Imagine a Fractal

California poet Carol Dorf is also a math teacher and is poetry editor of the online journal TalkingWriting.  In the most recent issue of Talking-Writing is this fascinating poem by Brooklyn poet, Nicole Callihan, "How to Imagine a Fractal."  Enjoy Callihan's poetic play with recursion and infinite nesting -- be lulled by the back and forth of forever.

Carol Dorf's work has appeared in this blog:

  Her fan-letter to the author of a math book is here 

and a poem about fear of math is posted here.

How to Imagine a Fractal     by Nicole Callihan 

March 21 -- World Poetry Day

Yesterday poetry was celebrated around the world -- the Guardian reported the event with mention of Cafés around the world that offered a cup of coffee in exchange for a poem.  The occasion caused me to turn to one of my favorite international collections, The Horse Has Six Legs (Graywolf, 2010) -- an anthology of Serbian poetry translated and edited by poet Charles Simic.  On 29 April 2011 I posted "Forgetful Number" by Yugoslav poet Vasko Popa (1922-1991) -- and here is another of Popa's poems.  This one is part of a cycle of poems about "the little box" and it involves recursion.

       Last News about the Little Box     by Vasko Popa

       The little box that contains the world
       Fell in love with herself
       And conceived
       Still another little box.   

Similar, self-similar -- fractals, a poem

      In geometry two objects are said to be similar if they have the same shape --- which happens if their angles are the same size and occur in the same sequence. For example, any pair of triangles with angles 30, 60, and 90 degrees are similar; also, the lengths of pairs of corresponding sides of these triangles have the same ratio.
      A term used in the terminology of fractals is self-similarity: a self-similar object has exactly (or approximately) the same shape as a part of itself.  A variety of objects in the real world, such as ferns and coastlines, are approximately self-similar: parts of them show the same statistical properties at many scales. At the end of this post are a couple of diagrams that illustrate how a fractal may be developed.  But first, experience the generative beauty of self-similarity via a poem by Maryland poet Greg McBride.  Mathematician Benoit Mandelbrot (1924-2010), quoted in McBride's epigraph, often is nicknamed "the father of fractals."

JHM -- many math poems

     Volume 2, Issue 2 (July 2012) of the Journal of Humanistic Mathematics has recently become available online -- and it has lots of poetry.  One valuable resource has been gathered by Charlotte Henderson, a participant in the January 2012 poetry reading at JMM in Boston; Charlotte offers a report on that reading and also has prepared a folder of the poems read there, collected for our ongoing enjoyment.  In this issue also there are poems by Florin Diacu, Ursula Whitcher, and Paige S. Orland and some kind words about this blog by Gregory E. Coxson (JoAnne Growney's Poetry-With-Mathematics Blog -- An Appreciation); many thanks, Greg.
      In the wake of the BRIDGES math-art conference at Towson University last week I also want to mention the lively blog posting about BRIDGES by Justin Lanier at Math Munch. 

Recursion

A mathematician may face a dilemma over the meaning of an ordinary term -- for words like "group" and "identity" and "random" (to name a few) have precise mathematical definitions that differ from their common meanings. Canadian poet Peter Norman's title, "Recursion," however, uses the term as it is used mathematically.  While a definition of "recursion" is widely available in mathematics texts, it was missing in my several English dictionaries -- and I found it only in the OED (though, even there,  noted as now rare or Obs.) : "a backward movement, return."   The term "return" indicates previous forward motion. In mathematical recursion (illustrated below by the Fibonacci sequence) as in Norman's poem, going backward is possible only because forward motion is known. (Interested readers will find an introduction to mathematical recursion following the poem.)

     Recursion    by Peter Norman

     I fall awake alone. Outside,
     nocturnal rain ascends.