I haven’t written in a little while but I now have some great news for followers in the area who haven’t had a chance to see my fractals in person yet. I am showing those that are left (31 pieces) at the Station Arts Centre in Tillsonburg for the month of March. The show opens March 6 (this Friday) at 7-9 pm. It runs until April 7. The show is called, this time, A Fractal Universe. Come land in it!
I have mentioned a few times in previous posts about fractal images often being archetypal. I’m not really sure I was correct in describing them that way, but what I will say is that they often look familiar in a way that transcends their immediate translation into a real object. For instance, when I first looked at this fractal image, I immediately thought of the Aztecs and the patterns they incorporated into their art forms. Having now looked at some Aztec art in more depth, I’m not even sure why I thought of them, other than the feather motif and the colours. That’s just what immediately came to mind. And I have other fractal images created (not shown here) which really speak to me of Native American blanket patterns. Others might look at this piece and be more immediately aware of the hourglass shape. Maybe you will look at it and see something else entirely.
My point is, from near the beginning of humanity, we have been making patterns, whether or not they were drawn with a stick in the sand, sculpted along the edge of a stone building’s rooftop, painted on a cathedral ceiling, or digitally on a tablet. Possibly for 60,000 years, we have been making patterns! And if you look at all the patterns we have been making, you may notice that many of them are self-similar on smaller and smaller scales. We were making fractals and we didn’t have a name for what was common to them all. And we didn’t have a concept of the way fractals were involved in the geometry of nature – not consciously, anyway. Maybe we were consciously inspired by nature, but didn’t recognize that specific aspect of it. Only for the last 30-40 years have we, thanks to Mandelbrot, come to an awareness of this common denominator. I like the way fractals connect all of humanity over time, and the way they connect us to nature. I’m really looking forward to exploring this with future pieces!
Examples of fractals in biology are not difficult to find, and indeed if the universe is fractal, there should be a fractal component to all biological forms. In the post entitled The Photographs, in which I have captured some natural fractal forms, there are at least five forms which are biological. In the post entitled Butterflies and Moths, there were several digitally generated fractals which just happened to look biological. Anyone who has looked up the word fractal has probably been given the example of the fern, or the romanesco, or even the tree. In fact, people can create extremely realistic looking plants using software that takes advantage of fractal geometry. Our lungs, and our vascular systems are obviously fractal in nature. Ever looked at a sea slug? Beautiful little fractals.
When I create my fractal digital art, and sometimes watercolours, I don’t try to make things that are biological, but I recognize natural forms when I see them and they pop up on their own all the time. The fact that I’m not making them on purpose somehow speaks to my scientific side, and relates them to evolutionary theory. I talked about this a little bit in The rose and the creation process as well.
These two pieces are examples which are maybe not as obvious as the butterflies but do remind me of biology just the same.
If I am postulating that the universe is fractal in nature, it makes sense that structures formed by molecules behaving in their natural way should be recognizable as fractals. Such is the case with frost, turbulence, and bubbles. Just do a little Google search with each of those terms alongside fractal, and you’ll see what I mean. Mandelbrot made groundbreaking progress modelling turbulence, which had confounded mathematicians before him, using fractal geometry.
It also makes sense that in my random wanderings through the fractal universes I create, I encounter images that remind me of these phenomena. Such is the case with these two fractals which I chose to paint. I especially like the way the bubbles in Turbulence & Bubbles look like they are in the process of being blown, sometimes from multiple locations, and melding together when they meet, just like real bubbles would.
As you may know, if you have been reading all of my blog posts, I like to dabble a little in cosmology. Not that I really know anything about it, but it fascinates me, and I like the kind of abstract thought it stimulates. I was given a Great Course one Christmas on Dark Matter, Dark Energy, The Dark Side of the Universe, which I’ve enjoyed a great deal. Dr. Sean Carroll is great at explaining cosmology in a way that I, at least, can understand. I also read Brian Greene’s The Hidden Reality, a fascinating book. I subscribe to many Facebook Pages which post news about the latest pieces of knowledge in this field. The abstract thought appeals to me, and I think I’m pretty good at it, but my math and physics skills are limited to helping out my children when they were doing grade twelve homework. Which may be nothing to sneeze at, but is less than what is required for particle physics.
One of the things that really strikes me, is that the visual components, be they illustrations or actual data translated into an image, of almost every piece of news in cosmology, are recognizable to me as being fractal in nature. Perhaps it is because I’ve spent so much time looking at fractals, zooming in, and examining them from every angle, that I notice this. I am always mystified when no mention of fractals is made, in these cases. I’ve written a whole post (and another) about fractal dimensions before, so I won’t go into that here, but that’s another part of the puzzle I like to think about.
I know these two fractals don’t really illustrate anything in particular, but they make me think along the lines of particle physics, and stardust, and the early universe.
