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!


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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