Spira Mirabilis

After the snail shells I photographed on Tuesday night started me thinking about spirals and the geometry of nature, I noticed, on the shelves of Lancaster Library, a book called ‘Patterns of the Earth’.

It is a collection of (mostly) aerial photograph categorised into Bands, Stripes, Ripples, Circles, Spots, Grains, Forks, Branches, Webs, Curves, Ribbons, Swirls, Spikes, Grids and Cracks.

It shows how the same patterns emerge in widely disparate locales and hugely different terrains.

Because the photos are mainly aerial, the patterns seen are on a geological scale.

To me a more interesting book would seek out those same patterns from microscopic  to galactic scales.


Just along the shelf I spotted ‘What Shape is a Snowflake?’ by Ian Stewart.

This explains the mathematics behind how the same basic patterns and shapes recur frequently in nature.

Then Ron from Walking Fort Bragg left a link in a comment to photographs on Astronomy Photo of the Day of a typhoon and a nebula, both of which are logarithmic spirals.


These equiangular spirals crop up in all sorts of places. They can be generated in a most elegant way using the Fibonacci sequence.

(The squares have sides 1, 1, 2, 3, 5, 8, 13, 21 and 34)

So with all this running around my head, imagine how thrilled I was today when Amy picked an Oxeye daisy and presented it to me:

And I discovered that it too had logarithmic spirals to display.

Spira Mirabilis

5 thoughts on “Spira Mirabilis

  1. WOW (that’s MOM upside down) – that is a simply SPECTACULAR photo. Do you ever sell your prints? I think you should/could. I would like the one above on my office wall – the entire wall, that is.

    I envy you your math understanding. I get glimpses of the beauty of math (though “Euclid alone has looked on Beauty, bare” says ESVM) but never had a very good math teacher. Have your children appeared to inherit your strength in that respect? My poor two completely bypassed their math-teacher grandfather’s and father’s genes and both got my math moron one. Some day I hope to convince them that we can explore the incredible beauty of numbers together.


    P. S. When they’re old enough, I know a trick with the number 9 that has dazzled even some math teachers I know. Kids love it.

  2. beatingthebounds says:

    I would love to sell prints – what a fabulous idea. I have no idea how to go about doing it, but shall have to look into it. I think that you could probably get a print of this from flickr but I’m not even sure about that. You are of course welcome to take this and get a print if you want to.
    I’m not sure about the kids maths capabilities yet. Amy certainly has artistic leanings: she loves dancing, singing, acting, painting, reading, writing but she loves solving problems too – aged four I suppose you don’t differentiate it’s all just part of her natural curiosity.

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