Further Fractal Frenzy

OK, you may have noticed I’ve been focused on the fractals lately. This is a hallmark trait of ADD known as “hyperfocus”, in which an individual who usually can’t pay attention the entire way through the sentence “Dave, do you think you could please take the trash out when you get a chance?” can suddenly, miraculously, spent hours or even days completely obsessing on a topic of interest. I would like to take this opportunity to apologize on behalf of all my fellow ADDers to all of our friends, coworkers, and life partners,  for whom this trait invariably produces fits of apoplexy. Sorry guys, we’re really not deliberately ignoring you, it’s just that OMIGOD LOOK WHAT THE IMAGE DOES WHEN I DO THIS TO IT!!!

I’m sorry, where was I?

Oh, yeah, the fractal thing.

While the artwork I am producing may not be “fractal” in the strictest mathematic sense, I am using concepts that I gleaned from my studies on fractal geometry. I am creating complexity from relatively simple images by repeating, scaling, flipping, and rotating them, then producing further complexity by layering them one atop the other, with the layers reacting to the layers beneath them in different ways.

A concept that I did not mention in my earlier posts is that one quality of fractal objects is that they exhibit “self-similarity across scale”. This is a fancy way of saying that if you look at a small portion of a river, say a creek or other tributary, it will have a shape that looks very similar to what you see when you zoom out and look at the river as a whole. If you look at a single branch of a tree, you may see that the way the smallest branches divide looks very similar to the way the main branches divide from the trunk. Repetition and alteration of scale of a simple pattern achieves the same self-similarity in my fractal-inspired pieces.

Here are two pieces I did in the last couple of days, one being a self-contained piece, and the other designed for some iterating into different versions. I tried for something a little more painterly than the strict geometry of the “Kaleidomorph” series.

First, the self-contained piece, “Spiral Intersection”. I started with a drawing of some spiral roll forms, which I colored in. Then I duplicated the image on several layers, which I flipped and/or rotated to change their orientation. Next, I set up the layers to react with the other layers, experimenting with different settings until I found something I liked. Finally, I painted over portions of the image on a final top layer, to isolate the parts I liked and create the impression of a figure on a ground.(you can see it’s got a little of that Cubist flavor that I love so well.)



I created “Echoes 1” using techniques similar to the ones I used making “Spiral Intersection”.

Echoes_1webI then made a merged copy of the final “Echoes 1” image. I rotated, flipped, and scaled it, and set it atop the first image. I played around with different ways of making the two layers interact, and ended up with “Echoes 1A”.

Echoes_1AwebI liked this image for its added complexity, but I wanted to see if I could make a lighter version, with a bit better color range. This is the result, “Echoes 1B”.

Echoes_1BwebAlthough I like the way the results look when I print them out, the colors are not quite as brilliant as they look onscreen – doubtless an issue with color gamut (meaning that I have colors in the file which will show onscreen, but the printer is unable to produce that color on paper). I hope to figure a way around that; it will probably involve having to work in something like Photoshop, as Procreate (the iPad program I made these pieces with) does not give one much control over the color space. That is NOT a knock on Procreate…I paid less than $10 U.S. for it, vs the $120 a year that I pay for the privilege of access to Photoshop, and it is far and away my favorite art-making app on the iPad, as you can see by the number of pieces I have created with it that are featured on this blog. Shout out to the Tasmanian devils at Savage for their excellent product! Learn more about it here:


Thanks for visiting! Please take a moment to share your thoughts below…


Kaleidomorph 2 – More Iterations

Here are a few more iterations of the Kaleidomorph 2 file. As I discussed in my last post, this is a file with multiple layers; it generates different images depending on which layers are turned on at the time, yielding a very large number of potential images.

I have developed a naming protocol that identifies the active layers used to make each image. The name of each image starts with the artwork name (in this case, “Kaleidomorph 2”), followed by a space, after which each active layer is listed, separated by a dash.

For example, this is “Kaleidomorph 2 1-4-7-11”. Note its similarity to an image from the last post, “Kaleidomorph 2 1-7-11-13”. They both have layers 1, 7, and 11 active, then each has one other layer added, layer 11 in this instance.


Here is “Kaleidomorph 2 2-3-5-7-10-11”.


Turning off layer 10 from the previous image yields “Kaleidomorph 2 2-3-5-7-11”.


And here’s one I especially like, “Kaleidomorph 2 6-7-8-13”.


To see all these images together with the ones from my last post, head over to my Artist’s Page on Facebook:


Look under “Photos” for the album, “Kaleidomorph 2 Iterations”. I will add more images there if I do further iterations.

I’d love to hear your thoughts on these images! Which one is your favorite, and why? (don’t worry, there won’t be a quiz later!) 😉


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?