FRACTALS
In very simple terms, fractals are geometrical figures that are generated by starting with a very simple pattern that grows through the application of rules. In many cases, the rules to make the figure grow from one stage to the next involve taking the original figure and modifying it or adding to it. This process can be repeated recursively (the same way over and over again) an infinite number of times.There is a complex, formal definition of a fractal, but there are some more informal definitions. One way is to define fractals as processes or images that exhibit self-similarity. In other words, reduced versions of the fractal appear throughout the fractal. Many natural objects have parts that are similar to other parts of it, like the fern. This is just the beginning of the usefulness of fractals. Many phenomena like heart beat, turbulent weather, the stock market, and mountains also exhibit self-similarity. For instance, on a graph of the Dow Jones Industrial will have periods that are similar to other longer periods. Another great example are landscapes. Fractals are excellent at creating realistic images, because they can model natural objects well. The study of fractals has been around long
Like all great thinkers (e.g. Newton, Einstein), Mandelbrot's work used the discoveries made by great mathematicians before him. Gaston Julia, Pierre Fatou, and Felix Hausdorff were some of the pioneers in this field that gave way to Mandelbrot's revolutionary ideas. His work inspired interest in the field of fractals and has made fractals a very popular field of study. L-systems are a relatively new way of creating fractals. The technique, designed by Aristrid Lindenmayer in 1968, was originally created for the study of biological models for plant development. By looking at an L-System tree, you can really see why L-System fractals were designed to model plants. While complex L-systems can take a lot of time to run, the formulas that specify them are usually very small.
Some common words found in the essay are:
Properties Fractals, Sets Mandelbrot, Function System, Theory Relativity, , Function Systems, Benoit Mandelbrot, Aristrid Lindenmayer, Actually Julia, Felix Hausdorff, iterated function, julia set, iterated function system, function system, exhibit self-similarity, function systems, self-similarity fractals, sierpinski's triangle, iterated function systems, modelled fractals, field fractals, infinite detail, property fractals self-similarity, called father fractals, generate iterated function,
Approximate Word count = 1976
Approximate Pages = 8 (250 words per page double spaced)
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