October 11, 2011

The "Growth and Form" of Pasta

This weekend, I found a really interesting book called "Pasta by Design", which approaches pasta with the eye of an industrial designer or engineer. Thinking it was a novelty at first, I found out later that there is a related book called the "Geometry of Pasta". I'm not sure if books like this are released to compete with each other, but there is apparently an interest in this topic.

I find the links between the quantification of pasta and the growth/development of living systems interesting. In "Pasta by Design", each type of pasta is cataloged and quantified, having their own geometry as determined by artificial selection (in this case human preference). Are these simply the most "elegant" forms, or are they the most efficient forms given the need to shape the pasta by hand and incorporate it into cuisine? In the end, I was most intrigued by the functions that describe the geometry of each type of shell. This method for quantifying form goes all the way back to D'Arcy Thompson and his seminal book "On Growth and Form".

Thompson's book featured many different conceptualizations of form, especially as they relate to development and variation observed in animal and plant morphology. Most importantly, he observed that growth trajectories can be distilled to a series of recursive, geometric functions. His examination of shell accretion in marine invertebrates is a direct parallel with pasta.

Picture from http://www.darcythompson.org/about.html

Of course, the most famous example of using simple geometric functions to produce complex geometries is the book "Fractal Geometry of Nature". This work was extended in the direction of discrete dynamical simulation by Steven Wolfram in his book "A New Kind of Science". What is intriguing about both of these books is that they assign something called intrinsic randomness to the role of self-organizer. While the equation or ruleset guides the system, random processes produce the fine structure. Is pasta partially the product of intrinsic randomness? That's sounds like an Ig Nobel prize-winning question.

Finally, a book called "On Growth, Form, and Computers" (1992) more explicitly extended the ideas of Thompson to evolutionary algorithms and other such simulations (e.g. artificial life). Such simple geometric functions can be used to render complex computer graphics. As in the case of biological development, these relatively simple equations provide a mechanism for self-organizing processes.

So, is making pasta a combination of self-organization and artificial selection? Probably not in the conventional way of thinking about these two things, especially by themselves. Yet by making comparisons with living complex systems, I think the answer could be "yes".

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