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!
Aztec Gold.
Watercolour on Gessoed Paper.
20×20″.
$650.00.
Artist Lianne Todd
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.
Hot Frost.
Watercolour on Aquabord.
6×6″.
$175.00
Lianne Todd
Turbulence & Bubbles.
Watercolour on Gessoed Paper.
20×20″.
$650.00.
Lianne Todd
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.
“Stardance”. Watercolour on gessoed paper. 20×20″.
$650.00
Lianne Todd
“Particles and Fields”.
Fractal Digital Art on Metal, single edition print. 20×20″.
$345.00
Lianne Todd
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.
Often, when I’m voyaging through the through the little fractal universes I have generated using the software which I am so thankful exists, I encounter ‘places’ that look like they belong in an illustration for a book I’ve read somewhere along the way. I also encounter characters that look like they belong in those places. Such was the case for this piece:
The Mage Emerges
Digital Art Printed on Metal, single edition
24×24″
SOLD. Private collection.
Artist Lianne Todd
Congratulations to the European Space Agency, and to all of humanity, for boldly going where no one has gone before… for landing the human-built robot Philae on a comet!!
This is truly a historic moment and an example of how our imaginations can lead us to realities our ancestors may have considered impossibilities. It will lead to a greater understanding of our solar system and of the universe.
In honour of this event, I’m posting my piece called The Landing. I can’t think of a better day to do it! It’s purely imaginary, constructed of three different fractals, and belongs in the realm of fantasy or science fiction. But then, not so long ago, so did landing on a comet…
The Landing
Digital Art printed on metal, single edition
20×20″
Artist Lianne Todd
SOLD. Private Collection.
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?:
Nebula Negative I
Watercolour on Yupo
10×10″ (sold)
Lianne Todd
Nebula Negative II
Watercolour on Yupo
10×10″ $125.00
Lianne Todd
Negative Nebula III
Watercolour on Yupo
10×10″ (sold)
Lianne Todd
Negative Nebula IV
Watercolour on Yupo
10×10″ (sold)
Lianne Todd
Here is what they looked like at the exhibit:
Curious to know what they do really look like when you invert the colours?
Non Negative Nebula I
(the inversion)
Lianne Todd
Non Negative Nebula II
(the Inversion)
Lianne Todd
Non Negative Nebula III
(the inversion)
Lianne Todd
Non Negative Nebula IV
(the inversion)
Lianne Todd
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!
I touched earlier on the aspect of self-similarity on smaller and smaller scales in fractals. I find the ones that are exactly the same on smaller and smaller scales a bit boring – like the Koch snowflake or the Sierpinski arrowhead or the Menger sponge (though it has a nice surprise). It’s the fractals that take on the slightly chaotic characteristics of nature that are the most interesting, and which stimulate the most thought about how this whole complex universe of ours developed.
The series I am presenting to you here does not really look like something you would find in nature, strictly speaking, (except for the parts that look like peacock feathers) but I thought it lent itself well to the illustration of self-similarity while emphasizing the variation. And because it already included elements of a human game, why not present it as a game?
The series is called “The Ball Went Over the Fence”.
Up until this point, you have probably looked at the fractal images on this site and you’ve detected the self-similarity, but what you maybe haven’t seen is what happens when you travel into a fractal. You can’t properly zoom in on a fractal without the equipment to do so – i.e., the software which allows you to make the fractal in the first place, or a video or .gif someone has prepared that takes you through it. When I say travel into a fractal, I mean precisely that – it resembles exploring a new realm. You enter the realm, you set your sights on a distant object, and when you get there, your surroundings have changed – you know you’re in the same realm, because it all looks familiar, but that which was tiny is now large and detailed, and you can see off into a new distance. You set your sights on that, and continue on your journey…. and you can keep doing this over and over again for a long time, depending on how many iterations of the formula you’ve rendered.
So I travelled into this fractal I created, and I stopped along the way and saved some images. The game is for you to try to figure out where I zoomed in to get to the next image. Give it a shot. In a couple of days, I’ll edit this post with the key at the end so you can have the answers. Hint 1: the orientation of the image doesn’t change. Hint 2: Some of these are a lot easier to find than others. Also, the first two images will open larger if you click on them, but the rest are locked at their size. (They are all scaled relative to their actual artwork size). The key at the end will open larger so you can see more clearly.
All images are watermarked and copyrighted.
The Ball Went Over the Fence 1, Lianne Todd. Original Fractal Digital Art, single edition print on metal, 28×28″ $550.00
The Ball Went Over the Fence 2, Lianne Todd. Original Fractal Digital Art, single edition print on metal, 20×20″ $345.00
If you are having trouble with the first two, try looking at #2 and #3, this is the easiest solution of all of them.
The Ball Went Over the Fence 3, Lianne Todd. Original Fractal Digital Art, single edition print on metal, 16×16″. SOLD. Private Collection.
The Ball Went Over the Fence 4, Lianne Todd. Original fractal digital art, single edition print on metal. 12×12″. SOLD. Private Collection.
The Ball Went Over the Fence 5, Lianne Todd. Original Fractal Digital Art, single edition print on metal, 8×8″. SOLD. Private Collection.
And now, as promised, the key to where the zooms took place – a map through the series:
Zoom Key, The Ball Went Over the Fence series
FractaLiArt 