A fractal is an object that displays self-similarity -- roughly, this means that the parts have the same shape as the whole -- as in the following diagram which shows successive stages in the development of the "box fractal" (from Wolfram MathWorld).
Michigan poet Jack Ridl and I share an alma mater (Pennsylvania's Westminster College) and we recently connected when I found mathematical ideas in the poems in his collection Broken Symmetry (Wayne State University Press, 2006); from that collection, here is "Fractals" -- offering us a poetic version of self-similar structure:
Fractals by Jack Ridl
On this autumn afternoon, the light
falls across the last sentence in a letter,
just before the last movement of Brahms’
Fourth Symphony, a recording made more
than 20 years ago, the time when we were
looking for a house to rehabilitate, maybe
take out a wall and let the kitchen open
up into the living room, put in a window
so the morning light could fall across
the bed my wife’s grandmother made
the canopy for, the bed she slept in for
forty years. She was a doctor looking
for a town close enough that we can
drive past where she practiced, imagine
her picking up her violin when there
was time between patients, settle
it under her chin and play, looking
out the window into the same street we
drive down on our way to visit our
daughter in her studio. She creates
dresses, stitches turning into lines,
fabric turning into sculpture hanging
under her skylight, the dresses’ threads
knotted, their edges frayed. When
we knock on her door, she welcomes
us with cups of steaming tea, turns
down the jazz and kisses us. She
is happy in this light and later she
will ask us how we like our new place,
laugh when we begin to tell her all
our plans for tearing out the kitchen,
knocking out a wall so we can see
deep into the wood, along the creek
that twists itself around a pile of rocks
and through the trees. She makes us
dinner as we listen to Miles Davis,
“Birth of the Cool”—I always wonder
why he ended with a vocal, one
that sounds recorded twenty years
before. Its notes are sleepy,
the voices like smoke. At home
the dog and cats are sleeping. We
forgot to leave a light on for them,
but the radio is playing, and when we
get there, they will want to go outside.
The dog will pause for a scratch behind
his ears, his tail wagging as the cats
jump off the couch, hurry out the door,
disappear into the dark.
We’ll tune the radio to a symphony,
watch the moon harvesting
its light through the back window.
I discovered Ridl's collection while doing some background digging for other recent postings on fractals -- 16 December 2014 and 18 November 2014. Fractals also are found in these earlier posts: 10 April 2014, 17 October 2010, and 14 May 2010.
Adrian Morgan left this comment -- but some keyboard error of mine failed to publish it. And so I am copying and pasting here. Thanks, Adrian, for dropping by:
ReplyDeleteAdrian Morgan has left a new comment on your post "A Fractal Poem":
I haven't been able to find the fractal in this poem. I see a lot of nested subclauses and revisitation of themes, but I can't see a mathematical structure.
Here is a different approach to fractal poetry: one that rhymes.
This doggerel does not intend
To satisfy the reader's would
For art that is remotely good;
It will not serve to meet that end,
So don't imagine that it could.
But in its rhyming structure you
Might find, if you are able to,
A pattern to be understood
That's relevant to trees of wood
And clouds of water vapour, too -
The applications are not few -
For it possesses fractalhood.
Look closely, and you'll comprehend
The secret pattern, bad or good,
Which, if this text were longer, could
By iterative means extend.
To generate the rhyming structure for this, I used an L-system defined on the positive integers with the rule "n -> n, n+1, n+1, n", and then arbitrarily mapped each integer to a rhyme. After one more iteration, the structure would be as follows:
ABBA BCCB BCCB ABBA BCCB CDDC CDDC BCCB BCCB CDDC CDDC BCCB ABBA BCCB BCCB ABBA
Writing *that* poem would not be easy!
Adrian --
DeleteI agree with your interpretation of Ridl's poem. A fractal is suggested through nesting and revisitation but "poetic license" has also been used.
I want to add a bit more about Adrian Morgan -- who offered a comment above. From Adelaide, Australia, Adrian has a website (at http://quidjfravzgembtchowlkspynx.com/), a blog (at http://outerhoard.wordpress.com/me-and-my-blog/) -- and
ReplyDeletein this blog posting (at https://outerhoard.wordpress.com/2009/07/04/poetry-competitions-and-a-little-quantum/) we can learn about his and other poetry entries in a past competition entitled "How to Teach Physics to Your Dog." Enjoy!
http://talkingwriting.com/david-morimoto-math-poetry
ReplyDelete