Cellular Automaton Shading for Building Envelopes - Cellular Automata in Image Processing and Geometry - page 209

Fig. 11.6 T 2-CA: On the bottom: there are six T 2-CA with relatively low GFE (below 0.1).
The referential value for {3818817080,2,2} CA is shown with the dotted line. On the top: the
corresponding GF plots. The referential proportionality and the differences to it are shown
with the dotted line and gray filling, respectively.

128 totalistic automata of this kind (T 2-CA), of which 64 are EN T 2-CA, some of
them have rather good shading properties, as shown in Fig. 11.6. Figure 11.7 shows
sample patterns of the selected T 2-CA. Rules 112 and 120 are not shown as they
produce overly simple patterns.

11.3.5 Other Regular Tessellations: Hexagonal and Triangular

The square grid is one of three, regular, also called “Platonic” tilings. The remaining
two are: triangular and hexagonal. Regular tilings allow edge-to-edge tiling by con-
gruent regular polygons [11]. This property has been widely used in architectural
practice since antiquity, and the first systematic mathematical treatment was done in
the early XVII century in [30]. The properties of regular tessellations in the context
of architectural design and particularly for BE shading are collected in Tab. 11.3.
Although the original concept of CASS was based on an opto-mechanical system of
square plates made of polarized glass [66], the prototype was based on liquid crystal
(LC) technology [68]. The concept of polarized film shading system (PFSS), where
shading elements are composed of two polygonal sheets of normally-white polar-
ized films is explored in [65]. One of the parts of PFSS is fixed and the other rotates.