The self-assembled network of conducting polyaniline (PANI), protonate
d by camphor sulfonic acid (CSA), in a matrix of insulating polymethyl
methacrylate (PMMA) has a remarkably low percolation threshold. The cr
itical volume fraction (f(c)) of PANI-CSA phase segregated in PMMA is
f(c) similar to 0.003 (0.3%). The conductivity at room temperature nea
r the percolation threshold is quite high, 3 x 10(-3) S/cm. The system
atic increase in the exponent of the temperature dependence of conduct
ivity (gamma) results from transport on the fractal structure and to t
he related superlocalization of the electronic wavefunctions with syst
ematic variations in the fractal dimensionality upon dilution of the P
ANI-CSA. Below the percolation threshold, the temperature: dependence
of the resistivity is like that of granular metals with gamma = 0.5. T
he positive magnetoresistance (MR) shows a maximum upon decreasing the
volume fraction of PANI-CSA in agreement viith effective medium theor
y. Analysis of the MR indicates that the localization length near the
percolation threshold is approximately 25 Angstrom at 4.2 K.