  A model based on thermal fluctuations in conductors in random
resistor-capacitor (R-C) networks has been shown to generate a 1/f^s noise with
s in between 0 and 1, while in many real systems the noise exponent is between
0 and 2. The wider range of noise exponents is shown here to be generated using
a model of random R-C networks driven by white noise current source, and having
different compositions of resistors and capacitors. C-rich networks approach a
brown noise, 1/f^2 response, while R-rich networks approach a white noise,
1/f^0 response. Random R-C networks containing equal numbers of resistors and
capacitors generate the classic, 1/f pink noise. Thus, the composition unbiased
R-C networks produce the ubiquitous 1/f noise. Below a limiting frequency,
which is a function of the size of the network, the values of individual R and
C elements, and their relative numbers in the network, the power-law frequency
AC response of the network no longer holds, and the 1/f^s noise response, turns
into either capacitor (1/f^2), or resistor (1/f^0) response, depending on the
nature of the persistent conductivity structures: series R-C pathways, or pure
C and R percolation pathways.
