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.
The term fractal was coined by Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." Mandelbrot's book, The Fractal Geometry of Nature, unified the work of many predecessors as well as his own.
Few mathematicians are celebrated in poetry and song--but for Benoit Mandelbrot both have been done. And, during his lifetime. Tiel Aisha Ansari has given us the sonnet, "Benoit Mandelbrot and the Coast of Britain" and beneath Ansari's lines are openings stanza for song lyrics, "Mandelbrot Set," by Jonathan Coulton.
Benoit Mandelbrot and the Coast of Britain by Tiel Aisha Ansari
How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension by Benoît Mandelbrot
Water and land, like fingers interlaced
along a boundary of fractal length
divide and conquer self-similar space.
Like lovers in a close-contact embrace
they clasp each other in a couple-dance
in time stepped off in tidal increments,
the tango rhythm of retreat/advance
rekindled by each passing lunar glance.
So any scheme of finite measurement
of coastlines must require a leap of faith
from point to point along an edge of lace,
the moving merge of sea and continent.
And so Benoit walks on, his rule in hand
admitting he can't know the length of land.
Here are the opening stanzas for an enthusiastic tribute to Mandelbrot in song lyrics by Johanthan Coulton. The complete lyrics may be found online and, for even more fun, hear JC perform the song by linking to one or another of a variety of videos availble on You-Tube.
Mandlebrot Set by Jonathan Coulton
Pathological monsters! cried the terrified mathematician
Every one of them is a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set
And the Sierpinski Gasket makes me want to cry
And a million miles away a butterfly flapped its wings
On a cold November day a man named Benoit Mandelbrot was born
His disdain for pure mathematics and his unique geometrical insights
Left him well equipped to face those demons down
He saw that infinite complexity could be described by simple rules
He used his giant brain to turn the game around
And he looked below the storm and saw a vision in his head
A bulbous pointy form
He picked his pencil up and he wrote his secret down
. . .
Coulton's complete lyrics and 150 more mathematical poems are collected in Strange Attractors: Poems of Love and Mathematics.