If it was bottom up developed, it would be adaptive, and therefore not a computer as such. Adaptive systems manage to handle new input (or fail). The computer is only going to do what it's been programmed (however poorly) to do.
One of the things required for computation is predictable repetition - same inputs, same outputs. This is why error recognition/correction is so important for things like physical ram and ethernet packets - it's effectively trying to filter out any bottom up behaviour that could affect the environment of the computation/information transmission.
An ever so slightly different environment would affect the same inputs in a bottom up system - think along the lines of butterflies affecting weather systems by flapping their wings.
You could claim everything that happens is a result of 'some computation' but then you end up in semantic arguments how to define 'life' (or how to define what's 'computable', which is it's own entire problem). A couple of books from back in the day in my life relevant to this were these two, and they're still probably a good place to consider things from even today.
The Ur example of a bottom up computer would be the brain. It works on disparate unformatted inputs and can translate to a context appropriate output and while there's no programming language for the mind (unless you want to stretch a bit and say speech) you can instruct one in the particular ways you want input manipulated into outputs.
