Basin of Attraction : The set of points that evolve to an **attractor** is called its basin of attraction.

The **phase space** of a particular **dynamical system** is partitioned into one or many basins of attraction , perhaps intimately intertwined, each with its own attractor .

basins of attraction for a pendulum swinging over three magnets. (from Peitgen, Jürgens, and Saupe, Chaos and Fractals)

The boundaries between basins of attraction can themselves be **fractal**.

detail of boundary between the regions of the basins. They are fully entertwined.

(is this related to the "edge of chaos"..i.e. is the edge itself fractal?)

see **Mandlebrot set** for the extreme example of a complex domain of attraction.