
## 4 **Adamatzky Et Al**

population. The fittest individuals are more likely to be selected for reproduction through recombination and mutation.

The search space is the set of cell-state transition rules (each rule **represents**
a unique cellular automaton). An automaton of this space can be described by determining what will become of a cell in the next generation, depending on its neighbours. An individual is an automaton coded as a bit string of representing the values of a cell at the next generation for each neighbourhood **state. A string**
is composed of two sub-strings. The first substring represents the neighbourhood states used by mobile localizations (gliders) and their values are determined by the evolution of the glider. The second substring is initialized at random. The search space contains 336 **possible cell-state transition rules.**
A fitness function was computed as follows. Random configurations **of cells are**
evolved by the tested automaton. After this evolution, the presence of gliders is checked by scanning the result of the configuration of the cells. The value of the fitness function is the number of gliders that appeared divided by the total number of cells. The 36 bits of each individual are initialized at random. The mutation function consists of mutating one bit among 36, while the recombination is a random point crossover. An elitist strategy in which the best individual of population is kept is used. The value of the fitness function and the generation of the **best rule are**
memorized. If after ten new generations the algorithm has not found a better rule the algorithm stops.

## 4. Likehood Of Gliders

From the set of evolved functions we calculatedb **a set of matrices** F
z = (Fij ),
where i is the number of neighbours in state A, and j **is the number of neighbours**
in state B, z ∈ {A, B, S}**, which reflect likehoodness for any particular transition to**
contribute to glider dynamics. If one arbitrarily selects a glider from **the set of thousand gliders discovered, then the local transition function supporting the glider have**
transition [i, j] → z **amongst its state of transitions with probability** F
z ij **. We have**
also computed matrix F
\# **which indicate likehood of any particular state transition**
to be redundant, i.e. not necessary for supporting gliders. Exact **structure of the**
matrices is shown in Fig. 1. The matrices provide an adequate guiding choice when experimenting with randomly selected local transition functions, see demonstration applet in 6.

Just a few examples of mobile localizations discovered are shown in Fig. **2. Most**
typical localizations are gliders, which change their configuration every second time step (Fig. 2ab), and puffer trains - gliders leaving trail of breathers behind them
(Fig. 2cd). To complete this section we would like to stress that the evolutionary algorithm employed was tuned to select transition functions supporting localizations, b**The probabilistic matrices are calculated by Emmanuel Sapin, in the framework of EPSRC project**
EP/E005241/1