I have been interested in fractals and fractal geometry for some time now. A very simple explanation of fractal geometry is that it is the mathematics that explains how the shapes we see in nature – mountains, trees, rivers, animals – get their shape. A less simple explanation is that it is the geometry of regular, but non-repeating, patterns. This is why all oak trees look very similar, but no two are exactly alike…they are expressing a regular, but non-repeating pattern, that can be explained by the concept of fractal geometry.

Now before you run away in terror that I’m about to start going all “math” on you, and I’m gonna start spouting highly technical gibberish, relax. I don’t know anything more about the math of it than you do (unless you know about the math of it, in which case you are miles ahead of me).

The general concepts of fractal geometry are what excite me, and what I use as the inspiration for my “fractal art”. One basic concept is that complex systems (like an oak tree) can arise from a very simple type of formula, repeated A LOT of times (known as “iteration”). You take the answer that you get from the formula, plug it back in, and run it again, over and over and over. Eventually, voila… you got you an oak tree! [WARNING: VAST OVERSIMPLIFICATION].

OK, I can see that I am losing your interest already…let me get to the art part. I have been experimenting with building biologically-inspired forms, what I call “biomorphs”, constructed of shapes which I vary slightly in contour and scale, and combine into larger shapes. From simplicity, through iteration, to complexity.

I got the idea to start getting more complexity by layering these shapes in an image editing program (such as Photoshop), then changing how the layers reacted to one another…different settings such as Overlay, Subtract, Exclusion, etc. all make the layers do different things based on the layers beneath them. When you stack up several layers of different shapes, with different settings, you can get some very interesting results.

What I did for my second Kaleidomorph (kaleidoscope+biomorph) was to start with a simple shape. Here it is, repeated twice, in a very early stage of the process:


I then started to build up more complex shapes from this basic shape. I did this on a total of thirteen layers in my piece titled “Kaleidomorph 2” (there was a crude earlier experiment from some time back which I decided was the first Kaleidomorph). As I mentioned before, I put different settings on the layers to make them react differently in response to the other layers.

OK, this is where it gets really good. By trying out different combinations of the layers (iterating again!), I was able to generate several images from this one piece:








Yes, that’s right folks… all these images came from that one simple shape – copied, flipped, rotated, and scaled, then stacked into interacting layers. The different images are just different combinations of those layers. As I stated earlier, I am not particularly gifted in mathematics or science. I do know that with 13 layers, each of which can be on or off, and the ability to combine as few as two or as many as thirteen of them, that the total number of possible images is…ummm, let’s see…approximately a Metric F*ck Ton! (if you are reading this, and are good at math, I would love to know a more accurate number!) I don’t even know if it would be feasible to see every particular combo…certainly not by manually trying out different combinations like I did here.

I am very excited about this new development in my fractal art! I am looking forward to taking this even further. I would love to be able to get a program where I could have these layers rotating, and randomly switching on and off, to produce an ever-changing piece of dynamic art. Unless that program already exists, though, I am not likely to come up with it on my own. 😦

What do you think of these pieces? Do you consider it “cheating” to get this many images from one artwork?


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