Oil on canvas 12x12” Completion date 6/9/2012
My latest integrating both 2D and 3D fractals
Many know that Beethoven went deaf while he was still composing, but few, musicians, musicologists or mathematicians know that he used a fractal structure in his music. Since symphonies and concerti use sonata form, they also have the same type of hierarchical structure. The type of structuring where the smallest unit is echoed similarly into larger and larger encompassing units is often called architectonic in music and is virtually the definition of a fractal. Both, parts of Beethoven’s 9th symphony and Beethoven's piano Sonata no. 15, op. 28, third movement (Scherzo) consist of musical structures which form a Sierpinski's triangle.
Depicted are the forms heard in Beethoven’s deaf ear, including to the left, Sierpinski's triangle.
Dedicated to anyone who has ever had their hair stand up from hearing a piece of music. Aural Ecstasy



The Sierpinski triangle, also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński 

Originally constructed as a curve, this is one of the basic examples of self-similar sets, i.e. it is a mathematically generated pattern that can be reproducible at any magnification or reduction.