What if I say there is orderliness in chaos? People!! People!! I have not lost my mind; I am very much sane.
That's what Chaos theory is all about.
Chaos theory is the study of dynamic systems that are apparently chaotic; lacking order ; but studying them in depth reveals their orderliness. It imbibes physics and maths to explain that the unpredictable conditions occurring in nature are due to the initial conditions of the system. The predictions can be arrived from simple deterministic mathematical equations.
A very minuscule irrelevant and random occurrence can produce drastic results; by triggering a series of events. They call it the Butterfly Effect. Why so? Because it seems that the flapping of a butterfly's wings in one corner can set off a tsunami in other corner of the world. That is; the flapping of wings are the minuscule changes in the initial condition that can trigger a chain of events leading to a mighty phenomenon. Had the butterfly not flapped its wings, the chain of events might have been different.
So, being deterministic doesn't necessarily mean the events are predictable!!
There are lot of scientific terminologies which i wont use here; I want you folks to come back to my blog :-)
In other words, small and random things can cause complex and drastic events and these seemingly random events can be actually predicted from simple deterministic equations.
One of the most interesting subject in chaos theory is Fractals. They make the study of chaos theory simpler and applying the theory is easier when the subject is 'fractalized'.
Fractals are everywhere around you. Nature abounds fractals.
Fractals are geometrical figures; but you don't find perfect square, circle or rectangle in nature. The shapes are complex, chaotic but observe them in depth; you find definite patterns and order.
They have a unique property - self-similarity. A small split portion from a whole figure is a miniature replica of the whole.
The best example in nature is the Snow Flake and the Fern Leaf. Observe a portion of the whole and you can sense the portion is similar to the whole.
There are lot of examples in nature - The coastlines, the shell on a snail, cauliflower, water flowing, blood capillaries......
These fractals are generated to study the behavior of chaos theory by using recursive mathematical equations and recursive algorithms.
Few more fractals in nature
Fractals are applied in every field known to man - astronomy, medicine, meteorology, architecture, study of soils, seismology, enzymology, computer graphics, biology, robotics, economics, engineering, finance.....the list is endless.
-Images are compressed in computer storage technology on the theory of fractals.
- Architecture and construction - It is said that a tiny nail or a screw in a skyscraper can predict the strength and resiliency of the entire building
- Fluid mechanics - study of aircraft turbulence
- Special effects for movies; fractals achieve realism and the images need very less storage space
- Weather and natural calamities predictions
- Study of landscapes like mountains, terrains, coastlines and rivers
- Market prediction in economy
- Water retention properties of soil in the science of agronomy.
- Study of population growth
- Studying diffusion characteristics
And many many more!!!!
Fractals generated using recursive algorithms
There are detailed texts all over the net. There are fractal generating software and one can write recursive algorithm to generate beautiful fractals. Please try them if interested. Its intoxicating :-)
PS : None of these snaps belong to me. And I seem to have lost my collections of Fractal Generating programs :-(