Self-similarity is a fascinating and beautiful organizational scheme of nature. Organic structures that exhibit this property possess details on small scales that are intrinsically similar to the larger scale form (and vice versa). Consider your body. From the largest arteries to the tiniest capillaries, the self-similar branching design of your circulatory system makes it possible for oxygen-carrying blood to reach every part of your body, on all crucial scales. The self-similar branching network of the neurons, clusters of neurons, and clusters of clusters of neurons that make up your brain and nervous system make it possible for electrochemical signals to be transmitted efficiently throughout the assembly of your body. Consider the surface of the ocean, made up of tiers of waves upon waves upon waves, each smaller wave nested within a larger wave. Consider a mountain range, with peaks and valleys within peaks and valleys on scales ranging from kilometers to micrometers. Consider trees, galaxies, and lightning bolts. Google Earth allows us to zoom in and out to any height above the earth’s surface and see self-similar structures on all scales.

The concept of emergence has parallels with self-similarity. Throughout all scales of nature, order can emerge from the interactions of a multitude of tiny chaotic particles, just as new, complex behavior can emerge from simple rules. Consider an ant colony. A single ant behaves in a relatively simple way, but the self-organizing dynamics of a colony behaves as an intelligent and complex superorganism – information is processed by the collective and not by individuals. Consider your own consciousness. A single neuron in your brain behaves according to relatively simple rules, but the complex network of billions of these cells somehow gives rise to intelligence. Scientists have discovered that simple computer programs governed by simple rules can produce infinite complexity. Cellular automata is one model that gives rise to a wide variety of complex patterns and behavior, an analysis of which may illuminate some of the deepest mysteries in nature.

How did the universe get so complex from simpler beginnings?
How does order emerge from such complexity?

Automata explores these ideas in music. Its structure is self-similar: the large-scale form mirrors patterns on smaller scales.The musical structure of Automata consists of recursive phase patterns unfolding on three independent, yet interconnected, levels. The lowest level consists of the rhythmic ratio 11:10; the mezzo level consists of accented notes; and the highest level consists of free improvisation. All levels have the same structure, but they unfold on different temporal scales.

As time passes in Automata, the improvisation regions grow in length until the final measures of all the scores; here, the music flows seamlessly into free improvisation, the length, character, and structure of which is decided by the ensemble.

Automata was commissioned by Matthijs Lunenburg and premiered in Amsterdam (2006) for recorder, flute, 2 saxes, bass clarinet, 2 pianos, and 2 electric organs. Zeelab performed the piece at the Musica Moderna Festival in Łódż, Poland (2007) for automechanical organ and 2 pianos.


A variation of this piece, Automata II, was commissioned by Hesperides XXI, and is scored for flute, percussion, and sine waves. It was performed by Carmen Ojeda (flute) and David Hernandez Deniz (percussion) at the Muziekgebouw, Amsterdam.