Wednesday, September 14, 2011

Fibonacci hares



I've just received some prints I've ordered from The Printspace, my favourite high quality photographic printer in London. I ordered a few copies of my 'fibonacci hares' photograph as a giclée print on hahnemuehle photorag paper and am really happy with the results.

The photo was taken a couple of years ago when I was on a site visit for a windfarm proposal. There had been particularly heavy snow in the preceding few days and visibility was pretty poor so the site visit was compromised somewhat. Mainly just to have a bit of a walk, myself and a colleague decided just to head out into the snow and see what was there.

I remember it being very quiet, other than the sound of our footsteps in the snow. We stopped walking briefly and out dashed three hares from the hedgerow. I'm no biologist but from watching the events that followed I can be fairly sure that they were two males chasing after one female.

I managed to take a few frames, one of which was the basis of the print. I particularly like the faint triangular silhouettes of fir trees in the background. 

Why call the print 'fibonacci hares'? Well, briefly after I took the photo I was watching a really interesting documentary about the origins of the Fibonacci sequence. Supposedly, the Fibonacci sequence first appears in the book Liber Abaci (1202) by Leonardo of Pisa, who was known as Fibonacci. He was considering the growth of a hypothetical rabbit population (yes- I know rabbits and hares are different species but forgive my artistic license).

His assumptions were as follows:
  1. That a newly born pair of rabbits, one male, one female, are put in a field and the rabbits are able to mate at the age of one month.
  2. With a pregnancy duration of 4 weeks. At the end of its second month a female can produce another pair of rabbits.
  3. That rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on
The puzzle that Fibonacci posed was: how many pairs will there be in one year?

He concluded that:
  1. At the end of the first month, they mate, but there is still only 1 pair.
  2. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
  3. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
  4. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.
  5. At the end of the nth month, the number of pairs of rabbits is equal to the number of new pairs (which is the number of pairs in month n − 2) plus the number of pairs alive last month (n − 1). This is the nth Fibonacci number.
This results in the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...) where the next number is the sum of the previous two numbers. 


The documentary went on to explain the relevance of this sequence, two aspects of which I found really interesting. Firstly, how closely the sequence relates to the golden ratio, which is conveniently evident in the photograph itself - with the horizon placed 1/3rd of the way down the page. Secondly, how the sequence appears in numerous biological settings. It is suggested that everything from the gaps between branches in trees, arrangement of leaves on a stem, the flowering of artichoke, the shape of an uncurling fern to the arrangement of a pine cone all display a adherence to the Fibonacci sequence. 


Given the events that occured in the snowy field that day, it seemed appropriate to name the photograph after a study of breeding rabbits. This is also why I have decided to give the photograph as a wedding present to a few close friends of mine.