at exactly the same time. If i look back now i would have to say the computing, alien as it was, was what saved and shaped me as a mathematician. Otherwise i would perhaps be bent out of shape by the ludicrousness of the enterprise. Nobody told me , as i tell you to play at mathematics, to find an interesting diversion in mathematics and enjoy and explore it; to relate it to real objects as referents. They were too busy arguing about what maths was and who was right!

Brilliant as Bertrand Russel Was, he has a lot to do with making mathematics subservient to philosophy and philosophical logic, and queering the pitch.

I believe that the platonic notion of mathematics suffers from the same difficulties as any other notion of any human endeavour: lack of knowledge of the epistemology of the notions, and no common accepted viewpoint on our experiential continuum.Benoit Mandlebrot is perhaps the only classical mathematician who addressed these issues experimentally because he was heir to increasing computing power. The other "mathematicians" who tugged at the issues were physicists, mechanics and applied mathematicians. The "roughness" of "reality" is what Benoit meant by fractal. And he was thinking geometrically when referring to reality.

Our collective consciousness of things informs our thinking, and only changes slowly and by accretion. We rarely get the chance to start from ground zero. For me, Fractalforums and fractals in general have provided that opportunity. And because i am on a personal journey with this i do not see any need to challenge or exhort convince or cajole or persuade or belittle etc...All the tools of the trade of philosophical and ungentlemanly logical argumentation!

So cellular automata, like computers did for me in the past, cut to the chase when i explore them. This is pure Epistemology, applied; but applied to a finite system of processing data iteratively. It is a model of How we know things, how we construct things and how we perceive things. But it has one thing missing: What the heck are "things"?

In this area of computation we learn not to think about "things", per se. we concentrate on the rules. In doing so we invalidate our model because, the rules do not include the iteration per se, we impose it; the rules actually act on physical memory in the ALU and the DATA store and we idealize those "circuit functions"; and we generally exclude our entire input into the action by calling it "automatic". We cannot here or in mathematics exclude our symbiotic involvement, our feedback feed forward cybernetic intervention, and our necessary paradigmatic perceptual frameworks.

There is a lot more i could address but enough is enough. Time to play and enjoy the euphony of it all. ;D

  E=mc²

A strange serendipity linking Marko Rodin's Rule of 9 to cellular automata!

hermann told me I ought to share this in this thread, so here goes:

(http://www.fractalforums.com/gallery/3/2624_01_09_10_8_36_56.jpeg)

Obviously, made using cellular automata. There's nothing mathematically groundbreaking going on here (I used a cellular automata formula in UF's public database. Each pixel's color is tied to a value between 0-2, which is determined by the sum of the values assigned to the three pixels above it) but I don't know if I've seen anybody pursue CA artistically in quite this fashion before.

The three "panels" are independent images; each in turn is composed of three different renders of the CA formula, each render with different settings.

It is always interesting to see the patterns produced by cellular automata without thinking deeply in mathematics.

Very nice. Don't you feel the texture in these renderings? Something is missing in that regard by just exploring in 2 d.

Mathematics is not where to start from. Spaciometry maybe, but definitely your Logos Response.

spaciometrically, you reference  definitions of spaciometric form, surface and structures, spaciometric mass and spaciometric density.

Nassim Haramein shows a CGI animation

http://youtu.be/vThC_5Yznro
http://www.youtube.com/watch?v=vThC_5Yznro