Fractals
From GenerativeArt
(Difference between revisions)
(first stab at fractals) |
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* Statisical. (Where an empirical measure remains constant across scales). | * Statisical. (Where an empirical measure remains constant across scales). | ||
| - | <html><div style="border:1px solid black; background:#dddddd; padding: 5px; font-size:smaller; width:400px; float:left; margin:5px"><img src="http://www-viz.tamu.edu/students/ablev/genart/fractalANI.gif" style="float:none">Fractal example - Koch Curve</div></html> | + | <html><div style="clear:none"><div style="border:1px solid black; background:#dddddd; padding: 5px; font-size:smaller; width:400px; float:left; margin:5px"><img src="http://www-viz.tamu.edu/students/ablev/genart/fractalANI.gif" style="float:none">Fractal example - Koch Curve</div></html> |
| - | <html><div style="border:1px solid black; background:#dddddd; padding: 5px; font-size:smaller; width:400px; float:left; margin:5px"><img src="http://www-viz.tamu.edu/students/ablev/genart/nonfractalANI.gif" style="float:none">Non-fractal function example</div></html> | + | <html><div style="border:1px solid black; background:#dddddd; padding: 5px; font-size:smaller; width:400px; float:left; margin:5px"><img src="http://www-viz.tamu.edu/students/ablev/genart/nonfractalANI.gif" style="float:none">Non-fractal function example</div></div></html> |
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| + | Taken loosely, fractals can occur in a number of ways. For example: | ||
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| + | * Simple iterative recursive geometric constructions can create fractals. | ||
| + | * Some natural phenomina exhibit a fractal nature. e.g. Clouds, coast lines, some plants, some forms of shattered material, lightning, mountains, patterns in frost on windows and other forms of crystal growth, etc. | ||
| + | * Some mathematical functions define sets of points where the boundry between in-set and out-of-set points exhibit self-similarity across scales. e.g. The Julia set, the Mandelbrot set, and others. | ||
| + | * In chaotic systems a phase diagram will exhibit fractal behavior about a strange attractor. (To be covered later). | ||
