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The Experiment
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
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Open Studio/Gallery
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!
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A Game of Ball
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
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Fried Eggs
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.
Fried Eggs
Collection the Artist Lianne Todd
Watercolour on Aquabord
6×6″
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Patterns
This piece is called Looking Through.
“Looking Through”
Digital Art printed on metal, single edition
20×20″
$345.00 Artist: Lianne Todd
Looking through what? A microscope? A telescope? A porthole?
In a fractal universe, it doesn’t really matter. Similar patterns are present on multiple scales. Use your imagination!
This image is actually a combination of fractals – one for the thing we are looking through (the self-similarity on smaller scales provides the illusion of perspective and depth here), and one for what we are looking at (this is a flame fractal – more about them later).
As illustrated here, fractal geometry is quite versatile. I’ve seen some discussion on ‘true’ fractals versus ‘near’ fractals and I would like to address that here for a moment. There seems to be an opinion out there that for a fractal to be ‘true’ it must be a)infinite and b)exactly the same no matter what scale you look at. Having read most of Benoit Mandelbrot’s Fractal Geometry of Nature, I have a problem with these stipulations. First of all, the equation for Mandelbrot’s set is 
, with n as the number of iterations, where c is a complex parameter.
There is more to explaining the Mandelbrot set than that, of course, but that is the equation, and if n is a given number, then it’s not infinite, is it? Perhaps the possibility of an infinite number of iterations exists, but that’s an argument for another day.
And even Mandelbrot’s set is not exactly the same on multiple scales. The PATTERN is there, it’s just slightly altered at different scales. It is self-similar. This is one of the things which makes fractal geometry so suitable for modelling the universe.
In my understanding, there was never a suggestion by Mandelbrot, the founder of fractal geometry, that a “true” fractal had to be infinite OR exactly the same on multiple scales. Rather, a fractal is strictly defined as “a set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension.”
So, perhaps I’m getting it all wrong, but if you would like to argue I would welcome your discussion.
And now, because I was once a biologist and if you’re anything like me you need a more highly magnified look at that thing, here is a zoom of what you were “looking through” at:
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Butterflies and Moths
Insects, and particularly butterflies and moths, are recurring motifs that I often encounter when I’m creating fractals. Sometimes, it’s just the simple shape, and other times it seems to be a whole detailed creature. Sometimes it’s done with what I call the ‘regular’ fractal generator and other times with the flame fractal generator (more on those differences later). If a mathematical formula iterated over and over by a computer can randomly generate images like these in a matter of minutes or hours, imagine what the physical forces of nature and a few billion years of evolution can do with a periodic table of elements (and, shall I say, an underlying fractal structure?). Oh wait, you don’t have to imagine. You can go outside!
(All images are watermarked and copyrighted)
Butterfly Hub – Artist Lianne Todd
Digital Art printed on metal, single edition
20×20″
$345.00
Detail of Butterfly Hub
Butterflire – Artist Lianne Todd
Digital Art printed on metal, single edition
20×20″
$345.00
Detail of Butterflire
Mother of Moths – Artist Lianne Todd
Digital Art printed on metal, single edition
12×12″
SOLD. Private Collection.
Pollinator – Artist Lianne Todd
Digital Art printed on metal, single edition
16×16″
$240.00
A thumbnail of the raw generated fractal – just to illustrate part of the process.
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Some of the early ones.
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.
The Way
Watercolour on Paper, 20×20″
Lianne Todd
$650.00 framed
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!)
Fire Dance
Watercolour on Paper
20×20″
Lianne Todd
$650.00, framed
Happy Hill
Watercolour on Paper
20×20″
Lianne Todd
$650.00, framed
Here is what they looked like at the show (on the left):
The Fractal Nature of Our Universe exhibit, East wall.
Lianne Todd artist.
And here is a detail of The Way:
Detail of The Way
Lianne Todd
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Publicity!
I made the news today – and while an actual review would have been nice, I will take free advertising without complaint! This article appeared on the front page of the Today section in The London Free Press, and I am grateful to them! Nice to be featured with these other excellent artists as well.
I have decided to post my own watermarked photo of the featured painting they chose for the article – it will give you a better idea of the colour. This is one of the five watercolours on gesso that are in the exhibit, and it’s called Colourfest. Like the others, it began as a digitally generated fractal, and developed from there.
Colourfest, 20×20″, Watercolour on Gessoed Paper. Lianne Todd
Another item of publicity is this video made by The ARTS Project. It was the end of the day we hung the show, so I hope I am not rambling too much in it. You can see Colourfest hanging behind me!
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The ‘rose’ and the creation process.
See the “rose” in the header of this blog? It’s a selected portion of one of the first fractals I ever generated, using one of the many programs available for such purposes. It was a completely random occurrence, really. I was playing around with formulas, and voila! One of nature’s most recognizable shapes, noted for its beauty, appeared before me. A little colour tweaking, some removal of extraneous image parts, and there it was.
This is the wonderful thing about working with fractals. It becomes readily apparent that mathematics is truly the language of the universe. The fractal rose is not one of the pieces of art I’ll be showing at the upcoming exhibit in London, but it symbolizes the exhibit very well, which is why I have chosen it for my promotional materials.
Mathematicians have spent a good deal of time and effort to demonstrate the fractal geometry of various parts of nature, tweaking formulas for the very purpose of modelling it. This has (in most cases) involved an analysis of natural shapes and distributions prior to the effort of coming up with a formula. I, however, am not a mathematician.
Most of my images start on a whim. I should qualify this with the statement that I am standing on the shoulders of the people who have created the software I use. Without their brilliance I wouldn’t be able to do any of this. So… my images start on a whim, and they continue with further whims (what happens if I change this?), and even further whims. The possibilities really are endless. If the image strikes me, I render it in high resolution and save it. Sometimes I save the parameters as well, sometimes I don’t. So, in a way, I am the natural selector, deciding which image survives, which parameters get passed along to the next selection process. It never ceases to amaze me how often I am confronted with an image that triggers recognition of something that exists in our universe – or at least, the universe within my imagination. These are the ones that are most likely to be selected for the creation of my art. The next step is the editing that occurs before I consider a digital piece finished (sometimes several images are combined into one piece), or, the painting of the image that I was inspired by. The paintings require a great deal of patience to execute. I draw them on the paper (or gessoed paper, or aquabord) freehand, but I start with very precise measurement of the positions of the largest features. I decide which pigments are best to represent what I like about the digital image, and if there is any element I don’t like and wish to change or omit. Then comes the sorting out in my brain of the pattern, and how it repeats on smaller and smaller scales, and exactly how small of a scale it is possible for me to keep painting this pattern. It is like a puzzle and I’m drawing the pieces and fitting them inside each other, to the limit of my brush size and my eyesight (and my resolve). The results are very satisfying but I am usually at the end of my rope by that point and have to switch to my traditional paintings for a while just to retain my sanity! This is one reason why this upcoming show is the culmination of three years of work.
Ultimately, all of my fractal art, digital or paintings, or photographs of nature, comes from the place in my brain where reality meets imagination. A place where the universe seems to reveal itself to the part of my brain that can imagine both its most vast and its most infinitesimal features, and how they relate to each other.
I hope my fractal art will trigger your imagination as well! Stay tuned (follow my blog please!) and don’t forget to save the date: July 8, 7-9 pm for the opening, and the exhibit runs until July 19, at The ARTS Project in London, ON. (See previous post for more info)
FractaLiArt 