Chaos theory: an exerpt
OOC: Most of the information in here is actually a summary of a bunch of research that I have done, put into my own words. It is mostly meant for me to figure out what Sarah knows already. If you're truly interested in it, go right ahead and read, otherwise, it's kinda dry and uninteresting.
Introduction
Chaos theory is a description of randomness as it converges into order. A system that is seemingly chaotic can have an underlying pattern that explains its randomness. In effect, chaos theory is about order within unpredictability. It is a holistic approach to systems thinking...
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Chaos theory is so universal that it has been applied to many other disciplines. Indeed, it has been incorporated in such diverse areas as meteorology, physics, biology, mathematics, chemistry and economics. A single function has been known to describe the growth patterns of algae and also stock market trends...
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Original Julia sets, done by Gaston Julia and Pierre Fatou, have illustrated the complexity and beauty of fractals and have further shown the connexion between mathematics and nature… The results of some sets echo certain natural phenomena such as corals. These corals are the result of a single iterative function that contains a complex number, i. The simplicity of the function allows for all that information to be stored in the DNA of corals and just replicated over and over again. Yet this results in even more diversity within the similarities because the function is an iteration...
... a 3-dimensional graph can reflect a gradual change towards disimilarity by merely rounding off the results of a particular iteration, as Lorenz found out during his meteorological experiments...
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Fractal patterns, such as those made famous by Benoit Mandelbrot, are essentially a graphical representation of these iterations…
Classical geometry, as seen by the Greeks and mathematicians such as Descartes, is merely a simplification of the fractal forms… Basic geometry assumes even-ness and regularity, which is rarely, if ever, present in nature… Fractals try to represent the uneven-ness and irregularities and as such, is actually closer to nature than the supposed ideal of earlier eras. ... Biologists and other medical researchers have come to the conclusion that complete regularity and perfect order is not the ideal state of being for the human body. The ideal rhythm of all life is ordered chaos. Once perfect order or equilibrium is achieved, death results.
Introduction
Chaos theory is a description of randomness as it converges into order. A system that is seemingly chaotic can have an underlying pattern that explains its randomness. In effect, chaos theory is about order within unpredictability. It is a holistic approach to systems thinking...
......
Chaos theory is so universal that it has been applied to many other disciplines. Indeed, it has been incorporated in such diverse areas as meteorology, physics, biology, mathematics, chemistry and economics. A single function has been known to describe the growth patterns of algae and also stock market trends...
......
Original Julia sets, done by Gaston Julia and Pierre Fatou, have illustrated the complexity and beauty of fractals and have further shown the connexion between mathematics and nature… The results of some sets echo certain natural phenomena such as corals. These corals are the result of a single iterative function that contains a complex number, i. The simplicity of the function allows for all that information to be stored in the DNA of corals and just replicated over and over again. Yet this results in even more diversity within the similarities because the function is an iteration...
... a 3-dimensional graph can reflect a gradual change towards disimilarity by merely rounding off the results of a particular iteration, as Lorenz found out during his meteorological experiments...
......
Fractal patterns, such as those made famous by Benoit Mandelbrot, are essentially a graphical representation of these iterations…
Classical geometry, as seen by the Greeks and mathematicians such as Descartes, is merely a simplification of the fractal forms… Basic geometry assumes even-ness and regularity, which is rarely, if ever, present in nature… Fractals try to represent the uneven-ness and irregularities and as such, is actually closer to nature than the supposed ideal of earlier eras. ... Biologists and other medical researchers have come to the conclusion that complete regularity and perfect order is not the ideal state of being for the human body. The ideal rhythm of all life is ordered chaos. Once perfect order or equilibrium is achieved, death results.