This paper introduces Equilibrium Reasoners (EqR), a novel framework that conceptualizes iterative AI reasoning as a dynamical system converging toward stable latent attractors. By treating the reasoning process as a series of repeated updates to an internal state, the researchers demonstrate that models can scale performance at test-time by simply increasing the number of iterations (depth) or using multiple random starts (breadth). This approach allows a model trained on only 16 iterations to generalize to over 1,000 steps during inference, effectively unrolling the equivalent of 40,000 neural layers. This "attractor perspective" ensures that as the system reaches a mathematical equilibrium, it simultaneously settles on a correct task solution, resulting in near-perfect accuracy on complex benchmarks like Sudoku-Extreme and Maze-Unique. Ultimately, the research proves that aligning a model's internal landscape with task-specific goals enables adaptive computation, where harder problems receive more processing power to reach a valid conclusion.