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Chaos Theory – Is there a pattern in randomness?

June 17, 2009

Chaos theory is not about disorder. It is about finding an order in disorder.

Can you imagine that a mathematical equation can predict the next earthquake? Can you imagine that a mathematical equation could be used by your DNA or a plant’s DNA to replicate patterns? Can you imagine that even the stock market and change in commodity prices follow a certain pattern? Chaos theory addresses such complex questions (No doubt, it introduces further complexities πŸ™‚ ).

The name “Chaos Theory” comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is about finding the underlying order in apparently random data. Chaos theory is the qualitative study of unstable aperiodic behaviour in deterministic non-linear dynamic systems. Aperiodic behaviour is observed when there is no variable describing the state of the system, that undergoes a regular repetition of values. Unstable Aperiodic behaviour is highly complex: It never repeats and it continues to manifest the effect of any small perturbation. A chaotic system needs to show high degree of sensitivity to initial conditions. Only then, it is classified thus.

The research started with Edward Lorenz. He was a meteorologist and was working on systems that predict the weather. He had some equations which he used for it, and in 1961, he needed to wait for hours before getting the results from the computer, as existed back then. On a particular simulation, he wanted a second analysis using the same data. So, instead of starting from the beginning, he run the simulation from the middle by manually entering the values of that stage. But this time, the end result was totally different. The cause for such a result, he later found out, was that – instead of .506127, he just entered .506 – That small rounding off created totally different results!

This was called the butterfly effect – an offshoot of the chaos theory. In the above case, a small change in the input variable could cause a huge change in the result. Like wise, the flapping of a single butterfly wing today produces a tiny change in the state of the atmosphere. So, there is a chance that over a period of time, what the atmosphere does, diverges from what it would have done. So, a tornado that was supposed to occur in a different place could have been diverted because of this small flapping (OR) the tornado which was never supposed to occur, might occur in some place! So, all our actions might be interconnected after all!

Interconnection is fine, after all we are in a complex system with multiple variables. But could there be a pattern to the interconnection? Can the interconnection be predicted?

Natural phenomena seem to have some sort of inbuilt rhythm or an established pattern – Like planets going around the sun in a cycle, the decay of radio active elements etc. But what about activities that have heavy human intervention – Like the prices of a commodity? Now it gets complex.

An employee of IBM, Benoit Mandelbrot, was studying cotton price fluctuations. He obtained all the data available on cotton prices from 1900 to about 1960. When he analysed the data with IBM computers, he found out that each particular price change was random and un-predictable. But the sequence of changes was independent on scale : Curves for daily price changes and monthly price changes matched perfectly. The degree of variation remained constant over a sixty year period that saw two world wars and a great depression!! That’s scary, isn’t it πŸ™‚ ?

Now you need to know about ‘Fractals’ – which is defined as an object whose irregularity is constant over different scales. It is a rough or fragmented geometric shape that can be split into parts, each of which (at least approximately), is a reduced size copy of the whole by a property called self similarity (An object that is exactly or approximately similar to a part of itself).Β  You might want to watch the video at the end of this article, where one such fractal pattern is shown.

Fractal structures have been noticed in many real world areas – Blood vessels branching out further and further, the branching of a tree, the internal structure of lungs etc – They are all self similar. In fact, researches developed a simple set of three equations that graphed a fern (A branch of a fern, which shows a good degree of similar patterns at multiple levels).

This started a new idea – perhaps DNA encodes not exactly where the leaves grow, but it just encodes a formula that controls their distribution. This can apply to the distribution of blood cells in the human body too, which shows a fractal characteristic. So, by using fractal formulas, DNA might control how the blood vessels might branch out and the nerve fibers get created. Is there a possibility, then – if the DNA does not hold the entire information, that even the behaviours can be mapped by some equations? DNA is a complex subject, and maybe some time in the future we might get some of the answers.

