Fractal criticality refers to a state where a system displays a critical behavior that exhibits self-similarity at different scales. In other words, a fractal structure emerges in the system as it approaches a critical point.
A critical point is a point in a system's parameter space where small changes in input or conditions can lead to large changes in output or behavior. Fractal criticality arises when the system is poised at this critical point, with the dynamics of the system exhibiting fractal behavior. Fractals are self-similar patterns that repeat themselves at different scales, meaning that the same pattern is observed when we zoom in or out of the structure. Fractal criticality implies that a system's behavior is self-similar at different scales, and thus, its dynamics can be described by fractal patterns. Examples of systems that exhibit fractal criticality include earthquakes, financial markets, and the human brain. Understanding the dynamics of systems at critical points and their fractal behavior can lead to important insights into the behavior of complex systems.
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