I spend some of my spare time in discussions with a very interesting group of people who like to discuss philosophy, science, and all kinds of other things.  It’s fun for me.

One of the favourite topics in this group is the concept of free will.  It seems that many of the most vocal people in the group favour the idea that there isn’t any.  I am not one of them!  I have made my arguments for free will to them, but these arguments fall on deaf ears, most of the time.  I have, for some time now, thought my experience zooming in to the deepest parts of fractals was somehow illustrative of the (in my opinion) flawed logic that is often used as “evidence” that we have no free will.  I was wondering how I could bring this visually to the group and make them see the idea I was trying to convey.

Last night I realized I already have this illustration fairly handy.  It’s the Key, from my series entitled “The Ball Went Over the Fence”.  Some of you may remember this one from several years ago.  The Key shows what part of the large fractal image I zoomed in on to make the next smaller fractal image.

Zoom Key, The Ball Went Over the Fence series

Wikipedia defines Free Will in the following way:  “Free will is the ability to choose between different possible courses of action unimpeded.” The argument many in the group make, against the existence of free will, is that everything is caused by what went before it. Wikipedia also states that “Some conceive free will to be the capacity to make choices in which the outcome has not been determined by past events.”

My main problem with this is that while it is usually easy, from the standpoint of the outcome, to see what came before, and possibly follow a chain of causality, there is no reason to assume that means a choice made is the only choice that could have been made, given all previous conditions.  We can see into the past just fine.  The future, however, is indeterminate.

So, looking at the Key, shown here, you can see a white outlined square in each square image of the key (click on the image to make it bigger, if that helps).  From each outlined square, you can follow the white angled lines to the image found at that location if you were able to zoom in while in the fractal software.  If we start at the smallest square image (the final outcome), we can see where it came from (it’s very close to the top of the next larger image).  Likewise, if we follow to the next one, we see that it came from a very tiny place in the top middle third.  And if we keep going, we can see that the third image came from a recognizable portion of the second largest image.  And that image came from a very tiny spot in the largest image.

This is the chain of causality – it goes from the outcome back to the origin.  It would, however, be impossible to go from the largest image to the smallest one without the Key in place to guide you.  There is no chain in that direction, because it looks into the future.  The outcome would never ever be the same twice.  There is absolutely no logical reason why that particular tiny spot was the one chosen on the first image to zoom in on and make the second one.  In a fractal, while constrained by the mathematics of that fractal, the possibilities at each level of zoom are for all practical and human purposes, infinite.  I’ll grant you that maybe I would have zoomed in on an area near it, or any one of the areas where you can see the little greenish greyish balls.  Just because those areas look interesting to me.  But they all look interesting, and certainly from the perspective of the large image, equally so.  If we look at the second largest image and are choosing where to zoom in for the third… even if you make the argument that I will almost definitely choose a square featuring a ball… that square is never going to be the same exact square.  And now we get to the third image, and you can see no reason why I would have chosen to zoom in as much as I did, and in the area that I chose.

It was my free will in action, plainly and simply.  I chose, unimpeded.  The outcome was never a given.

# Utaopiah

I’ve never been to Utah, unless you count a layover at the airport on the way to California.  It was snowing in Salt Lake City at the time.

However, I have seen some photos of the landscape there.  Somehow, when I created this image, I was reminded of those beautiful rock formations on a clear hot sunny day.  I imagined hiking through this fantasy landscape, and the name for this image came to me and stuck.

‘Utaopiah’ will be available for viewing (along with many other pieces) in person on May 4 & 5, from 10 to 5 p.m. during the Oxford Studio Tour, at my home gallery, which is Location #4 on the tour.  It is the only one of my metal prints that actually has a frame (the frame is black) – something new I tried out this time!

Utaopiah. Digital fractal art. Single metal print. 12×16″. Artist Lianne Todd

# Time for Tea

Every once in a while I discover and develop an image that is just uncannily familiar.  From the similarity of “Pollinator” to an actual pollinator, to the “Ocean Floor” that isn’t actually an ocean floor, we see how nature follows the patterns dictated by the geometry we know as fractals.   However, it is not strictly ‘natural’ things which follow fractal patterns.  We can see fractal patterns in things like architecture, art, music, and… fancy china dishes!

