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 Digital Art printed on metal, single edition 20x20" $325.00

Butterfly Hub – Artist Lianne Todd
Digital Art printed on metal, single edition

Detail of Butterfly Hub

Detail of Butterfly Hub

Butterflire - Artist Lianne Todd Digital Art printed on metal, single edition 20x20" $325.00

Butterflire – Artist Lianne Todd
Digital Art printed on metal, single edition

Detail of Butterflire

Detail of Butterflire

Mother of Moths - Artist Lianne Todd Digital Art printed on metal, single edition 12x12" SOLD

Mother of Moths – Artist Lianne Todd
Digital Art printed on metal, single edition
SOLD. Private Collection.

Pollinator - Artist Lianne Todd Digital Art printed on metal, single edition 16x16" $225.00

Pollinator – Artist Lianne Todd
Digital Art printed on metal, single edition

A thumbnail of the raw generated fractal - just to illustrate part of the process.

A thumbnail of the raw generated fractal – just to illustrate part of the process.


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


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, 20x20", Watercolour on Gessoed Paper.   Lianne Todd

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!

Last Night’s Opening

A big thank you to everyone who helped me celebrate the opening of my exhibition last night.

Here are some pictures  (I didn’t remember to take any until the end of the night!):

photo 3 photo 2 photo 1 photo

The Fractal Nature of Our Universe

Tonight is the night!  Yesterday we hung the art and it is all ready for viewing.  My husband helped, and he was wondering where I had been hiding it all.  Here is a sneak peak at some of the titles for you, and a photo of me hanging some of my first ones on the wall of the lovely gallery at The ARTS Project.

“Turbulence & Bubbles”; “Stardance”;  “Nature’s Drapery”;  “Negative Nebulae”;  “Mother of Moths”; “Fried Eggs”;  “The Mage Emerges”…  There are 39 pieces of art in all.

Here I am hanging "Happy Hill"

Here I am hanging “Happy Hill”

The ones  you see in the photo are watercolour paintings on paper.

I would like also, at this time, to acknowledge the excellent digital image printing services of Posterjack, of Toronto.  They are the company which I use to print my digital fractals on metal.  Over the course of three years they have consistently provided wonderful service and attention to quality.  The show consists of 18 paintings, 15 metal prints, and six photographs.  The photographs were printed using high quality archival paper and inks by Highlander Studios, of Woodstock, and I am so pleased with the results!

Some other tools I have employed to make my art are the software which I use to generate the fractals I start with.  I have primarily used Spangfract XTel, and Oxidizer, on my iMac.  These programs provide me with infinite possibilities and I thank them for that!  My frames and many of my other art supplies were purchased at Guthrie’s Art Supplies & Framing, of London – mainly because they also provide excellent service and reasonable prices – and Olga knows me when I walk in.  Richard and Sandra, at The ARTS Project, were very helpful with advice and equipment for hanging yesterday.  Finally, I would like to acknowledge the funding support from the Ontario Arts Council, an agency of the Government of Ontario.

I hope, if you are able, you will join me tonight as we celebrate the show opening.  7-9 pm!

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