A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale. If the replication is exactly the same at every scale, it is called a self-similar pattern.
A tree for example; imagine zooming in from a way away. At a distance you see the branches, close up you see the twigs. They all display a similar pattern but on a different scale. That’s self-similar patterning fractals.
Odd, hey but this is where maths and art overlap.
Fr’instance some people say Jackson Pollock is a great American artist; others look at his drip paintings and meah. But they are loved because of fractals
In Jackson Pollock’s drip paintings, as in nature, certain patterns are repeated again and again at various levels of magnification (physicist and art historian Richard Taylor)
Yep, Pollock painted fractals. He captured an aesthetic element that is everywhere in nature, in sponges and succulents, trees and trilobites. That’s why, at an instinctive level we can dig it.
Looky here
And after Pollock came Loren Carpenter a genius animator and co-founder of Pixar. Here‘s the first fractal film, the basis of much of Pixar’s unique genius.
I mentioned fractals in a post a while back and recently maths has cropped up as a topic leading me to pen a poem on fractals, well kind of..
I found fractals dripping
from a branch;
lines of splods
taking shape from chaos.
That’s the beauty,
nature pulling tricks right under your nose,
blind until see.
Onion skins of secrets,
always there, always been there
but
you need to know it.
How do you look at a branch?
Is it a twig by any other name?
Or is a tree a twig grown up?
Everywhere you go, how far back you go
it looks like a twig on a bigger twig
on another big twig.
That’s fractals, sprouting from within to without.
Close up it’s just a word, growing to a sentence.
But step back
and it grows to a paragraph,
then a page.
The depth of vision doesn’t change the essential sameness.
A writer is like a tree sticking a twig of a word on another
making a branch of a sentence and a trunk of pages.
Stand well back and
it’s a novel
but only when you know where to look.
Otherwise you just see splods.
Have faith fractal penspeople;
someone will see it and explain.
See, it’s a novel, a proper book only
you didn’t realise it was there all the time.
You were too close.
That’s why I love writing in fractals.
TanGental 
I love the word fractal and I have used it often in poetry. 🙂 xx
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I nearly wept at the line, “You were too close.” How you tie in the pom to the art to nature and back to writing is all fractally accomplished. What amazes me about Pollock is that he did fractals intuitively. The physicist’s device and Carpenters program are mathematical accomplishments that Pollock did freehand. May penmasters one day accomplish the ability to write as Pollock painted.
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tanks Charli; the first poem I’ve written in a while
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Thanks for this post explaining fractals. I wouldn’t have even thought of them, or of understanding them before your mention of them in a comment last week. I must say though that, when I read the introductory explanation, I didn’t think I was going to be any the wiser! It didn’t make much sense to me. But your explanation throughout the post, supported by videos, worked well to explain this phenomena. I was particularly interested in Pollock’s technique. I probably wouldn’t have appreciated his paintings without this explanation. Sometimes we need to know what we are looking at to truly see and appreciate it. It’s a bit like making snap judgments of a person and writing them of as a (insert whatever) without looking further into the depth of being.
Your poem is a beauty. I love the way you have used the phenomena to explain writing. It is true that a word can hold so much meaning. I would love to see a visual far away to close-up done for a book as you describe. Lovely.
Thank you for teaching me about fractals. I’m sure to see them everywhere now. 🙂
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It took Marcus de Sautoy and a BBC documentary to explain them to me and help me see their beauty. I’m so glad you liked the poem and so pleased your thoughts prompted mine to write it; first one in quite a while.
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And I’m pleased you did! 🙂
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Oh, I love this. The post, the poem. Painted fractals — what an awesome concept. Thanks for sharing this, Geoff.
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Maths and writing; so much in common
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