(for Teacher2Teacher Service)
Date: Jul 16, 1998 at 09:37:42
Subject: Re: Can fractal systems evolve?
The applications of fractals and chaos theory span a range of disciplines, from economics (modeling the stock market) to science, from modeling the eye of Jupiter to predicting when a person is going to have a heart attack. The "patterns" are based upon iterations (the process of taking "an answer" and letting it become the feed number to evaluate in a system. The coloring of fractals is determined by how fast the points go off toward infinity. There is always a point where self-similarity can be found. In terms of investigation, you can appear to be in a totally new realm and suddenly come upon the original fractal design. This can be seen when viewing the Mandlebrot set from various perspectives. There is an interesting video entitled, "Zooms, zooms and more zooms" that addresses this topic. So to directly answer your question, then, a fractal can't evolve in the sense I think you mean, change into something different from the first, without at some point coming back to it. It can become very complex, and when chaotic, you can find order. One way to get an interesting perspective is to read Jurassic Park. Each chapter begins with a more complex iteration of the design known as the dragon curve. Although the reference to the number of the iteration is incorrect, the basic ideas are there. Malcolm, the mathematician, predicts the chaos because all the signs are there based upon what he knows about fractals and chaos. Although most of the investigations have been done up to this point by mathematicians, there are several other areas that are now taking a very close look at fractals. There are many great sources of information out there. On the Web, see the Math Forum's Internet Resource Collection page of links to sites about fractals: http://mathforum.org/library/topics/fractals/
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