Artificial Life 8, Sydney, December 2002


Dynamical Hierarchies


Alan Dorin & Jon McCormack{aland, jonmc}

Centre for Electronic Media Art
School of Computer Science & Software Engineering
Monash University, Melbourne, Australia


  • Motivation

  • Previous work

  • The model
  • Hierarchies

  • Properties

  • Questions


  • emergent property
  • dynamical hierarchy


Previous work

The model

A screen grab is available from software which runs this model (using squares).

Some sample structures


Division/Nested hierarchy


A different hierarchy
(Differently shaped at each level)

As well as this hierarchy seen earlier,


This is also a hierarchy,




Measuring & Comparing Hierarchies


Consider a structure X of order n, written Xn.



So, for n levels, Xn can be specified hierarchically in: p*4*(n-1) bits.



The hierarchical description is measurably more efficient than the non-hierarchical one.


Properties are observed by people.


In a simulation, properties may be distinguished where the machine has states to represent them.


Trivial Properties in the Model

Each level in the hierarchy has a property not found at lower levels.

This sounds like Bedau's "Nominal Emergence".


Not So Trivial Properties in the Model

We have built an infinitely-levelled dynamical hierarchy which exhibits emergent properties at each level and has base units of fixed complexity!


So why are we not excited?


The Artificial Life mantra:



"We seek interesting behaviour"



Multiple-levels of trivial behaviour may produce a level of interesting behaviour.


Perhaps the stuff of our simulations is just too boring to ever produce anything interesting.





The issue hinges on the Artificial Life mantra.

©Copyright Alan Dorin/Animaland 2002