13th International Conference on Membrane Computing - MTA Sztaki

L. Cienciala, L. Ciencialová, M. Perdek
– Env =
⎡
(6 × 6, w E ),
⎤
D D D D D D
D S S D D D
– w E =
D S S D D D
⎢ D D D S S D
,
⎥
⎣ D D D S S D ⎦
D D D D D D
– B 1 = (ee, P 1 , [1, 1]), B 2 = (ee, P 2 , [1, 2]),. . . , B 16 = (ee, P 16 , [4, 4]),
– f ∈ A is the final object of the colony.
The states of the automata are stored inside the cells ( D - dead automaton,
S - live automaton ). There is only one kind of agent in this 2D P colony, so there
are sixteen identical agents located in the matrix 4 × 4 of inner cells (see fig.2).
The sets of their programs are defined according to the rules of the automata:
– Any live automaton with fewer than two live neighbours dies, due to underpopulation.
– Any live automaton with more than three live neighbours dies, due to overcrowding.
– Any live automaton with two or three live neighbours lives, unchanged, to
the next generation.
– Any dead automaton with exactly three live neighbouring automata will
come to life.
The first program is to initialize the agent 〈e ↔ e; e → Z〉;
We sort the programs using the number of copies of object S in the condition
of the movement rule.
1. when neighbouring automata are dead - a single program for both dead as
〈 ⎡
well as live automaton ⎣ D D D ⎤
〉
D e D ⎦ → ⇑; Z → M .
D D D
2. when there is one live neighbouring automaton - there are eight possible
〈 ⎡ ⎤
〉
S D D
programs for dead as well as live automata ⎣ D e D ⎦ → ⇑; Z → M
D D D
and seven other combinations.
3. when there are two live neighbouring automata - twenty-eight programs for
〈 ⎡ ⎤
S S D
〉
live automata ⎣ D S D ⎦ → ⇑; Z → O and other twenty-seven combinations.
D D D
4. when there are two live neighbouring automata - twenty-eight programs for
〈 ⎡
dead automata ⎣ S S D
⎤
〉
D D D ⎦ → ⇑; Z → M and other twenty-seven combinations.
D D D
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