A line has one dimension. A square has two dimensions. Fractals lie somewhere between the two. Fractals occupy more space than a straight line but they are not a solid surface. Think of a toddler with a crayon scribbling inside a square on a piece of paper. The scribble is all over inside the square to the point where it is approaching the dimension of the square's planer surface but not quite filling it.
Research shows that we enjoy looking at objects that have a fractal dimension. I created a fractal tree to create the fractal dimension.