As you can see my webpage is adorned with ammonites.
These long since extinct creatures are exquisite treasures; and behind their alluring surface lies some beautiful science. As a former geologist and an admirer of creative and artistic things, I find this rocky marriage of maths and art very appealing. Here follows a brief (I promise!) explanation of the science along with some personal ramblings.
So, it turns out that the seductive spiralling shape of an ammonite is a good fit to one of nature’s magical equations – the Fibonacci series.
The equation is as follows:
x(n+1) = x(n) + x(n-1)
So the sequence goes like this:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … and so on infinitely.
In the case of the ammonite its shell spirals out with approximately this ratio as the illustration below shows.
The Fibonacci series crops us in many natural forms, including the spiral of a galaxy, the arrangement of leaves around a plant’s stem, the structure of a pine cone and the pattern of seeds in a sunflower head.
In many cases it seems that using the Fibonacci series is Mother Nature’s way of saving energy – this packing arrangement provides sunflowers with the maximum number of seeds on their flower-head. I haven’t been able to find out why ammonites grew in this way, but I guess it might have been the most energy efficient way to grow a shell – can anyone answer this question for me?
I never tire of looking at this pattern – somehow it just really pleases the eye. And once or twice my fondness for this pattern has left me in deep water. Most memorably, my determination to extract a superb golden ‘pyrite’ ammonite from its rocky bed nearly left me stranded under the crumbling sea cliffs near Whitby. Luckily for me, my companions had more sense than I, and insisted I leave the tide to claim its prize. My stubbornness led to us all having to squelch back through Whitby, having waded through waist-high water.
There is no need to go to these lengths to collect lovely ammonites – these fossils are in abundance along many sections of British Coast and across many other parts of the world. Most notably they can be found along the ‘Jurassic coast’ of the south west (Dorset and Devon) and along the East coast near Whitby and Robin Hoods Bay. These creatures were an evolutionary success story, first emerging in the mid Devonian (around 390 million years ago), and surviving several mass extinction events, before finally being wiped out with the dinosaurs, in the KT extinction, 65 million years ago.
Their shells were divided into segments which they used to control their buoyancy, by filling or emptying them of gas. Most likely they lived out in the open waters of ancient oceans, which explains why we find so many fossils today: oxygen-free mud at the bottom of an ocean is an optimum place to be preserved. The closest living relative to ammonites today is probably the squid.
For me ammonites are both beautiful and fascinating. They are something that I love to draw, and they served as the inspiration for the woodcut and print that I did for my webpage. Over time I hope to add some more examples of beautiful things to this page, and to explore the science of why these things appeal to our senses. Feel free to furnish me with suggestions and let me know your views.