The Sunflower Spiral and the Fibonacci Metric

(Proceedings pages 483–486)

The sunflower spiral is a well known and attractive pattern often
seen in the arrangement of leaves or other features in plants
(phyllotaxis), with close connections to the Fibonacci sequence.
We describe an interesting colouring of the points of the sunflower
spiral, involving a “metric” on the positive integers
which counts the number of distinct non-consecutive Fibonacci numbers
needed to sum to a given number. We also explain some initially
surprising features of the resulting coloured pattern.

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