I think `trhway above has it right. A 2.1 dimensional fractal would be very much like a bumpy sheet in 3-space. A 2.9 dimensional fractal would be a fairly conv

I think `trhway above has it right. A 2.1 dimensional fractal would be very much like a bumpy sheet in 3-space. A 2.9 dimensional fractal would be a fairly convoluted crumpled sheet. [0] You'd be amazed how much of the fractal stuff is practical. You don't need to deal with infinities before it becomes useful. For example, fractal antennas can filter for multiple frequencies well (instead of tuning for just one perfectly)[1]. On this topic, check out space-filling curve - it's pretty cool stuff, and the wiki page has a nice diagram of the Peano curve[2]. It's sort of like imaginary numbers. At first glance they seem like a very theoretical construct, but it soon becomes apparent they're everywhere. You can't hardly do any sort of electrical engineering with out them. Likewise with fractals (and the oft associated field of chaos). [0] http://en.wikipedia.org/wiki/Fractal_dimension#Introduction http://en.wikipedia.org/wiki/Fractal_dimension#Introduction See paragraph 3. It makes intuitive sense as you see a 1-dimensional line fill the space of a 2-dimensional plane. [1] http://en.wikipedia.org/wiki/Fractal_antenna http://en.wikipedia.org/wiki/Fractal_antenna [2] http://en.wikipedia.org/wiki/Space-filling_curve http://en.wikipedia.org/wiki/Space-filling_curve EDIT: whoops, missed a reference. (And sorry they're all Wikipedia - there's a ton of great material on this stuff. Many books on chaos will talk about fractals extensively, but the best don't shy from the math!)