Computer architecture paradigms

Some different paradigms of how to build a computer from the ground-up:

RAM machines

These are the types of computers with a CPU, computer memory, etc., which understand basic instructions in a machine language. The concept evolved from the Turing machine.

Brains

Brains are massively parallel processors made of neurons, wired in intricate patterns, that communicate via electricity and neurotransmitter chemicals.

Programming languages

Such as the lambda calculus, or modern programming languages, are virtual computers built on top of other computers.

Cellular automata

For example, the game of Life can create "gliders" and "loops" and other constructs that transmit information; this paradigm can be applied to DNA computing, chemical computing, etc.

Groups and committees

The linking of multiple computers (brains) is itself a computer

Logic gates are a common abstraction which can apply to most of the above digital or analog paradigms.
The ability to store and execute lists of instructions called programs makes computers extremely versatile, distinguishing them from calculators. The Church–Turing thesis is a mathematical statement of this versatility: any computer with a minimum capability (being Turing-complete) is, in principle, capable of performing the same tasks that any other computer can perform. Therefore any type of computer (netbook, supercomputer, cellular automaton, etc.) is able to perform the same computational tasks, given enough time and storage capacity.