In some situations, a C compiler is run several times without any human input, getting a "better" compiler each time.
Fortunately (or unfortunately, from another point of view) this process plateaus after a few steps -- further iterations generate exactly the same compiler executable as the last.
We have all the GCC source code, but the only C compiler on this machine available is not GCC.
Alas, parts of GCC use "extensions" that can only be built with GCC.
Fortunately, this machine does have a functional "make" executable, and some random proprietary C compiler.
The human goes to the directory with the GCC source, and manually types "make".
The make utility finds the MAKEFILE, which directs it to run the (proprietary) C compiler to compile GCC, and use the "-D" option so that all the parts of GCC that use "extensions" are #ifdef'ed out. (Those bits of code may be necessary to compile some programs, but not the next stage of GCC.). This produces a very limited cut-down binary executable, that barely has enough functionality to compile GCC (and the people who write GCC code carefully avoid using functionality that this cut-down binary does not support).
The make utility runs that cut-down binary executable with the appropriate option so that all the parts of GCC are compiled in, resulting in a fully-functional (but relatively slow) binary executable.
The make utility runs the fully-functional binary executable on the GCC source code with all the optimization options turned on, resulting in the actual GCC executable that people will use from now on, and installs it in the appropriate location.
The make utility tests to make sure everything is working OK: it runs the GCC executable from the standard location on the GCC source code with all the optimization options turned on. It then compares the resulting binary executable with the GCC executable in the standard location, and confirms that they are identical (with the possible exception of irrelevant timestamps).
After the human types "make", the whole process runs automatically, each stage generating an improved compiler (until it plateaus and generates an identical compiler).
http://gcc.gnu.org/wiki/Top-Level_Bootstrap and http://gcc.gnu.org/install/build.html and Compile GCC with Code Sourcery have a few more details.
I've seen other compilers that have many more stages in this process -- but they all require some human input after each stage or two. Example: "Bootstrapping a simple compiler from nothing" by Edmund Grimley Evans 2001
http://homepage.ntlworld.com/edmund.grimley-evans/bcompiler.html
And there is all the historical work done by the programmers who have worked on GCC, who use previous versions of GCC to compile and test their speculative ideas on possibly improved versions of GCC. While I wouldn't say this is without any human input, the trend seems to be that compilers do more and more "work" per human keystroke.