Another property of fractals is they have something called a Fractal Dimension where the dimension of the object is not a whole number like 1, 2 or 3 dimensions…but somewhere in between. In other words, the dimension of a fractal is a “fractional” number. That’s why they are called fractals, because the dimension that they “exist in” is a fraction. For example you can have a fractal dimension of 2.5 or 1.777 or PI for instance.

The fractal in this image is also generated using a small set of simple rules which includes scaling and translation (but no rotation). It has the properties of self-similarity (or self-sameness in this case) and scaling and its fractal dimension is measured to be the irrational number 1.58496... It's curious that this simple fractal has an irrational number as its fractal dimension. In fact, I believe that all real fractals that exist must have irrational fractal dimensions and I'll get into why I think this a little later.


If our universe is a fractal, then I wonder what its fractal dimension is? Since PI is an irrational number, I would hazard a guess that our 3+ dimensional universe has a fractal dimension of PI (3.1419265…).