Visualizing Computation/Function Machine

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Function machine is a popular metaphor for visualizing input and output of a procedure, or the idea of a function, and related notions. It is accessible to toddlers, yet is robust enough to be taken to college-level work.

History and Known Uses[edit]


What is Being Visualized[edit]

  • Input and output
  • Function

Visualization Techniques[edit]

The basic visual metaphor is a machine that "does something" to objects that enter into one of its openings, and exit through another. In this form, it immediately supports:

  • Input and output
  • Inverse functions ("machine working backwards")
  • Domain and range ("what can go into the machine and what can come out")

Extensions of the metaphor include:

  • Iteration and cycles("a tube connecting the output of the machine to the input")
  • Multi-variable functions ("many input openings")
  • Composition of functions ("two or more machines attached together")