= Brad Klee <bradklee@gmail.com> wrote:
...Chebyshev polynomials are of more fundamental importance
They are anyhow the "trig parts" of exp n log z which seems pretty core.
...what is the shortest gene sequence that expresses a logarithmic spiral in the morphology
I think the global form is emergent from the basic nature of the local growth processes, rather than being explicitly programmed anywhere. For example the code just says something like "increase tube diameter steadily while keeping in contact with previously grown tube wall". Particularly intriguing is that discontinuities can even arise out of continuity -- Rene Thom's morphogenetic "catastrophes" etc. Perhaps more likely to be explicitly encoded somehow are discrete values -- such as 5-fold symmetry (why is 7-fold so much rarer?)