Fractal Dimensions

This post is going to be a little different.  Let me start by stating the obvious:   I am not a cosmologist.  Nor am I a physicist.  What I am is a person with a lot of time alone to think.  I have that chance to see the forest without the trees getting in the way.  I could have once called myself a scientist, maybe, and perhaps at heart I am as much a scientist as I am an artist.  But then, the two are very closely related.  Observation, appreciation, pattern recognition, attention to detail, pursuit and expression of ideas, and sharing those ideas with the world are all very important to both.  Basically, science and art seek to reveal the truth.  One main difference is that science tests the ideas to see if they are, indeed, truth.  In art, it remains a question.

So.  I have an idea, and I am hoping some physicists will test it out someday and say that I was right.  I’ve been casually exploring fractals now for about a year and a half.  My comprehension of the math is certainly minimal – what I’m really interested in is the images themselves.  Since I’ve been studying them, I now see fractals everywhere I look.  I really mean everywhere.  And also, when I look at the fractals I create with the lovely programs I use, I see the universe.  I know I’m not the only person who sees this.  I even see what I recognize as generated fractals being used as illustrations in scientific documentaries for concepts seemingly unrelated to fractals.  Which brings us to my idea.

In their quest for the grand unified theory of everything, physicists do a lot of math.  For this, I have the utmost admiration and respect for them.  When you study biology, as I have, you realize much of it is chemistry.  When you study chemistry, you realize much of it is physics.  When you study physics, you realize it all comes down to the mathematics.  Having done the math, they have realized there is something missing.  Well, six things actually.  Six extra dimensions would make string theorists very happy.  (I would like to thank Dr. Brian Greene, here, for his book “The Hidden Reality“.)   We are accustomed to three-dimensional space, and we have realized time is also a dimension, but it turns out there should actually be ten dimensions.  So, they’ve been trying to figure out what these are.  I’m not going to go into what they have come up with, except to say that it hasn’t given them an answer to this particular question.  My main argument for why it hasn’t would be that it seems like they are still using three-dimensional space to describe or define the extra dimensions.  We don’t really use any of the four known dimensions to describe each other, do we? And what if we are thinking of dimensions all wrong?  Most of us think of dimensions as things that can be measured, right?  But wait – how long is a piece of string anyway?  What if we should be thinking of dimensions as just “a way for something to exist”.  For instance, something can exist by taking up space.  Something can exist through time.  Something can exist as a fractal.  Think about it.  Maybe, instead of the extra dimensions being all around us but too small to be seen, they are all around us and we just haven’t recognized them as dimensions because we’ve been defining dimensions in the wrong way.  Actually, I just looked up the dictionary definition of dimension, and it says that in physics, dimension is “an expression for a derived physical quantity in terms of fundamental quantities such as mass, length, or time, raised to the appropriate power”.  Interesting.  Mass.  Mass is measurable, and something can exist with mass.  But I digress.

Even though fractal geometry is fairly new (Benoit Mandelbrot passed away in the fall of 2010), the philosophy of “as above, so below” is ancient.  I am certainly not the first to notice that galaxies, hurricanes, and water going down the drain are all the same shape.  Not the first to suggest that from the tiniest particle to the largest expanse of the universe, a repetitive geometric law prevails.  But I think I might be the first to suggest this new way of looking at dimensions, and that fractals probably play a key part in the mathematics of string theory, and that maybe mass does too.  If somebody  has already published such suggestions, I would love to hear about it.  Well, Dr. Hawking? Dr. Greene?  What do you think?   That is my grand idea, and I think it’s worth spreading,  but it’s unlikely to end up as a TED talk.  Although I hope to do an exhibition of art exploring our fractal universe, this post is my best way of publishing the idea.  Maybe someday, some physicists will test it out and the paper will be in a scientific journal.  And if they do, I want my name on that paper!

One of the many portions of fractals I have generated. It is unedited from the form in which it was generated. In it, I see the same patterns we find in a piece of wood.

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2 responses to “Fractal Dimensions

  1. Benoit Mandelbrot himself spoke of fractals as dimensions – not in quite the same way, but as if they provided dimensions that are between the dimensions we think of. i.e., instead of something being 2D, or 3D, it could have a dimension(D) of, say, 2.3. I’ve been reading his book and still trying to understand fractals better.

  2. Please check out three of my fractal watercolour paintings at the link to the side, under ART, called Some different work… I hope to do a whole show in the near future.

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