Fast 2d brown/pink noise generation?

Robert Kern rkern at
Sat Mar 5 01:57:55 CET 2005

Mathias wrote:
> Dear NG,
> I'm looking for a fast way to produce 2d-noise images with 1/f or 1/f^2 
> spectrum. I currently generate the noise via inverse FFT, but since I 
> need lots of data (~10^7 for a monte carlo simulation) it needs to be 
> really fast. Does someone know a faster way than my approach?
> - Dimensionality is between 20x20 and 100x100
> - The spectrum doesn't need to be exactly pink/brown, an approximation
>    is fine.
> - Implementation in either matlab or scientific python (LAPACK anyway)

This is a 1D version that I have using scipy. It's naive, so I'm sure 
that it is slower. However, I believe the general technique can be 
implemented on a larger scale.

The basic idea is to sum up a bunch of white time series with different 
time steps. The first level is white noise at every time step. The 
second level changes at every second time step. The third changes at 
every fourth, etc.

I think you can replicate this by generating a few white noise arrays of 
the appropriate sizes, judiciously using repeat(), and summing them 
together. I got this scheme from an article I found by googling for pink 
noise algorithms, I believe.

from scipy import *

class PinkGenerator(object):
     updateTable = [0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4]
     del updateTable[-1]

     def __init__(self, rng=stats.norm):
         self.key = 0
         self.rng = rng
         self.whiteValues = self.rng.rvs(size=5)

     def getNextValue(self):
         self.key += 1
         self.key = self.key % len(self.updateTable)
         self.whiteValues[self.updateTable[self.key]] = self.rng.rvs()[0]
         return (sum(self.whiteValues) + self.rng.rvs()[0])/6

     def getManyValues(self, size):
         data = zeros((size,), Float)
         for i in range(size):
             data[i] = self.getNextValue()
         return data

     def sampleData(self, size=1024):
         data = self.getManyValues(size)
         p = power(absolute(fftshift(fft(data))), 2)/size
         f = fftshift(fftfreq(size))
         return data, f, p

Robert Kern
rkern at

"In the fields of hell where the grass grows high
  Are the graves of dreams allowed to die."
   -- Richard Harter

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