Chance operations & probability theory
From GenerativeArt
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(→Pragmatic notes on using random numbers in art) |
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In this example the intent is to suggest a large circle by populating a 1 unit radius with small circles. Using the programming environment Matlab pairs of random numbers from -1 to 1 ar generated and then tested. Those with a distance from the center (0,0) greater than 1 are rejected. The remaining (x,y) pairs are plotted as small blue circles. | In this example the intent is to suggest a large circle by populating a 1 unit radius with small circles. Using the programming environment Matlab pairs of random numbers from -1 to 1 ar generated and then tested. Those with a distance from the center (0,0) greater than 1 are rejected. The remaining (x,y) pairs are plotted as small blue circles. | ||
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| + | {{SingleImage|imageWidthPlusTen=594|imageURL=http://www-viz.tamu.edu/courses/viza658/wiki/prob/04.jpg|caption=While a large circle is formed, the smaller circles tend to clump up as is typical when using small quantities of random numbers.}} | ||
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| + | {{SingleImage|imageWidthPlusTen=594|imageURL=http://www-viz.tamu.edu/courses/viza658/wiki/prob/05.jpg|caption=Here are the same points adjusted via software to reduce clumping.}} | ||
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| + | {{SingleImage|imageWidthPlusTen=594|imageURL=http://www-viz.tamu.edu/courses/viza658/wiki/prob/06.jpg|caption=The de-clumping algorithm works by first analyzing each center point and finding the nearest neighbors.}} | ||
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| - | The distances between nearest neighbors are then iteratively adjusted. Points that | + | The distances between nearest neighbors are then iteratively adjusted. Points that are "too close" are moved a bit apart, and others "too far apart" are moved closer together. This is repeated a number of times until a balance is achieved. Note the flaws and irregularities that make the image more interesting than the result of a |
| - | are "too close" are moved a bit apart, and others "too far apart" are moved closer together. | + | |
| - | This is repeated a number of times until a balance is achieved. Note the flaws | + | |
| - | and irregularities that make the image more interesting than the result of a | + | |
tiling algorithm which would enforce strict symmetries and measurements. | tiling algorithm which would enforce strict symmetries and measurements. | ||
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| + | <span style="font-size:larger;text-decoration:underline">Other Statistical Distributions</span> | ||
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| + | To be artistically useful random numbers must be mapped into an aesthetic parameter (e.g. color, pitch, size), or a transformational parameter (i.e. a point in space or time). Uniform distributions will provide selections and mappings that are totally without bias. But in setting up a situation without bias the artist misses an opportunity to blend choice with randomness. A normal distribution is a way to express a choice but to allow for the kind of variation one frequently sees in nature. While uniform and normal distributions can be useful in some cases an artist may want to find expression in designing distributions not found in nature. The following are techniques for doing this. | ||
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| + | <span style="font-size:larger;text-decoration:underline">Designing Arbitrary Discreet Random Distributions</span> | ||
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| + | A discreet random distribution is simply a random selection among a finite number of alternatives. Where each selection is equally likely a device such as a die is often used. But where different selections may have different probabilities a device such as a game spinner can be used, where various "slices" of the "pie" diagram have different sizes. | ||
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| + | {{SingleImage|imageWidthPlusTen=594|imageURL=http://www-viz.tamu.edu/courses/viza658/wiki/prob/07.jpg|caption=}} | ||
== Links == | == Links == | ||
