Definition
Fractal basins are basins of attraction whose boundaries are self-similar at every level of magnification, so that zooming into a boundary region reveals the same intricate mixing of outcomes rather than a clean line. When a map of how long a system takes to settle, plotted against its starting state, shows this structure, it signals extreme sensitivity to initial conditions — tiny differences in starting point can send the system down wildly different, though still fractal-patterned, paths.