Cellular Automaton Shading for Building Envelopes - Cellular Automata in Image Processing and Geometry - page 214

Fig. 11.13 The strong appearance of triangular tessellation can be advantageous. Despite the
simplicity of the pattern produced by T2-CA rule 56 it becomes more visually attractive on
triangular grid. IC rate of opacity: 0.5. Two PFSS modules are shown on the top, from the
left: E and O.

Fig. 11.14 Two patterns showing essentially the same CA at the same IC. On the left: ECA
rule 142. On the right: analogous CA realized by combination of two modules (O and E) of
PFSS T .

Fig. 11.7. A small modification to the modules shown in Fig. 11.13 allow to emu-
late hexagon A O PFSS, as shown in Fig. 11.14. The logic of both PFSS T modules

shown in Fig. 11.14 is identical to the logic of the corresponding ECA. However,
otherwise rather plain patterns gain certain visual attractiveness. The implementa-
tion of half-distance CA by PFSS T also requires two type of modules. However,
creating perforated PFSS T by removing every other triangular facet allows to use
only one type of module. Moreover, such an arrangement seems particularly inter-
esting for BE, as every void in the tessellation can represent clear glass or solid
walls, as shown in figures 11.15 and 11.1. Since the area of PFSS T is perforated in
50%, it should be taken in consideration, that the pattern is not as legible as in other
shading systems presented here.

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11.4 Two-Dimensional Cellular Automata on Surfaces

As mentioned in the beginning, controlling of the state of a BE surface with 2D
CA seems intuitive, but the actual implementation is in fact more challenging than
with 1D automata. As previous sections demonstrated, it is rather straightforward to
apply any of regular tessellation, that is triangular, square or hexagonal on a planar
surface and apply an automaton into it. For the overview of CA, in particular the
Game of Life (GOL) in triangular, pentagonal and hexagonal tessellations see [6];
for the corresponding interactive demonstration see [5]. Modest size examples of
GOL in triangle, square, and hexagon planar topologies and hierarchical hexago-
nal grid on the sphere intended for modeling of biogeographical, ecological and