The Cantor function g(x) is a weird function often used as a counterexample in analysis. It takes constant values on the middle third of intervals:                             g(x) = 1/2 for x ∈ (1/3,...

The Cantor function g(x) is a weird function often used as a counterexample in analysis. It takes constant values on the middle third of intervals:

                            g(x) = 1/2 for x ∈ (1/3, 2/3),

                            g(x) = 1/4 for x ∈ (1/9, 2/9),

                            g(x) = 3/4 for x ∈ (7/9, 8/9),

and so on. Royden (1968, p. 47) gave the following precise definition. Begin with the base-3 expansion of x = ∞ j=1 aj 3−j and let N be the index of the first-time aj = 1. Now let bj = aj/2 for j N (notice that bj is 0 or 1) and bN = 1, so that g(x) = N j=1 bj 2−j . The Cantor function is monotone nondecreasing and continuous almost everywhere, with a derivative existing almost everywhere that is zero, although the function goes from g(0) = 0 to g(1) = 1. However weird it may be, can you write an algorithm to compute g(x) for all representable numbers F ? Plot it on (0, 1). Does it appear as you would expect?