Posts Tagged ‘patterns’

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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 🙂 ).

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 🙂 ?

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).  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.