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: