From Exponential to Gaussian Tails: Fractal Wavefront Scaling and the $\kappa$-Weibull Distribution at Phase Transitions

O. V. Pavlovsky; M. Yu. Satleikin

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arXiv · 2607.28172

From Exponential to Gaussian Tails: Fractal Wavefront Scaling and the $\kappa$-Weibull Distribution at Phase Transitions

O. V. Pavlovsky·M. Yu. Satleikin

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Abstract

The paper examines the features of critical evolution in an active medium modeled by a cellular automaton. The system evolves according to stochastic rules, exhibiting two qualitatively distinct dynamical regimes: one of fading activity and another of all-filling activity waves. Each regime is characterized by its own fractal dimension and fluctuation statistics, both of which are analyzed in detail. Within the critical interval, the system displays a nontrivial fractal dimension and a fluctuation distribution that bridges the two regimes. This bridging behavior arises because, in the critical interval, the dynamics are governed by avalanches.

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O. V. Pavlovsky, M. Yu. Satleikin. 2026-07-30. From Exponential to Gaussian Tails: Fractal Wavefront Scaling and the $\kappa$-Weibull Distribution at Phase Transitions. https://arxiv.org/abs/2607.28172

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