Section 6
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Section 8
7. Cellular automata
Diffusion-limited aggregation and growth represent one extension of Eden's
model explaining the formation of branching patterns. Another extension
was proposed by Ulam [Ula1962], the
co-inventor of cellular automata. A cellular automaton consists of cells,
arranged in a (usually) square grid, and communicating with each other.
Ulam assumed that new cells can be added on the border of the structure
formed so far only if these cells do not collide with each other or with
the previously added cells. The development of the resulting branching
structure, which he called Maltese crosses, is illustrated in Animation 3 (see caption). An interesting feature of
this model is its sensitivity to the environment (note that DLA models are
also sensitive to the environment). For example, Animation 4 (see caption) presents the development
of a Maltese cross affected by an obstacle (shown in white). Although the
structure is somewhat distorted, it accommodates the presence of the
obstacle and grows around it without loosing its branching character.
A three-dimensional extension of this basic concept was applied by Greene
[Gre1991] to model the development
of tree roots around the stones in the ground (Plate 11, see caption). A similar concept was
applied in [Gre1989] to simulate
the development of vines around a house.
Section 6
Table of Contents
Section 8
