Career interview: computer music researcher

Career interview: computer music researcher

March 2006

The maths behind the music

The transformation rule which is the basis for Nick's composition uses the complex function

  \[ f(z) = 0.5(-z + \sqrt {12 - 3 z^2}). \]    
Iterating this function starting with a given value $z_0$ gives a sequence of complex numbers:
  \[ z_0, z_1 = f(z_0), z_2 = f(z_1), z_3 = f(z_2), ... . \]    
Any complex number z = x+ iy can also be thought of as the pair (x,y) of real numbers, so the formula does indeed transform one pair into another pair, as described above (see Plus article Curious quaternions for an introduction to complex numbers).

Return to the article

CAPTCHA
This question is for testing whether you are a human visitor and to prevent automated spam submissions.