Sunday, December 28, 2014

A Fractal Poem

    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.


  1. 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:

    Adrian 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:


    Writing *that* poem would not be easy!

    1. Adrian --
      I agree with your interpretation of Ridl's poem. A fractal is suggested through nesting and revisitation but "poetic license" has also been used.

  2. I want to add a bit more about Adrian Morgan -- who offered a comment above. From Adelaide, Australia, Adrian has a website (at, a blog (at -- and
    in this blog posting (at we can learn about his and other poetry entries in a past competition entitled "How to Teach Physics to Your Dog." Enjoy!