My opinion is that Chebyshev polynomials are of more fundamental importance than the Fibonacci sequence, so this definition seems worthwhile. Also, what is the shortest gene sequence that expresses a logarithmic spiral in the morphology of a plant or animal species? I.e., When growing a spiral pattern, is a sunflower somehow more efficient than a pine cone or a nautilus? I don’t know too much about programming DNA, but would be interested to learn more. —Brad
On Mar 19, 2020, at 9:29 PM, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 20/03/2020 02:06, Bill Gosper wrote:
Even shorter: Fib(v+1) = |Uᵥ(*i*/2)|.
Bah. Even shorter: Fib(n) = F_n.
(More explicitly: how can it make sense to call something a "short Fibonacci formula" when it depends on a one-letter notation for something that is both less familiar and requires a longer definition than the Fibonacci numbers themselves?)
-- g
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