Eight hundred years ago Fibonacci identified a remarkable fact about the simplest of additions. When you start at 1 and just add the previous number, you get this series of numbers: 1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 etc. In other words, 1 plus 0 is 1, 1 plus 1 is 2, 2 plus 1 is 3, 3 plus 2 is 5, 5 plus 3 is 8, etc. Any value in this series is a Fibonacci number and these numbers are often spotted in nature when one considers the number of petals on flowers, seeds in a sunflower or scales on a cone.

Another aspect of Fibonacci numbers is that very early in the series the ratio of two sequential numbers moves towards 1.618, being the “golden ratio”. For example in the series above, 34 divided by 21 is 1.619 and 55 divided by 34 is 1.618.  

A Fibonacci spiral is a curved shape made by drawing quarter circles inside squares whose sizes match the sequence - as the squares get bigger, the connected arcs form a natural, expanding spiral. In nature, the logarithmic spiral of an ammonite shell approximates this Fibonacci spiral and snail shells often exhibit a similar pattern.

Many woodland trees also exhibit the ratios of the Fibonacci numbers in their leaf arrangements. This is because such patterns make the most efficient use of space or create the best way to maximise the capture of sunlight or water.  For example, in many plants the leaves are arranged so that after you have gone round the stem 3 times, you will have passed 8 leaves, after 5 turns you will have passed 13 leaves and after 8 turns you will have passed 21.

The head of a sunflower often has spirals of seeds in these ratios, such as 34 in a clockwise spiral and 55 in a counterclockwise spiral. Similar Fibonacci patterns are seen in pine cones, artichokes, Romanesco broccoli and pineapples. It isn’t that the plant is *calculating* Fibonacci ratios but that there is “emergence” of these ratios - the plant follows the rule of “putting the next leaf in the biggest available space.” One human-centred result in a pattern that be very appealing.