Is it possible?

Question

Can you have a computer code a machine thats building a computer that codes for another machine and so on.

Answer 1

You know how two mirrors work when they face each other, right. By the same logic, you write a code which compiles to produce a program which writes, compiles and runs itself, etc. It's perfectly possible, just redundant in most cases. Why would you want to create a bottomless pit with a vacuum in it which sucks everything up just for a moment of amusement.

Answer 2

Possible, just not yet.