I recently have taken a class that required me to understand the physicist's version of what chaos is. I also learned about what the Butterfly effect is and how any of this makes any difference to me. I got hooked. Not just because of the far reaching consequences of understanding chaotic systems, but also the elegance that lies within one. The patterns that are evident beneath and its effects on our understanding of the Universe.
All my friends who have had anything to do with physics, will know what I mean by a deterministic system. Determinism is the basis of a lot of physics. All systems that are deterministic show a very defined relationship between cause and effect. This is a part of Newtonian physics. We believe that if we can understand the initial conditions of a system, and mathematically compute all its interactions, we can reasonably predict the outcomes down the line. The path of planetary orbits were calculated this way rather reasonably.
However things were not quite as simple as they seemed. Since measurement is one of the cornerstones of science, a lot depends on the accuracy of these measurements of the initial conditions. Earlier it was thought that a very small discrepancy could hardly affect the outcomes of the systems. However Edward Lorenz in 1961, found out that that was entirely wrong. Some systems, especially weather systems, show very remarkable sensitivity to the initial conditions. So remarkable in fact that it lead Lorenz to hypothesize that the fluttering of the wings of a butterfly could change the conditions enough to create a cyclone in the future. Thus giving birth to the term, the 'Butterfly Effect'. (Women, stop thinking of Ashton Kutcher now!)
Such systems, showing this sensitivity were called chaotic systems. This chaos however again has nothing to do with the frenzy associated with the lay use of the word. Scientists soon found some patterns hidden within this chaos. These were termed as 'attractors'. The famous 'Lorenz Attractor' actually does look like a butterfly weirdly :)
Image on the left, is a plot of the Lorenz Attractor taken from Wikipedia. Patterns in chaos meant something very interesting. We may have a problem predicting systems right now, but if patterns exist, then can't they be explained by some sort of equation? Finding equations is apparently the no. 1 preoccupation of physicists.
Now comes the more interesting part. People who have fallen asleep can wake up now. What is a little more fun about these patterns in chaos, is the structures they create. Some attractors were found to consists of self similar structures known as fractals.
Fractals are probably one of the most fascinating geometries in the world. What is meant by self similar is that every part of the fractal when magnified consists of the entire structure of the fractal. This keeps on going ad infinitum till it is resolved to its smallest structure, and it creates insanely beautiful things. To put this in perspective, DNA is a fractal. So are mountain ranges, coastlines, snowflakes, etc. Nature abounds in examples of fractal geometries and scientists are extremely excited about that.
Why am I excited? and why do I subject you to this lecture? Well its a two part answer. Fractals and computer generated fractal images spoke to me, like no other art form has ever done. Every new image I see just makes me gasp in wonder. It opens up lines of thought I did not think I was deep enough to have. I am going to attach a few images. You will see for yourself, the beauty of these images.
Secondly, this is one scientific theory that makes sense to me. I can understand why anyone would pursue a lifetime trying to understand this. It epitomizes all that I believe science should epitomize. It is truly inter disciplinary. It has repercussions all throughout the physical world, from space to DNA. It is just beautiful and elegant. These I believe are reasons enough to care.
I shall leave you with some gasping and awing. Here are a few images of fractal art I found.
The above image is entitled 'Spectral Staircase'
This one is called 'Birds of Paradise'.
The resolution is not the greatest on these as they are on the post, so do click to enlarge. I am adding the URL to the site where you can see these and many other fractal images created by this artist. http://content.techrepublic.com.com/2346-10878_11-33277.html?tag=gald
Also I will give you the URL to a website where you can download a fractal creator if you would like. You can actually feed in basic equations to create your own fractals and can select color schemes etc. http://www.majorgeeks.com/Fractal_Forge_d4493.html
To all the people who's website links and images I have used, please don't be upset. None of this is for profit. In fact I just thought it would be great to let people know about this.
So, I am expecting comments, I hope I get some. Don't think of this as a boring science lecture. I encourage you to explore these topics. I do believe they hold a fascination for anyone, not only those connected with science.
