Information Technology Reference
In-Depth Information
The combination change of signal 06 at the joint point is as follows, from
which we can see the expansion of data path.
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 1 0 6 1 1 1 1
ŗ
1 1 1 0 7 1 1 1
2 2 2 2 6 2 2 2 2 2 2 2 0 2 2 2
* * * 2 0 2 * * * * * 2 1 2 * *
* * * 2 1 2 * * * * * 2 1 2 * *
* * * 2 1 2 * * * * * 2 1 2 * *
Our construct the following transformation rule table, based on which the
growth of cellular automaton in the two-dimensional space can be given.
f(0,1,2,7,6)=1 f(7,0,0,0,2)=3 f(2,0,0,2,3)=7 f(1,0,2,3,2)=6
f(0,1,2,3,2)=1 f(3,0,2,2,1)=0 f(7,0,2,1,2)=0 f(1,0,7,2,2)=3
f(4,0,2,0,2)=2 f(2,0,0,2,4)=0 f(2,0,2,6,2)=4 f(2,0,0,1,4)=2
f(4,0,2,6,2)=2 f(2,0,4,6,2)=4 f(1,2,4,2,6)=4 f(4,1,2,2,2)=0
f(2,0,0,4,2)=0 f(2,0,2,4,2)=0 f(2,0,1,2,4)=2 f(6,0,2,4,2)=4
f(7,0,0,2,1)=0 f(0,1,2,7,2)=4
In the table above, the first independent variable of the function
is the state
of the center cell. And the following 4 independent variables are the states of 4
neighbors, which rotate clockwise in order to generate the minimum 4-digit
number.
The concept of cellular automata can be established in the following ways: At
first, we have a cellular space which constitutes the
f
-dimensional Euclidean
space, as well as the neighbor relation defined in the cellular space. Because of
the neighbor relation, each cell must have a limited number of cells as its
neighbors. A cellular automaton system (“cellular system” for short) is defined as
follows: In this system, each cell is given a limited number of states, a
distinguishing state (called the “empty state”), and a rule. The rule is a function
of the states of the cell itself and its neighbors at time
N
t
, which provides the state
of each cell at time
+1. All the possible states of a cell together with the rules of
its state transformation are called the transformation function. So a cellular
automaton system is made up by a cellular space and the transformation function
t
