Nature inspired algorithms for computers for problems without obvious “normal” solutions. (If you want to use computer-inspired algorithms for nature, that is the dual to this, bio-computing.)
The problem to be solved is usually a search/optimisation one. Normally evolutionary algorithms are in here too. (ant colonies, particle swarms, that one based on choirs… harmony search?), Typically these are attractive because they are simple to explain, although often less simple to analyse.
Is this is a real field separate from all the things that looks similar to it? Often they are asymptotically the same as a conventional stochastic method. e.g. particle swarms and particle systems, or evolution and stochastic gradient descent. Somewhere in this mix is artificial chemistry, where you use a simplified model of a natural process as a simplified model for computing about other natural processes, or showing that natural processes might be computing, or something like that.
…and quorum sensing? How about that? Multi-agent systems?
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Floreano, Dario, and Claudio Mattiussi. 2008. Bio-Inspired Artificial Intelligence: Theories, Methods, and Technologies (Intelligent Robotics and Autonomous Agents). The MIT Press.
Kennedy, James, and R Eberhart. 1995. “Particle Swarm Optimization.” In, 4:1942–8. https://doi.org/10.1109/ICNN.1995.488968.
Straszak, Damian, and Nisheeth K. Vishnoi. 2016. “IRLS and Slime Mold: Equivalence and Convergence,” January. http://arxiv.org/abs/1601.02712.
Venter, G. 2002. “Particle Swarm Optimization.” In.