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Fractal Function

Let F(x) be a non-decreasing function for all x in [0 1], such that

2F(x/3)=F(x) and F(x)+F(1-x)=1

1. Find F(173/1993) and F(1/13).

2. If possible give a general algorithm to find F(x) for any x.

Other questions:

3. Is F(x) uniquely determined(in [0,1])?

4. Is F(x) continuous(in [0,1])?

Source: unknown

Click here for the answer.

Internet references

Wikipedia: Cantor function 

Cut-the-knot: Cantor Set and Function -- A continuous function may grow considerably virtually without changing.

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