In fact, some equations are already being used in Earthquake detection, which can predict an earthquake based on a lot of input factors. Or the weather forecasting. These are examples of applications of Chaos theory.

So, can things in nature be simplified to a set of equations? Is there a pattern to certain seemingly random happenings? Does this impact free will? See the video below which explores more on this subject.

References:
http://www.imho.com/grae/chaos/chaos.html

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

There was one recent movie – Dasavatharam (Dashavatar) which used these concepts to create a story line. There was more to that movie than just butterfly effect says my friend – You can read his analysis of the movie in two parts – Part 1 and Part 2.

Destination Infinity

PS: This article will keep changing, as I am too confused! So, if you notice any mistakes or have more interesting information, you could reperesent the same. You could visit the Concepts and Ideas section of this website for similar articles.

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46 comments

  1. Chaos theory is very very interesting to the point of making us understand that there is a possibility of order and pattern even in randomness!

    I strongly believe that despite what things appear to be, they have a certain set pattern, one that may not catch the eye prima facie!

    Add the theories of general relativity and quantum mechanics to it, the ‘game’ become more interesting!


    • I too believe that there is an underlying pattern. But I never thought it would apply to data like cotton price fluctuation! I was not able to understand the general relativity, quantum mechanics i should give a try!

      Destination Infinity


  2. Nice post..
    Have you read ‘Chaos’ by James Gleick? Good layman’s intro to chaos theory..


    • Well, I have not yet but I will for sure. But I am afraid to read a whole book on this topic, as it is taking a lot of time for the concept to sink in! But it is interesting for sure πŸ™‚

      Destination Infinity


  3. You have touched a chord here . There was a time when I was obsessed with it , so much that my Orkut screen name was , Professor Chaos . πŸ˜€ .


    • Ah, that is interesting. I am also thinking of changing my blog name to infinite chaos!!

      Destination Infinity


  4. hey thanks for this informative post, I think its a lot of information which I will take back and try to read more..thanks again


    • Yeah, it is quite a lot of information. It took me one and a half days to come up with this post. So, go slow on it!

      Destination Infinity


  5. Quite an interesting post πŸ™‚ There is a movie called “Butterfly effect” wherein the hero can go back in the past and change it.. and that change reflects in the present when he comes back..


    • There is a movie called Chaos theory too, it seems.

      Butterfly effect manifests a small inconsequential change into a huge one! Generally, it cannot be expected. Time travel is another thing altogether! Did you see the video? They are suggesting that if time is infinite and space is finite, then everything could repeat like a cycle. We had blogged some milleana ago the same things, and we will be blogging some milleana later, the same things. They are asking if we have been created to fill the void to an already set pattern!!!

      Destination Infinity


    • I liked that movie too..Butterfly Effect’
      interesting story…


      • I have not seen the movie till now! I guess, I will have to see it now – thanks for the recommendation.

        Destination Infinity


  6. There is something beyond everything πŸ™‚

    And maybe the idea that everything repeats goes along with that energy is neither created nor destroyed..

    And funnily enough this is the riddle – how to arrive at an end ? By saying we can’t do it any more , maybe that is how much we can “see” ?

    After all infinity is nothing but the fact that one cannot be divided among nothing but that nothing still happens to be something πŸ™‚


    • What is startling to me is: We are not even sure about how things happen and in this rate, when are we going to see why things happen?? The answer to that question is as cryptic as your comment πŸ™‚

      Destination Infinity


      • well I don’t think “at this rate” is applicable … if were stuck to a simple progression , we would still be many many many years from nukes…

        As it is , there a few moments , i.e. miracles or epiphanies or a time when the whole universe sees the same result and at that point something extra ordinary happens…


      • This extraordinary occurrence which you describe may also be programmed – I mean the rate at which they occur!

        Destination Infinity


        • it could be or it could have been naturally created while other things were…In fact everything is like a song and every note has to fall in place..while we can say that the first line repeats itself after every para and that this line repeats itself every 1008th line , but every line in between is something new..

