An attractor or attractor state in mathematical terms is a closed invariant set toward which system trajectories converge over time. Formally, it's a set A where all nearby trajectories approach A as t → ∞.
In dynamical systems, an attractor basin is a region of phase space in which all trajectories converge on a fixed point, limit cycle, or strange attractor.
Visually, one can think of a Fixed Point Attractor as a sink (like a marble settling in a bowl), a Limit Cycle Attractor as a closed track (like a train orbiting a looped rail, always returning to start), and a Strange Attractor as a fractal “tangle” or strange landscape in which the system roams indefinitely.
Behaviorally, as we move from fixed to limit cycle to strange attractors, the system's long-term behavior becomes more complex: from static, to periodic, to chaotic. This progression often occurs via parameter changes – e.g. a simple steady-state can give way to oscillations and then to chaos as a control parameter passes critical thresholds (as seen in the logistic map or Lorenz system, where a single system can exhibit all three types of attractors depending on parameters)
In social systems, Attractors represent stable configurations of organization - the cultural norms, institutional arrangements, and power structures that societies naturally evolve toward and maintain.
If Conquest Theology functions as such a basin:
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Then even creative, divergent strategies (networking, coalition-building, leaning in)
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Are curved by the field geometry
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Toward Trespass Theology's ends: containment, commodification, co-optation
No matter how nonlinear the path, the endpoint is overdetermined. Not by force—but by topology.
The math is merciless because it isn't about intention. It's about field structure of the Attractor.
You cannot escape a basin of attraction using operations generated within that basin.
