of generators of localizations, or glider guns. The presence of both types of reactants in a localization is essential for the majority of propagating localisations, which is identified by the similarity of the dynamic of concentration profiles of **reactants** A
and B **shown in Fig. 5.**

## 6. Reductions Of Transitions Functions

What would be the behaviour of automata governed by the most likely **cell-state**
transition rules? In order to find an answer we decided to reduce matrices of glider likehoods to their most articulated forms. First, we have made matrices more symmetrical by the following procedure. If |F
′

ij − F
′′

ji| < ǫ **then we updated entries (**ij)
and (ji**) as follows:** F
′

ij = F
′′

ji =12
(F
′

ij + F
′′

ji)**. We do this because we assume that**
in evolutionary experiments reactants A and B **have the same diffusion coefficients.**
Then we perform the following operation. If |F
A
ij − F
B
ij | > 0.**2 and** |F
A
ij − F
S
ij | >
0.**2, or** F
B
ij **= 0 and** F
S
ij **= 0 then** MA
ij = 1. We also discard entries of (0, **5) and**
(1, 4) of the matrix MB **as being negligibly small, and omit the matrix** F
\# **out of**
consideration. After these operation, we got the following matrix

![0_image_2.png](0_image_2.png)

$\begin{bmatrix}0,1,2]\ 0\ 0\ 0\ 0\\ a&a\ a\ a\end{bmatrix}$

$\small0$). 
0 0 0 [0, 1, **2] 0 0 0 0**
0 1 [0, 1, **2] 0 0 0 0**

![0_image_1.png](0_image_1.png)

0 0 ![0_image_0.png](0_image_0.png)

$\mathrm{O}$. 
$$0\ 0\ 0$$

![0_image_3.png](0_image_3.png)

where Rij is a set of all possible states that a cell x **can take if its neighbourhood**
u(x) has i cells in state A and j cells in state B**. We found that**
Finding 4. Starting its development from a random configuration a cellular automaton governed by a local transition functions expressed by matrix R **exhibits still and**
breathing localizations.

Most common localizations observed in cellular automata with local transition rules from the class R **are shown in Fig. 6. Minimal weight localizations are still**
triples of cells in state A or B, or triples switching between A and B **(Fig. 6a). These**
are followed by compact still patterns of four cells in A or B **states, see examples**
in Fig. 6bc, switching compact patterns of four non-resting states Fig. 6d; and, wish-bone shaped clusters of A and B **states Fig. 6e–h. The next heavier common**
localizations are the switching patterns of six Fig. 6i and eighth Fig. 6j non-resting states, and, the breathing localization Fig. 6k oscillating between 12 and 13 nonresting states.