          For those “special new lines ” it might be that there is enough stress for that creation … i.e. there is a need for it..

          And there is always a need for something “new” , so basically the fact that we need is constant but how much we need varies..this variation is dependent on so many factors including the way people perceive the world..

          What I am coming to say is while there can be a rate at which they occur ( and I say that it is constant through all phases of time) but the actual happening of extraordinary events is independent of the rate but dependent on other factors … and try considering the fact that the other factors can have highs and lows and also that no proper proportion is needed any will do…

          So while a constant rate is a rate , each individual event doesn’t follow any rate πŸ™‚ but rather is a “point” outcome of events at that time..something more like a balance sheet πŸ™‚


  7. Very interesting DI. I wonder if Numerology has something to do with this too? It says that the right numbers in your life can change your life for the better. About the importance of birth numbers matching the name numbers, house numbers, city numbers and so on. It’s quite frightening really because if it all adds up wrong then things could go wrong! Not that I believe in it.


    • Nita, I believe in Astrology. I think it is science and our ancestors did a great job in mastering it. Whether they make approximate predictions (based on patterns) or they can make accurate ones, is beyond my understanding. When it comes to numerology, I feel that may be the numbers come together and they organize themselves when they have to. A numerologist might help with it, or some of it might happen automatically too. If a numerologist helps in enhancing the betterment effect, I feel that the price for it might be paid by the beneficiary later. But there are a lot of assumptions in this comment. It is what I believe in, rather than what might be! I hope I am wrong!!

      Destination Infinity


  8. Excellent, DI!!!

    I’m no expert on the chaos theory and don’t even understand its intricate details, but there can be no doubt that it makes terrific sense!

    However, it does not need to have an impact of free will. Free will does exist, but is inextricably linked with what would follow. This indeed leads to an infinite number of possibilities πŸ˜‰ and can go hand-in-hand with the chaos theory.

    Henry Ford was once asked why he offered his revolutionary Ford Model T only in the colour black and didn’t offer his customers any other choice. He famously replied, They have a choice of colour as long as it’s black! (The real reason was that the pigments used in black paint of that time were cheaper and dried much faster than other colours, thereby reducing both the cost of the cars as well as speeding up the revolutionary assembly line manufacturing process.)

    Similarly, free will exists and life is all about choices. In other words, we have a choice as long as it’s the one we make! Needless to say, every choice is followed by its own consequences, just as every cause is followed by effects.


    • Free will exists, but it is not totally free! That’s what I am also afraid πŸ™‚

      Destination Infinity


      • yup we are free , but is it “that as long as it is that” ? no I don’t think so , simply put , you can’t be forced to use your head , so if you are being forced don’t use your head…


      • I am not able to understand your view point on this one…

        Destination Infinity


        • what I meant was

          /*we have a choice as long as it’s the one we make! */

          I don’t agree…we have other choices at every point … I believe we “give ” ourselves the choices and being forced into doing in itself is a choice , where in you can resist it..besides we are put into that situation because of our past choices …


        • WE have a choice – well we could be. But how much?

          Now I get your point.

          Destination Infinity


  9. A very nice introduction. It is not the question as to whether we believe in Chaos or not. It is there in all real life systems since these are all basically nonlinear. But what I see as a challenge is to use the concepts to design solutions to our real life problems — be it in any field of say, design, engineering, maintenance, economics or architecture. If this is done then only we would be able to make our world and lives better.


    • Well, application of chaos is different… they are already applying it in some weather and earthquake predictions and also some art forms. If chaos is there in all real life systems is something that needs to be found out!

      Destination Infinity


  10. mmmmmmmmmm


    • That’s how I felt too for about one and a half days!

      Destination Infinity


  11. very interesting!


    • Yeah, it sure is. I wonder how such an important branch of science is not getting enough publicity! A lot of work needs to be done here, and for a change I think India can start contributing in this topic too, instead of just being copy cats.

