Computable function, or total recursive function, a function computable by a Turing machine
For example, that a Watt governor is a better metaphorical description of the way humans think than a Turing machine style computer.
Genetix a virtual machine created by Bernard Hodson containing only 34 executable instructions
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A Darwin machine (a 1987 coinage by William H. Calvin, by analogy to a Turing machine) is a machine that, like a Turing machine, involves an iteration process that yields a high-quality result, but, whereas a Turing machine uses logic, the Darwin machine uses rounds of variation, selection, and inheritance.
The class LINSPACE (or DSPACE(O(n))) is defined the same, except using a deterministic Turing machine.
Marcus Hutter has used this consistency to define a "natural" Turing machine of small size as the proper basis for excluding arbitrarily complex instruction sets in the formulation of razors.
Iriyama, Ohya, and Volovich have developed a model of a Linear Quantum Turing Machine (LQTM).
Turing completeness, having computational power equivalent to a universal Turing machine
Von Neumann universal constructor – an attempt to build a self-replicating Turing machine