Chance operations & probability theory
From GenerativeArt
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(→Pragmatic notes on using random numbers in art) |
Current revision (04:15, 21 November 2012) (view source) (fix image urls) |
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| - | {{SingleImage|imageWidthPlusTen=655|imageURL=http://www | + | {{SingleImage|imageWidthPlusTen=655|imageURL=http://www.viz.tamu.edu/courses/viza658/wiki/prob/00.jpg|caption=Pinball Example}} |
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| + | [[http://philipgalanter.com/howdy/applets/ballDistribution/index.html Click here to run a pinball demonstration applet.]] | ||
<SPAN STYLE="font-size: larger;"><u>Pascal's Triangle</u></span> | <SPAN STYLE="font-size: larger;"><u>Pascal's Triangle</u></span> | ||
| - | {{SingleImage|imageWidthPlusTen=594|imageURL=http://www | + | {{SingleImage|imageWidthPlusTen=594|imageURL=http://www.viz.tamu.edu/courses/viza658/wiki/prob/01.jpg|caption=Gaussian Distribution}} |
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| + | {{SingleImage|imageWidthPlusTen=612|imageURL=http://www.viz.tamu.edu/courses/viza658/wiki/prob/02.jpg|caption=Faces generated with psuedo-random numbers}} | ||
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| + | {{SingleImage|imageWidthPlusTen=612|imageURL=http://www.viz.tamu.edu/courses/viza658/wiki/prob/03.jpg|caption=Faces generated with Gaussian Distribution}} | ||
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| + | [http://www.viz.tamu.edu/courses/viza658/wiki/prob/facedist.swf View Flash Application demonstrating the Normal Distribution vs Random Distribution] | ||
| - | {{SingleImage|imageWidthPlusTen=594|imageURL=http://www | + | {{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.}} |
| - | {{SingleImage|imageWidthPlusTen=594|imageURL=http://www | + | {{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.}} |
| - | {{SingleImage|imageWidthPlusTen=594|imageURL=http://www | + | {{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.}} |
| - | {{SingleImage|imageWidthPlusTen=680|imageURL=http://www | + | {{SingleImage|imageWidthPlusTen=680|imageURL=http://www.viz.tamu.edu/courses/viza658/wiki/prob/07.jpg|caption=Discreet Random Distributions}} |
| - | {{SingleImage|imageWidthPlusTen=665|imageURL=http://www | + | {{SingleImage|imageWidthPlusTen=665|imageURL=http://www.viz.tamu.edu/courses/viza658/wiki/prob/08.jpg|caption=Designing Arbitrary Continuous Random Distributions}} |
A Gaussian distribution can be described with two numbers, the mean and the standard deviation. The shape of the distribution is always the same, but the peak (the mean) and the degree of spread (the size of the standard deviation) will be specific to the subject matter in question. For example, consider IQ as (arguably) a measure of intelligence. | A Gaussian distribution can be described with two numbers, the mean and the standard deviation. The shape of the distribution is always the same, but the peak (the mean) and the degree of spread (the size of the standard deviation) will be specific to the subject matter in question. For example, consider IQ as (arguably) a measure of intelligence. | ||
| - | {{SingleImage|imageWidthPlusTen=601|imageURL=http://www | + | {{SingleImage|imageWidthPlusTen=601|imageURL=http://www.viz.tamu.edu/courses/viza658/wiki/prob/09.gif|caption=Designing Arbitrary Continuous Random Distributions}} |
The formula for the normal distribution density function is: | The formula for the normal distribution density function is: | ||
| - | {{SingleImage|imageWidthPlusTen=570|imageURL=http://www | + | {{SingleImage|imageWidthPlusTen=570|imageURL=http://www.viz.tamu.edu/courses/viza658/wiki/prob/10.jpg|caption=}} |
and is illustrated in the following fragment of Matlab code. | and is illustrated in the following fragment of Matlab code. | ||
| - | {{SingleImage|imageWidthPlusTen=500|imageURL=http://www | + | {{SingleImage|imageWidthPlusTen=500|imageURL=http://www.viz.tamu.edu/courses/viza658/wiki/prob/11.jpg|caption=}} |
The first line creates a vector of values from -4 to 4 incremented by .05. The second line creates a vector y plugging each x value into the Gaussian curve formula. The third line plots the results below. | The first line creates a vector of values from -4 to 4 incremented by .05. The second line creates a vector y plugging each x value into the Gaussian curve formula. The third line plots the results below. | ||
| - | {{SingleImage|imageWidthPlusTen=667|imageURL=http://www | + | {{SingleImage|imageWidthPlusTen=667|imageURL=http://www.viz.tamu.edu/courses/viza658/wiki/prob/12.jpg|caption=}} |
