Fibonacci

Nature can be So Perfect!, originally uploaded by hhsc_2000/Greg.

Today’s tag search was ‘fibonacci’. Fibonacci was an Italian Mathmetician, seen by many as the most talented mathemetician of the middle ages. His name was given to a sequence of numbers that he recorded in the Liber Abaci, a 13th Century ‘Book of Calculation’ responsible for spreading the Hindu-Arabic numeral system in Europe.

The Fibonacci sequence is based on what is known as a recurrance calculation. After two starting values (0 and 1), each number is the sum of the two preceding numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811…

To me, what is amazing about this sequence is that it is nature’s way of creating complexity from a very simple algorithm. It is evident in the branching of trees, the wonderful pattern in the flower head above, the spiral of shells and pine cones, the curves of waves and a myriad of other forms.

I studied a computer programming language called Postscript for a while at college. I was lousy at it, but it reminded me at the time of the Fibonacci sequence – you have a ‘stack‘ on which you can place a number, enabling you to add it to a new number. Then you can add those two numbers together to create the next new number, an so on. All that you require for this is operation is a stack of two places. One of the reasons why Postscript is used is because it is very efficient for certain operations. It struck me that nature must be using a similar routine – it’s own form of Postscript.

The Fibonacci sequence is also closely related to Phi or the Golden Ratio – it is basically nature’s working approximation.

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