**ACRI 2022**

**Tutorials**

__Tutorial on Cellular automata and their applications__

The goal of this tutorial is to introduce the concepts of Cellular Automata (CA) to PhD students and

young researchers, and to demonstrate its importance and relevance with respect to the

scientific approach and the way to formulate a question related to natural phenomenon et complex systems.

__Part I: Basic Concepts__

*Bastien Chopard, Jean-Luc Falcone*

By alternating theoretical concepts with short practical exercises, we will present the motivation to use

cellular automata as a modeling methodology. The basic definitions will be given together with historical notes

that will focus on the idea of self-reproducing systems. Then, the fundamental ideas related to the modeling of

natural phenomena will be presented, in terms of a fully discrete mathematical abstraction of the physical universe.

Several simple and less simple CA rules will be considered as examples which illustrate the emergence of complexity,

self-organization, emergence and spatio-temporal patterns. Finally, simple traffic models will be discussed,

as well as lattice gases, which are a way to model a fluid flow and which eventually evolved to the now famous

Lattice Bolttzman methods.

At the end of this first part, the participants1 should have an overview of the modeling capabilities of CA, as well as a basic

computer code that runs on any web browser allowing them to explore several simple rules and systems.

__Part II: Selected Applications__

*Antisthenis Tsompanas, Georgios Sirakoulis*

Following from the first part of the tutorial, some selected applications will be further described to understand

the developmentof the modeling methodology derived from a specific mathematical description. In specific, the modeling

of the Belousov-Zhabotinsky class of chemical reactions will be presented utilizing CAs. This class of reactions

is well-known for being utilized as a substrate to solve diverse problems, thus, a medium for unconventional computations.

Whereas, these unconventional computers do not aspire to replace their silicon-based counterparts in the eminent future,

they are perfect examples of truly ubiquitous computing and paradigms of broader computational thinking.

Moreover, this application will be demonstrated with several short practical exercises, for participants to experiment

upon different occasions. The basic Boolean logic gates (NOT, AND, OR) will be replicated in the CA simulated chemical medium.

Also, more complicated logic functions will be implemented such as binary adders.

At the end of the second part, the participants should have the experience to transform any Partial Differential Equation

into a local rule for CA. Also, they will have a computer code that runs on any web browser that will allow them to implement

the representation of the basic logic gates on chemical media as presented during the tutorial and, even,

experiment to discover their own novel architectures of logic gates.