It’s a little known fact that before Mandelbrot first pioneered his work on fractal geometry in the 1970s, Douglas Hofstadter first stumbled over the phenomena while working on problems in Number Theory.
During the 1960s, Hofstadter discovered a family of graphs that exhibited a specific kind of discontinuity. Hofstadter dubbed the main graph INT. The graph of INT(X) contains infinite many distorted copies of itself.
INT(X) is discontinuous at all rational values of X, but continuous at all irrational values of X.