      Destination Infinity


  12. I think nothing is random. There is always a series of A,B,C events which can lead to event D and if we are somehow able to know A,B,C then we can predict D. Its a chain.


    • A,B and C might be random, but the event D may be predicted if we accurately know all the factors affecting D. This is a related field of chaos. But scientists are not enthusiastic about it!

      For example, take a coin which is being tossed. It is possible to measure the force with which the coin is tossed but even if the coin is tossed with the same force and it goes to the same height, we can’t still predict if it will be a heads or tails. This is an example of a random event it seems. Some times, tosses change matches and science will take a long time to come to the point of explaining why things happen. For now, let us concentrate on how they happen.

      Destination Infinity


  13. Absolutely a pattern in randomness. It will eventually come back together. Interesting, I am writing a book and I touch on this some, because it has always fascinated me…


    • Oh, good to hear that you are writing a book! This subject suddenly became so interesting to me that I spent one and a half days on it! I too think there could be a pattern to randomness… nothing can just happen by chance.

      Destination Infinity


  14. Thanks a lot for this rich post. I once was hooked to chaos theory and then left it after reading a book or two. Fractals are a beauty :).
    Even for a beginner, this is a very good and informative article.


    • Thanks, it took me one and a half days! And you read a book or too about it? That’s casually said but too good πŸ™‚

      Destination Infinity


  15. whoa! too much of technicality involved!
    but very interesting concept…
    wish i had more of a head for science to drink it all in!
    to put it in layman’s terms… let me get this straight… the butterfly effect in terms of ‘what if’ this weren’t so… or this happened differently..
    something along those lines rite?


    • Yes. That is butterfly effect. There is one more to the what if – even if that ‘what if’ is a very small happening, the effect it could produce in the future could be very big. That is also butterfly effect. And the ‘what if’ in itself doesn’t happen randomly – there could be a pattern to when and how it happens. That is chaos theory. At least, approximately. I am still in the hangover of writing this post!!

      Destination Infinity


  16. lol yes πŸ™‚ that is pretty evident alright!


  17. Destination Infinity,

    That was an interesting read!

    I’ll deal with individual topics as I encountered in your post.

    Earthquakes can be predicted–as of now, not very accurately, but with growing accuracy with advancement in technology. I’d watched a documentary in ‘Science City’, Kolkata, and it talked of how predictability of earthquakes because of knowledge of fault lines. This makes prediction of location of earthquakes more accurate, because earthquakes happen in a linear fashion over a fault line. So, some earthquake in Istanbul was predicted, but timing was accurate only in a margin of around 5 years. Timing would be possible to determine with greater accuracy by refinement in ability to see beyond the Earth’s crust. But that as of now is not possible, and release of gases like radon, and activity of volcanoes along the fault lines is also being used. I’ve not heard chaos theory mentioned in this context, but I concede, my knowledge about chaos theory is nil.

    I’m not sure if you’re aware of the ‘Heisenberg’s uncertainty principle’. If you’d think of the purview of chaos theory in the definition you’ve given in the post, you’ll realize that ‘deterministic’ is a huge rider. πŸ™‚ It simply implies that chaos theory can only predict those things that follow as strict cause-and-effect principle. Thus, chaos theory works only for those events that are highly complex to begin with (because of overwhelmingly numerous factors involved, but which all are individually PREDICTABLE), inherently predictable.

    Yes, I’ve had an idea of the Butterfly effect. There’s no doubt apparently small events could have huge impact on future outcomes.

    But isn’t that somehow known to us empirically?

    Can’t a single, small spark blow up a whole petrol pump?

    Also, the theory appears attractive only because we’re not understanding that it’s not always so easy to delineate the exact factor governing complex events. And if we’re indeed able to make them out, what’s so special about being able to predict them?

    I personally feel, actually ‘indeterminate’ events are very few in the Universe. It’s just out technological limitation that’s limited predictability of many events. So no doubt, as our computing skills and speed improve, a lot of phenomena would enter the domain of ‘predictable’.

