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Bennett-96

At the time, Turing was seeking a mathematical explanation for the role of Fibonacci numbers in describing the fractions of a turn between successive leaves on the stalk of a plant. The differential equations describing growth were slightly nonlinear, and with a random starting disturbance, the final configuration was displayed on the MkI's monitors. It was always of interest to those of us watching to see what Fibonacci configuration would result.

I remember spotting a cactus with 12 segments (rather than the expected Fibonacci 13 segments) in my father-in-law's greenhouse - probably as the result of some injury at an early stage of its growth. I told Turing about it over coffee the next time we met. His immediate reaction was to propose the existence of a similar series that would include 12 and to ask whether there was a sufficient number of cacti in the green house to provide relevant statistics.

On p65 of Bennett (1996).

Jonathan Swinton 1/03/03

Turing and Morphogenesis