To go along with my other fractals: Tikz Fractal - Cantor Dust and Tikz Fractal - Menger Sponge, which you lovely people have helped my create, I would like to construct a "uniform Cantor set".
The construction is as follows:
Take the unit interval [0,1] and at each stage replace each interval with (a fixed number) n intervals of length less than |I|/n, where |I| is the length of the interval, and where an end point of the each of the subintervals coincides with the end point of its 'father' interval.
Here is a picture to try to make my shoddy explanation a little clearer:
The standard middle third Cantor set is where n=2 and |I|=1/3:
Short of working out all of the length and spacings, how can I construct this "automatically"? My thinking is that I should use a linedenmayer system but I have not done this for line segments before.