We describe a method which exploits discrete dynamical systems to generate suitable classes of polyominoes. We apply the method to design an algorithm that uses O( n) space to generate in constant amortized time all polyominoes corresponding to hole-free partially directed animals consisting of n sites on the square grid. By implementing the algorithm in C++ we have obtained a new sequence that does not appear in the On-Line Encyclopedia of Integer Sequences.

We consider two new granular dynamical systems obtained from the Sand Pile Model SPM(n) by adding a smoothness condition. First, we define the Smooth Sand Pile Model SmSPM(n) and we provide a characterization of the reachable states, together with some interesting properties of the resulting lattic e. Then we extend it to SmSPM*(n), a related dynamical system with a more complex lattice structure.

This special issue is devoted to various areas in Theoretical Computer Science. The issue took \ninspiration from the 13th Italian Conference on Theoretical Computer Science (ICTCS 2012), held at \nUniversity of Insubria in Varese, Italy, on September 19-21 2012. The special issue contains seven \npapers, that have been originated from the work in progress presented at the conference, and that have \nbeen accepted for publication after a rigorous review process and revisions. \nWe kindly thank all the authors of the published papers, as well as all the participants to ICTCS 2012, \nwho make it such an exciting event. \nWe are very grateful to the referees who devoted their precious time to produce thorough reviews. \nTheir valuable comments and suggestions improved a lot the submitted manuscripts. \nWe are especially thankful to Professor Damian Niwinski, Editor-in-Chief of Fundamenta Informaticae, \nfor accepting this special issue and for his help throughout the publication process. \nLastly, we wish to dedicate this special issue to the memory of Professor Alberto Bertoni, who was \none of the co-founders of the Italian chapter of the European Association for Theoretical Computer \nScience, and passed away on February 2014.