Originally posted by Malenfant:
AFAIK, Von Neumann machines are those that replicate exponentially. So an example would be something that makes two copies of itself, and each of those splits into two, and so on. So you start with 1 thing, then you have 2, then 4, then 8, then 16, etc.
Are there any biological organisms that do that? All I can think of are viruses and bacteria.
I'm not sure that that is part of the definition, but in any case biological organisms in general _can_ do that.
First of all, of course, where you have two sexes, your unit is a reproducing pair, rather than a single individual. That's no problem, conceptually. The actual structure of a Von Neumann machine is irrelevant at a logical/conceptual level.
So: a single pair can have four offspring (two reproducing pairs). Each of these can have four offspring, and so on. So the exponential effect still exists.
Now, of course, there can be errors in reproduction - mutation, not to mention problems of inbreeding(!) - but these are not obstacles at the abstract level.
Of course, any Von Neumann system will eventually run up against limits of energy and raw materials, and that applies to both biological systems and non-biological ones. So your exponential growth will eventually peak in a given context. Unless the population can colonise new areas...
Incidentally, your Von Neumann machines aren't inherently limited to only two copies, either, so your growth may actually be faster than the 2, 4, 8, ... sequence.
All good fun.