Computers are good at following instructions, but not at reading your mind.
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Very nice idea to plot this as graphics. Very interesting (even in general).
Using linear-speedup and dynamic recompilation, one could write a quite fast Turing-Machine-Emulator. Would be nice if someone would do that - but well, not very useful, even for TCS meanwhile. Still, this problem is not bound to Turing-Machines. In fact, something similar can be defined for any turing-complete Programming Language. And even for weaker (or stronger) machine models this type of problem (namely giving some upper bound of the time a program runs) can be formulated - thats basically what the ackermann-function is for loop-machines or typed lambda-closures. Basically, it is equivalent to the Halting Problem.
@Casey: The Tape of the Turing Machine can content 0 and 1. Initially, infinitely many 0's, but the algorithm can write 1's on it. Should be clear then.
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