We introduce a general theoretical scheme for a class of phenomena cha
racterized by an extremal dynamics and quenched disorder. The approach
is based on a transformation of the quenched dynamics into a stochast
ic one with cognitive memory and on other concepts which permit a math
ematical characterization of the self-organized nature of the avalanch
e type dynamics. In addition it is possible to compute the relevant cr
itical exponents directly from the microscopic model. A specific appli
cation to invasion percolation is presented but the approach can be ea
sily extended to various other problems.