\input zb-basic \input zb-ioport \iteman{io-port 05940128} \itemau{Perrot, Kevin; R\'emila, Eric} \itemti{Transduction on Kadanoff sand pile model avalanches, application to wave pattern emergence.} \itemso{Murlak, Filip (ed.) et al., Mathematical foundations of computer science 2011. 36th international symposium, MFCS 2011, Warsaw, Poland, August 22--26, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-22992-3/pbk). Lecture Notes in Computer Science 6907, 508-519 (2011).} \itemab Summary: Sand pile models are dynamical systems describing the evolution from $N$ stacked grains to a stable configuration. It uses local rules to depict grain moves and iterate it until reaching a fixed configuration from which no rule can be applied. The main interest of sand piles relies in their Self Organized Criticality (SOC), the property that a small perturbation | adding some sand grains | on a fixed configuration has uncontrolled consequences on the system, involving an arbitrary number of grain fall. Physicists L. Kadanoff et al inspire KSPM, a model presenting a sharp SOC behavior, extending the well known Sand Pile Model. In KSPM$(D)$, we start from a pile of $N$ stacked grains and apply the rule: $D\!-\!1$ grains can fall from column $i$ onto the $D\!-\!1$ adjacent columns to the right if the difference of height between columns $i$ and $i\!+\!1$ is greater or equal to $D$. This paper develops a formal background for the study of KSPM fixed points. This background, resumed in a finite state word transducer, is used to provide a plain formula for fixed points of KSPM$(3)$. \itemrv{~} \itemcc{} \itemut{discrete dynamical system; self-organized criticality; sand pile model; transducer} \itemli{doi:10.1007/978-3-642-22993-0\_46} \end