Pics of the current show

The Station Arts Centre has turned out to be a great location for my original series of fractal art.  Their new lighting system really shows off the metal prints well, and the one wall was the perfect length to show off the larger paintings all together.  Much better than crowding them into my home gallery, that’s for sure!

Here I am with a few of the pieces, on the night of the opening:

Lianne+Metal PrintsLianne+PaintingsAlso, the Station Arts Centre took a few photos on the night of the opening and posted them on their Facebook page.  You can view them here.

The show runs until April 7.

 

Show Reprisal!!

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!

AFractalUniversegraphicwb

Imagining the Cosmos

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. 20x20". $625.00 Lianne Todd

“Stardance”. Watercolour on gessoed paper. 20×20″.
$650.00
Lianne Todd

"Particles and Fields". Fractal Digital Art on Metal, single edition print. 20x20". $325.00 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.

Further into the realm of Fantasy

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 24x24" $425.00 Lianne Todd

The Mage Emerges
Digital Art Printed on Metal, single edition
24×24″
SOLD.  Private collection.
Artist Lianne Todd

The Landing

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 20x20" Lianne Todd $325.00

The Landing
Digital Art printed on metal, single edition
20×20″
Artist Lianne Todd
SOLD.  Private Collection.

 

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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KONICA MINOLTA DIGITAL CAMERA KONICA MINOLTA DIGITAL CAMERAKONICA MINOLTA DIGITAL CAMERA KONICA MINOLTA DIGITAL CAMERA

 

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, 28x28" $525.00

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, 20x20" $325.00

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, 16x16". $225.00

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. 12x12". $145.00

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, 8x8". $110.00

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

Zoom Key, The Ball Went Over the Fence series

Patterns

This piece is called Looking Through.

"Looking Through" Digital Art printed on metal, single edition 20x20" $325.00 Artist: Lianne Todd

“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 z_{n+1}=z_n^2+c, with 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:

sea creature zoomed in

 

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
20×20″
$345.00

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
20×20″
$345.00

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
12×12″
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
16×16″
$240.00

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.