Thursday, 13 March 2014

Week 8, Part 2: Patterns in Nature

The Daisies are out in bloom now, their yellow centres arranged beautifully in Fermat’s spirals. This gives me the perfect opportunity to return to the idea of patterns in nature. Unfortunately, my brain is somewhat hampered this week and, so, this isn’t going to be quite the post I had intended. I won't go into Fractals, for example, but you can google those if you're curious (today's Oak photograph goes some way to illustrate a fractal in nature, sort of). However, I hope a glimpse will provide food for thought or spark some interest.

More than half a lifetime ago, I submitted an A-level Fine Art dissertation entitled “Mathematics and Art...?”. Ever since, the division between science, art and nature has, for me, been arbitrary at best. As far as I’m concerned, there is beauty in mathematics just as there is precision in art, and nature encompasses both. There is no better way to experience this than to take a look at one of the fields of mathematics which is expressed in the beautiful patterns of nature.

If you don't want to read the technical bit, feel free to skip to the video at the end. No words, just beautiful illustrations set to music.

In 1202, a chap known as Fibonacci proposed a sequence of numbers whereby successive integers are the sum of the preceding two integers i.e.

0,  1,  1,  2,  3,  5,  8,  13,  21,  34,  55,  89,  144 and so on to infinity.

The result of dividing the current integer in the sequence by its previous integer tends towards the value 1.61803399 (e.g. 89 / 55 = 1.618). This became known as the Golden Ratio, best illustrated in the Golden Rectangle, where the ratio of length of the long side to the short side is the golden ratio ((a +b)/a) = 1.618.

The golden rectangle is composed of a square and rectangle. Each rectangle can be subdivided into another square and rectangle with the same proportions, ad infinitum.

Incredibly, this simple series of numbers and its ratio can be expressed in the most wonderful and beautiful ways both in mathematics and in nature (the above illustration includes the golden spiral, which can been seen in the structure of Nautilus shells. And, the Fermat's spiral, in the daisy head, also derives from Fibonacci's numbers. In botany, there are phyllotactic spirals. And so it goes on). Hopefully, the following short video from Youtube will capture your imagination. If you have the time, it's worth viewing….full screen, with the sound switched on.

(A beautiful short film on the Fibonacci sequence in Nature – ‘Nature by Numbers’)

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