I have noticed that Gray code converted to decimal and plotted into a chart (for instance, 2 is binary 10, but in Gray code it's 11, 11 in binary is 3 so I plotted 2 to 3, and so on) give a fractal-like curve. Here is one with all the numbers that can be presented in a 7-bit Gray code (that is, integers less than 128):
So, I am interested, does that curve fit the mathematical definitions of a fractal?