# The Power of Fractal Dimensions: Infinity Within the Finite

I have been very obsessed with fractals lately, because I think they are very important!  I am learning a huge amount attending the delegate program for the Resonance Project right now.

Fractals are the idea that geometric shapes in our Universe are similar and repeated on the large scale.  I have used the example before of atoms, solar systems and galaxies being similar in structure, but this idea pervades nature.  Here is a great intro video that kind of got me started down this path:

But, fractals are able to accomplish and describe much more than this.  For example, since computers revolutionized the way that fractals are computed in the 80′s, they have been used to map virtual landscapes with much more realism.  That makes sense since I believe that fractal geometry very accurately describes what we see around us.  They are a perfect connection point between reality and “fictional” structures that we create.

Fractal computer rendering is a perfect example of the most important roles that fractal geometry fulfills.  Specifically, this is the idea that fractal patters are able to describe dimensions higher than that in which they appear.

An example that Jamie Janover gave in his Resonance Project presentation was to start with a circle.  If you embed a triangle and another it creates a star in the middle.  If we draw circles around each of these smaller triangles, we start to see a fractal pattern emerge.  This is the common flower of life that is widely discusses:

We can zoom in on any part of this fractal shape and it will continue to be similar to infinity.  So, what’s the importance of this example, and fractals in general, you may be asking?

This example of a simple rendering shows that we can represent infinite dimensions within a finite area (the original circle being finite).  I feel this is a vital tool that is used to describe reality.  Fractal geometry has shown in this way that we live within these infinite dimensions between three and four dimensions.

Along the same line of thinking is the idea that fractals are able to describe objects of higher dimensions compared to the media (or surface) that it is being described on.  In other words, when these fractal patterns are rendered on a two dimensional screen, a three dimensional (at least) object is represented.

Now, it’s time for one of my favorite things to do in the world: wild (and often reckless) speculation about fractals!

I like to think that we exist against the backdrop of a three dimensional (setting aside time for now) “membrane”.  If fractal geometry describes the structure of our Universe, can represent higher dimensions on their surface, AND describe infinite fractional dimensions, then I like to think that we are moving through time within an infinite amount of dimensions between three and four.

To extrapolate even more into our future, it may be possible that if we can someday fully understand and harness this structure of our Universe, we may be able to start studying, creating, or tapping into the dimensionality between four and five dimensions.

Again, this is wild speculation, and I have no idea what this would look like, but it’s fun to imagine!  Have a good one.