Cellular Automaton Shading for Building Envelopes - Cellular Automata in Image Processing and Geometry - page 202

Fig. 11.1 Simulation of CA on a free-form BE comprised of triangular panels of Hita City
Auditorium Competition Entry (2003, Oita, Japan, architectural design by Takehiko Na-
gakura). The 30 th time-step of two-color two-dimensional triangular CA rule 9622 is shown
(compare with Fig. 11.19).

of CASS on free-form surfaces described in Subsect. 11.4.2. Combination of the
last two properties from Tab. 11.2, that is determinism with emergence is the most
challenging. Both derive from the sequence of CA patterns displayed on CASS.
These patterns and their transitions must meet the following criteria:

1. Patterns to be visually interesting;
2. Ability of producing patterns of any average density between 0: full transparency,
to 1: full opacity;
3. Density transitions to be gradual;
4. Patterns to be evenly distributed.

From these criteria a straightforward constraint can be immediately derived. Namely,
only even-number (EN) CA rules should be considered. The shading action starts
arbitrarily from full transparency so all cells have value 0. An odd-number rule pro-
duces non-zero state from all 0s in the background, so in the first time-step the state
of practically entire CASS changes to 1, which precludes the third criterion listed
above. In the case of CASS, the visual attractiveness can be attributed to the emer-
gence, defined after [33] as: a property of a complex system that is not exhibited by

Table 11.2 Comparison of the key properties of CA and BE

Cellular automaton Building envelope

In principle, all the cells of a
particular CA's are identical.

Modularity is highly desirable in building industry, as it al-
lows for mass prefabrication and easy assembly.
Determinism The control of the state of BE, at least statistical, is crucial.
Capability of strong emergence Potential of the new, intriguing, organic-like aesthetics