posted 24 October 2002 13:24            

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Gaussiandistribution.kym

Several people have been asking about how to generate random numbers with distributions other than the uniform distribution currently generated by the Noise module and the nextRandom expression. Here are some examples of how to use the InputOuputCharacteristic to remap the uniformly distributed random numbers coming from the Noise module to a so-called "Normal" or "Gaussian" distribution (the familiar bell curve distribution) where most of the numbers are clustered around a center point (in this case it is zero). It has a hot parameter to control !sigma (giving you control over how broad and flat the center part of the curve is--ranging anywhere from nearly flat like a uniform distribution to a very narrow range just around zero).
I'm hoping that people will use this as a starting point for coming up with other interesting distribution functions and post these to the forum. Because you can never have enough flavors of noise!

(To convert a probability density function into a waveshaper, first integrate the PDF, then flip the x and y axes and choose some points to enter into the InputOutputCharacteristic (NB you also have to multiply the input values by 2 and subtract 1 in order to center them around zero with a range of -1 to 1). Then you can use a uniform random noise generator as the input to the InputOutputCharacteristic. Set the Smoothness interpolation to zero if you want discrete probability functions.)

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