    ONE VERY BIG OBJECTION. πŸ™‚ Decay of radioactive atoms is not predictable. What we know is the decay constant and the half-life–both are statistical figures…


  18. …If the half life of a radioactive isotope is 5 min, it does not mean that if you have 2 atoms EXACTLY, after 5 min one of them will necessarily decay. Plus, you’ll never be able to predict, which of the two will decay first. What we do know, but, is that if there 10 trillion atoms of the unstable isotope, then after 5 min approximately, and not exactly, 5 trillion atoms would’ve decayed.

    The cotton price change phenomenon must have been observed in the US. Honestly, pattern in even daily price change is somewhat suprising. I’m no economist, so I can only speculate. America has a very strongly capitalist economy. And, so government intervention (which is what acts as a buffer against price change) would be absolutely nil. So, because of free market concept, if more people buying clothes on holidays, and closer to winters cannot be ruled out. Same with seasonal variation in production of cotton. Free market is all about demand and supply. So, if they both show periodic fluctuations, prices of cotton showing such variation shouldn’t be extraordinary. But I repeat, again, economics is not at all my specialty. πŸ™‚

    Now, I know a bit about blood vessels and bronchi and bronchioles of the lungs, and I can tell you trying to make them fit a pattern of perfect fractals is a gross oversimplification. It is impossible for lungs’ bronchioles to show perfect fractal pattern because right main bronchus is shorter at more acute angle with the trachea as compared to the left one.

    Likewise, blood vessels have a very, very random pattern. In fact, every given day, a few vessels open up and close, new vessels are also formed depending upon pressure conditions in their region of perfusion. Yes, both have to have a somewhat regular pattern of branching, but that’s the most logical thing to happen. Think of drip irrigation system. Don’t those tubes have pores at regular intervals?

    Likewise, growth pattern in plants is determined by two major factors–gravity (geotropism) and sunlight (phototropism)–and both are fairly constant. Also at every nodal point, where new branches sprout, specialized cells produce plant hormones, so obviously, the concentration of these hormones would keep on decreasing with increasing distance from the nodal point, and when concentration reaches a threshold low, a new branch will sprout. I don’t see anything logic-defying in this. Also, plants grown in space don’t show such patterns because of lack of gravity…


  19. …What determines shape of individual parts in a developing embryo is under heavy investigation. But to the extent I know, DNA cannot completely code for shape of gross things. But what determines such shapes remains to be known.

    The last time I’d read about all this from a very old physics book, it stated that scientists know of laws of conservation of seven physical quantities, like linear momentum, angular momentum, energy+mass, charge, parity (right and left ‘sidedness’), and some two quantities related to subatomic particles. And these seven laws can explain EVERYTHING about the universe. But scientists want to know law of conservation of a single quantity that can replace all the seven existent laws. This is what is being attempted through the Unified Field Theory.

    Of course, free will is a very complex concept, and many scientists seem to believe there is no genuine free will. πŸ™‚

    Before you venture out to read my article on free will, it would do you good to just go through Wikipedia articles on ‘action potential’ and ‘synapse’. I think Wikipedia also has a comprehensive article on ‘free will’.

    TC.

    PS: Definitely read about Heisenberg’s uncertainty principle. πŸ™‚


  20. […] Our lives are a sum total of the choices we have made. (~ Wayne Dyer). Our choices do have Consequences (~ Chaos Theory). […]


  21. That was informative, I got this line, “Our actions have consequences” and it was really inspiring for me.

    I had made it a point to dig into the chaos theory, looks like I should start with the book by James Gleick.

    Nice work πŸ™‚


  22. very nice post. I actually met a man today that believes he has a solid theory that there is a patern in the randomness. He proved it useing just simple cards. Its quite an interesting theory.
    Just imagine if this is all prove true. This could be the beginning of not only time travel, but the ultimate grasp on gravity and many other phenonomes that we are constantly surround by today



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