\vspace{-1.5em}\begin{itemize}
\item Discrete Iterative System:
\begin{itemize}
\item $x=(x_1,\dots,x_n)$ : $n$ components, $x_i$ in $\Bool=\{0,1\}$.
\item A \emph{strategy}  \alert<2>{$(S^{t})^{t \in \Nats}$}: sequence of the
  components that may be updated at time $t$.
\item Components evolution: defined for times $t=0,1,2,\ldots$
by:
$$  
\left\{
  \begin{array}{l}   
    \alert<2>{x^{0}}\in \Bool^{n} \textrm{ and}\\
    x^{t+1}= (x^{t+1}_1,\dots,x^{t+1}_n) \textrm{ where } 
    x^{t+1}_i =  
    \left\{
      \begin{array}{l}
        \overline{x^{t}_i} \textrm{ if $i = S^t$}  \\
        x^t_i \textrm{ otherwise} 
      \end{array} 
    \right.
  \end{array} 
\right.
$$
\end{itemize}
\item Theoretical Results~\cite{GuyeuxThese10}\footnote{\bibentry{GuyeuxThese10}}: let $\mathcal{X}$ be 
$ \llbracket 1 ; n \rrbracket^{\Nats} \times 
\Bool^n$. We can define a distance $d$ on $\mathcal{X}$ and
a function $f: \mathcal{X} \rightarrow \mathcal{X}$ from the 
iterative process
s.t. $f$ is a continuous and chaotic function.
\end{itemize}

