I will speak on a simple dynamical system which models the Internet protocol TCP. The simple model embodies TCP's "additive increase, multiplicative decrease" rule. Two sources s1 and s2 send packets at varying rates r1 and r2 to a recipient; whenever packets are lost, the sender halves its sending rate.

We prove that for infinitely many choices of the parameters, the set of feasible rate pairs that can occur in the limit is a fractal. (This does not mean, however, that the traffic is statistically self-similar.)

No previous knowledge of TCP or of fractals will be assumed.

This is joint work with Anna Gilbert.