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, 20x20" Lianne Todd $625.00 framed

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 20x20" Lianne Todd $625.00, framed

Fire Dance
Watercolour on Paper
Lianne Todd
$650.00, framed

Happy Hill Watercolour on Paper 20x20" Lianne Todd $625.00, framed

Happy Hill
Watercolour on Paper
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.

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

Detail of The Way
Lianne Todd

Thoughts on fractals and dimensions

Back in 2012, when I had begun my study of fractals, and had begun painting them, I wrote a blog post on my other website, entitled Fractal Dimensions.  It contained my thoughts about the missing dimensions that some cosmologists would like to discover/elucidate in order to make sense of the equations describing String Theory.

While it may be a naive article to have written, given my minimal physics education, and I may be wrong in my approach, I do think there is still merit to the idea.  As it turns out, there is such an area of study as Fractal Cosmology, so I am not completely off the mark.  And since I wrote that post, I have read quite a bit of Mandelbrot’s The Fractal Geometry of Nature.  It turns out, (as I mentioned in my first post on this blog) fractal geometry is all about dimensions – specifically, a fractal is defined as:

A set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension.

i.e. every set with a non-integer D is a fractal, but a fractal may have an integer D

So, it has been established that much of nature can be interpreted or described using fractal dimensions.  Can ALL of it?  That is a big question.  And when we refer to fractal dimensions, are we referring to the same kind of dimensions that cosmologists refer to in String Theory?  I wish someone would tell me.

For now, and since I am an artist, I use what my eyes tell me.  In July of 2012, the Higgs Boson was finally found at CERN.  Here is a recent article referring to that discovery and its validity:

Check out the image in that article.  At the time of the discovery, I was already working on a painting based on this fractal right here:


Do you see the resemblance of the black parts of this fractal to the yellow parts of the collision image?  Not a proof, by any means, but it makes you wonder.

Here is the finished painting, which was beside me in the video I posted in “Publicity”:

The Higgs Boson Collision

I think this may be the first time I’ve shown both a digitally generated fractal and the painting based on it, at the same time!

More thoughts another day… it’s thundering a lot outside and I could lose power any second!


First of all, thank you to everyone who made it out to see the exhibit at The ARTS Project in London.  It was so nice to see friends, family, and new acquaintances, when I was occasionally there, and share my art with you.  It was also very nice to see some comments in the guest book from very old friends who I hadn’t seen in quite some time! And new friends too!  (You all know who you are!).  If you did get to the show, and didn’t see me or sign the guest book, I would love to know.  Please comment below, or send me an email.

Today I’m going to share one of my very favourite pieces, a metal print called Phoenix, in case you didn’t make it to the show.  I’m choosing it first for two reasons: 1) It isn’t what those who are only a little familiar with fractals might imagine when thinking of fractal art, and 2) It is a prime example of the way a metal print shows off the digital art I have created.

I will let you first refer to this photo from the opening night.  See the piece second from the end on the long wall?  The one that doesn’t look like anything?  That’s Phoenix.  It’s actually quite dark, and from the angle of the camera, the lighting isn’t picking up the image.  That’s one of the things I like.  It’s kind of mysterious.

photo 1

Now, I will show you what happens when you walk by this image as it was lit in the gallery.

Walking Past Phoenix

Walking Past Phoenix

Now that you’ve seen it in action, I will show you a watermarked image I took of it with my camera in the light of day.  I think this would be fantastic in a very brightly lit minimally decorated room, don’t you?  Alternately, it would be wonderful in a very darkly decorated room with a few track lights focused on it.  I hope it captures your imagination the way it does mine.

Phoenix, (c) 2014 Lianne Todd 24x24" original metal print (single edition)

Phoenix, (c) 2014
Lianne Todd
24×24″ original metal print (single edition) $450.00

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)