I'm not exactly sure whether this question belongs to this SE or not, but it doesn't seem to fit elsewhere.Say a process behaves in a deterministic fashion (that is, it gives the same output when an input is entered over and over again), then can we build it as an algorithm?; if not, can you think of a counter-example?, that is, a deterministic process which can't be modeled as an algorithm.
Does deterministic imply algorithmic?
algorithms
An algorithm must have a finite description, whereas a deterministic process according to your definition can use an infinite lookup table. For example there is a deterministic process that solves the halting problem for Turing machines, but there is no such algorithm.