Chance operations & probability theory
From GenerativeArt
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Here is a simulation of a pinball machine that demonstrates the Gaussian distribution of the result. Note how as more balls are put into play the distribution moves closer and closer to a Gaussian distribution. | Here is a simulation of a pinball machine that demonstrates the Gaussian distribution of the result. Note how as more balls are put into play the distribution moves closer and closer to a Gaussian distribution. | ||
| - | + | http://www.jcu.edu/math/isep/Quincunx/Quincunx.html | |
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| + | == Pragmatic notes on using random numbers in art == | ||
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| + | <span style="font-size:larger;text-decoration:underline">Pseudo Random Number Generators</span> | ||
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| + | Because a computer is a finite state machine it cannot generate truly random numbers. There are algorithms for generating pseudo random numbers which, however, for all practical art purposes can be thought of as random. Typically pseudo random number generators use a "seed value" to begin the sequence of numbers it will generate. If the same seed value is used, the same sequence will be generated, and the generative system will produce the same artwork over and over again. When using a random number generator be sure to use it in a mode where it changes the seed value every time it is used to prevent this from happening. | ||
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| + | <span style="font-size:larger;text-decoration:underline">Uniform Random Distributions and Clustering</span> | ||
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| + | Pseudo random number generators create a uniform distribution of values in the long run. Any value is as likely as any other value. However, as the Law of Large Numbers suggests, small collections of random numbers will not be distributed uniformly, For some artistic applications it may be useful to post process a set of random values by either removing outliers (extreme cases that stand out as odd), removing near duplications (where 2 cases are almost the same value), or smoothing the numbers to achieve a more uniform distribution without losing the random "feel" of the events. | ||
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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. | ||
== Links == | == Links == | ||
