Cellular Automaton Shading for Building Envelopes - Cellular Automata in Image Processing and Geometry - page 203

its individual component parts determined from a model of the system . The emer-
gence in CA is manifested by the simultaneous emergence of boundaries between
the domains, which take form of boundaries or “particles”, that is small regions of
cells separating two domains and persisting for a relatively many time steps [24].
Particular type of particle emerges in the so-called “solitons” — moving persistent
structures which pass through one another while preserving their identities [52]. The
subsequent sections describe various CA which meet the criteria listed above. The
review starts from the simple CA, preceded by a brief explanation of terms specific
to CASS. In all the instances, the CA update is synchronous.

11.2.1 The Nomenclature

A few practical terms often used in the context of CASS are briefly explained below.
For simplicity they were formulated and illustrated with rectangular, two-color (2C)
CA.

The Sequence of Initial Conditions (SIC)
In principle, CA pattern is determined by local transition rules (TRs), initial condi-
tion (IC) and the boundary conditions (BC). As a result, so is the average pattern
density, which is the ratio between the number of black cells (1s) to the number of
all cells in the array. An array with all black cells forms a completely opaque facade
(density 1), conversely, an array of all white cells (density 0) corresponds to 100%
transparency. For an interactive demonstration see [59]. In CASS the pattern re-
mains still until the next alteration in IC. Such changes to IC form a sequence(SIC),
which must meet two arbitrary conditions: 1) for k>1 ,the k th IC has exactly one
black cell more than ( k -1) th ; 2) all the remaining black cells to be preserved. A sin-
gle IC is a list of {0,1} of length n .SICisalsoa n -long list of such lists, forming an
n

n square matrix. Such SIC ensures that the displayed changes of the array will
not appear excessively chaotic or disturbing. An alteration of the state of a single
cell in IC propagates over the entire array, so the transition from one state of BE
to another can be traced, understood and interpreted by the observer. SICs can be
conveniently encoded into SIC* using order-based representation(OBR) [23]. A se-
quence of n ICs is represented by a list of integers of length n

×

1. Each integer is the
“distance to the most recently added 1 among the available positions”. Thus SIC*
is a “sequence of the leap lengths where consecutive 1s are located”. The position-
ing is done from left to right. Since in the very last step there is only one available
position, is it dropped, as illustrated in Fig. 11.2. For detailed explanation of this
encoding method see [67]. For the interpretation of the SIC shown in Fig. 11.2 see
Fig. 11.3.
Pattern grayness , in other words pattern density, is defined as a ratio between the
number of black (opaque) cells to the total number of cells. The grayness applies to

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