Autocatalytic sets are self-sustaining chemical reaction networks in which the molecules mutually catalyze each other's formation. They have been studied extensively both with computer simulations and in laboratory experiments, and are believed to have played an important role in the origin of life.
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Cellular automata are simple computational models of decentralized complex systems. They have been evolved to perform non-trivial tasks that require global information processing. Their evolutionary history and task performance have been studied in detail, also in comparison to natural systems.
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The theory of the adjacent possible states that evolving systems create their own future possibilities. It has been studied in the form of a simple equation that captures the core idea of combinatorial innovation, and which accurately reproduces the "hockey-stick phenomenon" of economic growth.
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Several chemical and biological systems form spontaneous spirals in their dynamical behavior. A cellular automaton based on a simple "ideal storage" equation has been developed to reproduce and study such natural spiral wave formation, resulting in a striking similarity.
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