Bridges 2010 Short Paper

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.