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."

Fractal Geometry

Lee Felice Pinkas is one of the founding editors of cellpoems -- a poetry journal distributed via text message.  I found her poem,"The Fractal Geometry of Nature" in the Winter/Spring 2009 Issue (vol.14, no 1) of Crab Orchard Review.

The Fractal Geometry of Nature       by Lee Felice Pinkas

               Most emphatically, I do not consider
               the fractal point of view as a panacea. . .
                                             --Benoit Mandelbrot (1924-2010)

Father of fractals, we were foolish
to expect a light-show from you,

hoping your speech would fold upon itself
and mimic patterns too complex for Euclid. 

From order to chaos -- a sonnet

Fractals    by Diana Der-Hovanessian

                             Euclid alone has looked on beauty bare
                                                    --Edna St. Vincent Millay

Euclid alone began to formulate
the relation of circle, plane and sphere
in equations making it quite clear
that symmetry is what we celebrate. 

The Length of a Coastline

In the nineties, fifteen or so years ago, when I began posting mathematical poems on the Internet, two of my earliest connections were Ken Stange, a poet and polymath and professor of psychology at Ontario's Nipissing University, and his daughter Kate, then a teen.  Kate publicized her love of mathematics and poetry by creating an online collection,"Mathematical Poetry:  A Small Anthology" which she has continued to maintain for many years--during which she has completed undergraduate and graduate studies in mathematics. 

Poems starring mathematicians - 6 (Mandelbrot)

More familiar than the name Benoit Mandelbrot are images, like the one to the left, of the fractal that bears his name.  Born in Poland (1924) and educated in France, Mandelbrot moved to the US in 1958 to join the research staff at IBM. A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole, a property called self-similarity.