Image Processing Reference
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Fig. 11.4 r- 2 CA: On the bottom: the GFE plot for all automata. Some of them with very low
GFE (below 0.1). The referential value for {3818817080,2,2} CA is shown with the dotted
line. On the top: the GF plots of six selected automata. The referential proportionality and the
differences to it are shown with the dotted line and gray filling, respectively.
1. CA Patterns to be vertical, or at least no direction (left or right) should be domi-
nant;
2. Pattens to continue for many steps;
3. Patterns to be distinct, preferably organic; for discussion on “man-made versus
organic appearance” see [63].
Evenness of the pattern distribution was not considered. Figure 11.5 shows sam-
ple patterns of these automata. Half-distance automata are particularly interesting
for CASS, since they can be applied on hexagonal and triangular tessellations, as
described in Subsect. 11.3.5.
11.3.4
Higher Order Cellular Automata
A k -order cellular automaton is a type of reversible CA where the state of a cell
at time t depends not only on its neighborhood at time t - 1, but on its states at
{
,...,
}
. These automata are particularity interesting due to their intrigu-
ing properties [3] and relatively simple implementation for CASS. The number of
second order 1D2Cr1 CA, or 2-CA is rather unmanageable for a simple search (to-
tal of 2 2 6
t
1
t
k
10 19 , half of them being EN), however, although there are only
=1
.
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