A common theme across many disciplines is the fact that simple systems and simple rules suffice to generate lots of complexity. Why is this so? I suggest that this is due to the phenomenon of universality: a system is universal when it can explore all complexity in its domain, and already very simple systems are universal. I will explain the phenomenon of universality for spin models, automata and neural networks, as well as the first steps toward a rigorous comparison between them. I will also talk about one of its most fascinating consequences of universality, namely undecidability.
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