Chaos in Max and PureData

We've looked at a few algorithmic composition ideas using Chaos in OpenMusic here, today's post applies some of these ideas algorithmic composition ideas in Max and PureData.

Chaos theory is a field of mathematics where dynamic systems are very sensitive to initial conditions. The famous 'butterfly effect' states that small differences in initial conditions can lead to large variations later: the small flap of a butterfly's wings may cause effects that later alter the path of a tornado.

As with our OpenMusic chaos patch, for this example of Chaos in PureData and Max we'll use a logistic map. The Logistic Map is a simple example of a discrete dynamical system that actually names a whole family of iterative functions described by the very common Logistic Equation:

f_n+1=cf_n(1-f_n)

That's to say: to get the next value of f, multiply the current values of c, f and (1 - f). This formula involves only 1 subtraction and two multiplies but it leads to chaotic behaviour. In this graph you can see with values of c below 3 the behaviour is very predicatable. However if c > 3.75 then very small changes in f lead to very large changes later on:

Tom Johnson's Algorithmic Compositions Part 2

A previous post looked at some of the algorithmic composition ideas used by American Composer Tom Johnson. Today's algorithmic composition tutorial looks at a few more of Johnson's concepts specifically his use of finite automata.

A finite automaton is a sequence using a finite number of symbols generated according to specific rules. In the case of Johnson's Automatic Music, six percussionists each have only two notes, high and low, and the alphabet is limited to 1 (the low note), 2 (the high note), and 3 (a silence) using the following rules:

1 --> 1 1 2
2 --> 3 2
3 --> 3 3

Beginning with 1 generates the following sequence:

   112112321121123233321121123211211232333233333332

Using this automaton it's easy to generate long sequences of numbers that can be then mapped to musical parameters. As ever with algorithmic composition, once you've created your patch or program it's easy to manipulate the formula or remap the musical output to generate new pieces.

Let's have a look at a simple example using PureData and Max. This screenshot shows the generation part of our algorithm in PureData.

The until object will output 500 bangs when the above message is clicked on, the counter outputs a running count of these bangs and this is used as a number to lookup the stored value in the coll object. The output of the coll is connected to a select object and this triggers the new messages that are stored within our coll object.

In Max the patch looks very similar though note the use of Uzi rather than the PureData until object.