Levi Bryant recently posted a wonderful explanation of attractors, and, in the comments, a nice explanation of how the idea relates to his "regimes of attraction." As I think about the example he uses - a marble dropped into a bowl from one edge - I enjoy it more and more as a metaphor for structure and agency. By modifying the metaphor gradually, we can see a variety of different social theories playing out.
In the most basic example, one positions a marble at the edge of a bowl and allows it to drop. The marble will fall towards the center of the bowl, bypass it, roll up the other side, and then back down. This will repeat several times until the marble eventually comes to rest at the bottom of the bowl (referred to as the attractor). This is a good description of a fully deterministic system - the marble has no choice, no agency, no ability to alter its own course. It's path is entirely determined by the shape of the bowl and the force of gravity acting upon it. There is no escaping the attractor. Now, the shape of the bowl may be different or the force of gravity may be altered by placing it on a different planet, and these will result in different outcomes, but the system is no less deterministic. This reminds me of Althusser, Adorno and other highly structuralist theorists for whom the system overdetermines our day-to-day lives.
In another example - slightly more complex - the marble is dropped, but this time it has some degree of ability to move about within the bowl. It will still be drawn towards the attractor, but now it may move on it's own to some extent. Thus instead of falling straight towards the attractor, it moves around it, passes through it, or dodges it - nevertheless, the attractor is always fixed and always exerts some force upon the marble. This corresponds to a deterministic system in which some small degree of choice is accepted. Individuals within a system are thought to move about within it, but are always drawn to a particular outcome determined still by structure of the system. This brings to mind Foucault, Bourdieu, and de Certeau for whom there is a degree of choice when moving about in the system, but our lives are still partly overdetermined by the system.
In a third example, the marble is dropped, but as it moves through the bowl, it alters the shape of the bowl very slightly. So, at every move, the attractor is slightly altered causing the marble to move more freely and not to be drawn deterministically to a single point. This is the beginning of real agency, in my opinion (as opposed to the false agency granted in the previous example) - the ability of an entity to alter and affect the world around it. This is reminiscent of Giddens' theory of structuration where agents within a system play an active role in its composition. Imagine many marbles placed within the bowl, all altering it with their own aims and ends, creating a complex movement within the system.
A final approach is even more revolutionary, and, I think, is what Bryant, Latour, Harman, Ivakhiv, Michael, and many others (including myself) are striving for. In this system, the bowl is not seen as a field upon which the marbles move, and which determines their actions to some degree - whether they are able to shape it or not. Rather the bowl is simply a part of the assemblage with an ability to act upon the marbles, and the marbles are a part of the system able to act upon one another as well as the bowl. In this case, the marbles are dropped into the bowl - they alter the bowl, they alter one another, and the bowl alters each of them in different ways. Thus there is no field, no structure, no single object which all others can be reduced to. There is only an assemblage - an ecosystem one could say - of different actors (human and non, material and semiotic, etc.) altering and affecting one another, composing a complex system together in every moment. This, to me, is the most brilliant innovation in social theory in ages!