Cantor sets seem rather bizarre because if each dot is made up of four dots ad infinitum , I'm left wondering whether there's anything there. The same is true of Sierpinski gaskets where a figure like a triangle is subdivided into sets of smaller triangles and so on. In two dimensions, this isn't really problematic, but Sierpinski gaskets can also be three dimensional where each hole is made up of holes again ad infinitum . It's best not to try an visualise these things in the real world. That guy Escher was bad enough.
Fractals can also occur in the real world.
Skin is a fractal as is the bark on trees or the coastline of a country. Geometrical fractals, on the other hand, have no such limitations, but can go on to infinity. Complex numbers Fractals like the Mandelbrot set depend on the behaviour of complex numbers . At a basic level, complex numbers are not difficult to understand because they're like latitude and longitude on a globe of the world, or like the grid references on Ordnance Survey maps or the co-ordinates of a graph. A complex number consists of two parts a real part and an imaginary part.