This past summer, during my exhibit, I was told about a person in the same city (London, Ontario) who, it seemed, had a lot of the same thoughts I was having about the fractal nature of the universe. She is a software engineer and has been studying fractals for much longer than I have! Needless to say, her math skills are much better than mine. I was fortunate to meet her (her name is Lori Gardi) this fall. She has two websites, the first of which I’m going to direct you to Here, in which she has laid out some of her thoughts in a pretty clear way. I’ll link you to the more recent one later… I think it’s a good idea to start at the beginning of her thought process. We (artists, software engineers, mathematicians, physicists, philosophers) may not all have the same thought processes or reach the same conclusions in our explorations of fractals and their role in the universe, but all avenues should be explored as long as they can exist within the rules that have been truly established by scientists and mathematicians in the past. I am, unfortunately, not capable of judging whether anything follows those rules, but others who can, need to at least look at this work with an open mind and decide for themselves. ESPECIALLY if it may help solve any of the mysteries still out there.
This series of four paintings was an experiment. Not a very scientific one but I did try to control variables and make predictions. My hypothesis was that since all pigments are different in their molecule size, shape, and hydrophilic and hydrophobic qualities, they would all move differently through the medium of water, and as they interacted with each other, and that their movement would be fractal. In other words, I expected them to appear, at the end, as if they were something like a cloud, or some other natural item that is already known to be able to be modelled using fractal geometry. A coastline, for instance.
All four pieces were executed and controlled in the same way (I won’t give away all my secrets!), the only differences being the pigments I used and the order they were used in. I tried to reduce the effects of gravity by levelling my table but it is kind of obvious there was a tiny bit of gravitational effect. I changed the orientation of the final products so that when they were hung together, it would be aesthetically pleasing. Other than that, the results you see here are basically the raw data.
I called them Negative Nebulae, because I looked at all the white space around them and imagined if it was black, and the colours were reversed, they would look a bit like those photos you see from NASA of distant nebulae. In other words, these would be like the negatives of those photos.
Here they are – what do you think?:
Here is what they looked like at the exhibit:
Curious to know what they do really look like when you invert the colours?
On the third weekend in November, every year, we hold a studio tour in my town. Otterville is a historic town located in Southwestern Ontario, Canada. This will be our 18th annual studio tour – we call it Welcome Back to Otterville – and every year the stops on the tour change slightly as the artists in town do. This year, there are eight stops on the tour, so it will be really easy to drive out, see all the stops, and return home if you live in, say, London, Kitchener/Waterloo, Stratford, or the western part of greater Toronto. It takes me less than an hour to drive to London, and about two hours to downtown Toronto, exactly an hour to Stratford. We aren’t on any major highway, but if you want directions please contact me and I’ll be happy to provide them.
If anyone reading this has been to my studio before, you will find this year quite different as I will be featuring my fractal work prominently. In fact, in the next few weeks I’ll be taking down all the art in my gallery at the rear of my house, and completely rearranging the walls to maximize the display. I always serve a lovely hot spiced cranberry punch during the tour, and I’m looking forward to the taste of it myself!
My gallery and studio are actually open all year to anyone who calls ahead or happens by on an afternoon when I’m home. I’ve just put a new sign out front (the old one suffered from weather damage) so you can easily find my location which is right on the Main Street downtown, just a few houses away from the historic mill and waterfall. Look for the yellow flags when you get here and use the map on the postcards (available at each stop) to help.
Here is some information for the tour, and a few photos.
If you find our Facebook page and “Like” us, or any of our posts, we would really appreciate the extra advertising and traffic that provides us – as you can imagine we are on a limited budget and every bit helps!
This is just one of my favourites. It’s only little, 6×6″, but like most fractals it took a long time to paint. So many tiny little fried eggs! It’s framed in a black lacquered shadow box frame so that it floats in the frame. The total size, frame and all, is roughly 12×12″.
Yet again, we see a natural shape. Well, natural, in that we are natural and we naturally like to fry eggs. Sometimes I find that it isn’t so much the repetition on smaller and smaller scales that makes me think of natural objects or phenomena when I look at fractals, but the shape that is being repeated.
As usual, it’s copyrighted and watermarked.
Those who have been following my art for a few years may have seen these three before. They were the only pieces I had allowed the public to see, prior to holding The Fractal Nature of Our Universe exhibit this summer. I entered them, in 2011, in the Los Alamos MainStreet Science and Math-Based Art Contest. I wish I had saved what I wrote about each of them then, but while the images are still out there on the web as a result of the contest, the statements I made about each of them are gone. Perhaps it’s for the best – this way each viewer can interpret the images themselves. The wonderful thing about fractals is the way they translate pure mathematics into something that appeals to – well, it feels to me anyway – something ancient in our minds. They are often archetypal. As such, I think they can bring us all together as humans. We need something to unify us, don’t we? So I will leave interpretation out… for while inspired interpretation as an individual is wonderful, sometimes expressing that interpretation divides us from those who would interpret differently.
This was the first fractal piece I ever created – The Way.
Fire Dance and Happy Hill were the second and third pieces I created (but I can’t remember which was second and which was third!)
Here is what they looked like at the show (on the left):
And here is a detail of The Way: