Perfect square wave sounds

[Rob Strand]

'm still searching for any videos on Youtube to see any fuzzbox that is connected to an o'scope and then producing "perfect" square wave.

I doubt it will be perfect since the signals from a guitar are not 100% symmetrical.    In electronics if you want a square signal you try to extract the fundamental (using filtering and signal conditioning) then use that to clock a flip flop.  The output from the flip-flop is quite square.  A CMOS 4013 is very common.  The down side is the frequency is reduced by half.    The Blue-Box is one example of this idea but the signal conditioning isn't they great.   The Blue-box however modulates the square wave with the envelope.  One way to restore the frequency is to use a PLL but that's a different story altogether.