We assess a procedure for discovering the mixing ratios of transformat
ions within the bench of affine maps of a probabilistic iterated fuzzy
functions system which gives rise to 256 artificial color drawings. A
first hypothesis on these ratios is obtained from a pseudo-ergodic es
timate of the probabilities of matching special paths during the image
generation. The job of the neural network is to remove biases from th
is hypothesis after a proper training. The reconstructed images are ne
arly identical to their original ones also on instances not used to tr
ain the network, and their representation through the above ratios att
ains a very high compression rate.