Results
The languages provides many important insights into the relationship between
local and global descriptions of behavior.
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One can generate a wide variety of predetermined complex global shapes
and patternms, using only local communication and local computation.
The shapes are generated from a mostly homogeneous sheet using only a small
number of simple primitive behaviors.
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The primitive behaviors do not depend on regular cell placement or synchronous
behavior and are robust to a variety of failures of individual cells. Robustness
is achieved by depending only on the average behavior of cells, not individual
cells, trading precisions for reliability and by composing primitives in
a way that minimizes error.
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The local cell program is ``scale-independent'' and can create the same
shape at many different scales with no modification, even though the number
of cells involved may vary significantly. Many biological creatures, such
as hydra and sea urchins, develop normally over tenfold size variations
and internally complex structures such as lungs and kidneys appear at a
wide variety of scales. The languages provide insight into how scale-independence
can be achieved through local processes.
This approach differs from previous work such as cellular automata and
reaction-diffusion, where patterns emerge from the interactions of local
processes but no framework is provided for constructing local rules to
obtain any desired pattern. By contrast, this paper provides a high-level
language along with a compilation method by which the global goal is transformed
into appropriate local rules.