Harlan Brothers



Harlan Brothers, mathematician/composer

Fractal Geometry and Bach



Music and math are intimately related. 
What they do share is an abiding respect
for the power and the importance of pattern recognition,
whether it’s a sequence of numbers or a sequence of notes.



Bach did appear to think like a mathematician
because the techniques he used all have analogues
in the world of classical geometry.


Harlan Brothers with Benoit Mandelbrot at Yale University


But Bach's music can also possess characteristics of fractal geometry.
The term fractal was coined by the mathematician Benoit Mandelbrot. 
It deals with the concept of self-similarity. 
What this means is that if you zoom into such an object,
you see more and more structure that resembles the object as a whole.



From bacterial colonies to the distribution of galaxies in the universe,
an incredible variety of natural phenomena exhibit fractal structure.



And in that respect perhaps Bach best reflected the world around him,
the fractal nature of the world around him.



Bach believed that the microcosmic order
must be mirrored in the macrocosmic. 
It’s not surprising then that the Art of the Fugue
is in some sense composed of smaller copies of itself.




There’s a wonderful story about Carl Sagan and the Voyager I spacecraft,
our first attempt at communicating with beings beyond our solar system. 
He was talking to Dr. Lewis Thomas
about what kinds of things he should include. 
Lewis suggested, “I think we should send all of Bach
but of course we would be bragging.”

Fractals Generated by Harlan Brothers


People often refer to the timelessness of Bach. 
At this very moment the Voyager
is speeding through the galaxy with Bach as our emissary.




Harlan Brothers Website