Morteza Nattagh-Najafi, Mohammad Nabil, Rafsun Hossain Mridha and Seyed Amin Nabavizadeh

Entropy 2023, 25(6), 861

Inspired by recent observations on active self-organized critical (SOC) systems, we designed an active pile (or ant pile) model with two ingredients: beyond-threshold toppling and under-threshold active motions. By including the latter component, we were able to replace the typical power-law distribution for geometric observables with a stretched exponential fat-tailed distribution, where the exponent and decay rate are dependent on the activity’s strength (𝜁). This observation helped us to uncover a hidden connection between active SOC systems and 𝛼-stable Levy systems. We demonstrate that one can partially sweep 𝛼-stable Levy distributions by changing 𝜁. The system undergoes a crossover towards Bak–Tang–Weisenfeld (BTW) sandpiles with a power-law behavior (SOC fixed point) below a crossover point 𝜁<𝜁∗≈0.1.

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Lana Sinapayen

This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability, the descendant patterns exponentially drift away from ancestral patterns, even when the automaton is deterministic. While this is far from being the first instance of evolutionary dynamics in a cellular automaton, it is the first to do so by exploiting the power and convenience of Neural Cellular Automata, arguably increasing the space of variations and the opportunity for Open Ended Evolution.

Read the full article at: arxiv.org