(I do not speak English. Please, excuse my bad grammar.)
This is about fractals over the real line, composed of points or segments inside the real line.
If the integers set is a fractal with dimension D=0, and the real line is a fractal with dimension D=1, then is possible to continuously vary the dimension D from the integer set to the real line set? (making some continuous figure in the plane)
There is a drawing of all the fractals side by side? (something like this image)
I do not mean that all the fractals make one larger fractal, but just that for each value D there is one fractal over the real line with that dimension, and all the fractals "touch each neighbor" continuously.
In other words, I want to continuously transform a fractal, from the integer set to the real line, by continuously changing his dimension D from 0 to 1.