I really like the Busy Beaver stuff. I wish I had been exposed to it (at lest enough to play with it some) in high school. It reminds me some of Jorge Luis Borges' story "The Library of Babel".
Does anybody know of other interesting problems in the Busy Beaver space?
Fictionally, maybe the Mandelbrot Maze mentioned in Arthur C. Clarke’s 3001:
> Their approach
was more subtle; they persuaded their host machine to initiate a program which
could not be completed before the end of the universe, or which - the
Mandelbrot Maze was the deadliest example - involved a literally infinite series
of steps.
I loved that part of the book. I thought it was so cool how they thoroughly scrubbed the Internet of these dangerous programs, and then stored the very last copy on a disk in an ancient lava tube on the moon, just in case.
Does anybody know of other interesting problems in the Busy Beaver space?