I absolutely love this image which I’ve entitled ‘Time for Tea”.  To me it seems vaguely reminiscent of Alice in Wonderland and the interior of my Mom’s china cabinet.  I recently printed it on metal.  Here is what the digital image I created looks like.  In the metal print, the white parts are silver, so it does change the look of it a little.  It would be perfect in a super modern dining room, I think.

To see the 24×32″ metal print, you’ll have to come out to my gallery, as it is just very difficult to photograph the reflective surface.  Lucky for you, the perfect opportunity to do that is right around the corner, during the Oxford Studio Tour, May 4 & 5, 10 a.m. to 5 p.m.!

Time for Tea. Digital Fractal Art. Single metal print is 24×32″. Artist Lianne Todd.

# Square Foot Show 2018

But I know a picture is worth a thousand words, so here are my entries in the Westland Gallery’s Square Foot Show of 2018:

Frog Pond. Digital Fractal Art HD printed on metal. Single Print. 12×12″. \$300.00. Artist Lianne Todd.

I hope you enjoy the above fractal piece.  It is printed in high definition on metal, with a very glossy finish.  I hadn’t tried this kind of print before and I am quite pleased with how it turned out.  It doesn’t have the metallic sheen that changes with the light, like my other metal prints do, but that suits this image really well.  As usual, I only do one print per image, so all pieces are originals in every sense of the word.  I had a lot of fun creating this one, seeing all the different things in it that caused me to name it “Frog Pond”.  Do you see them too?  Please feel free to comment on what you see – I’m curious!

Kitchen Alcove, Il Convente dei Carmine. Watercolour on Paper. 6.25×6.25″. SOLD. Private Collection.  Artist Lianne Todd.

World Views. Watercolour on Gold Absorbent Ground on Canvas. 12×12″. SOLD.  Private Collection.   Artist Lianne Todd.

I’ll be at the Art in the Park in Woodstock with some of my other work this Saturday.  More about that tomorrow!

# Not-so-alien Vegetation

Have you ever wondered if there is any other life out there in the universe?  I think there must be.  The universe we can see contains around 100 – 200 billion galaxies and it is estimated that is only ten percent of what it actually contains.  That’s just galaxies – each galaxy contains perhaps 100 billion stars.  I don’t know about you but I have a hard time wrapping my brain around numbers that large.  The odds against this being the only planet to support life of some kind are huge.  So, then one wonders, what would alien life look like?  We’ve seen so many science fiction movies, now, where others have imagined it, and they’ve done a really convincing job.  It’s amazing, really, what our minds can come up with.

But what if we leave it all to the mathematics?  If fractal geometry is the geometry of nature, let’s assume that all nature, not just that of planet Earth, is governed by it.  I find it really fun to create a little ‘planet’ using Mandelbulb 3D, and then explore it, finding scenes that remind me of Earth.  I’ve done this before with ‘Climb it, Change’, ‘There is Always a Bridge’, ‘No Port in Sight’, ‘Ocean Floor’, and many more that I haven’t shown anyone yet. This one I call ‘Coniferous Tree on Planet B’. Obviously the ‘coniferous tree’ isn’t the only bit of vegetation on this particular ‘planet’.  I see vines, and cabbage-shaped types of vegetation, and driftwood – but you might have to come see the piece in person to appreciate all that.  Next weekend is the 11th annual Oxford Studio Tour and I am at Location #4.  Why not come out and see it for yourself?

Coniferous Tree on Planet B. Digital fractal art printed on metal, single print. 24×32″. Artist Lianne Todd. \$550.00

This is the first piece of fractal art I’ve created and shown that isn’t square, but rather a landscape format.  I hope that doesn’t throw anyone off!

# Feast

I cannot wait to show you this latest piece in person.  Some images conjure up abundance, richness, and decadence, and this is one of those images. There is plenty here for your own imagination to work on, but you won’t be able to properly see it unless you come to my studio!  Lucky for you, my studio is often open, all you need to do is contact me.  But even luckier, there are a whole bunch of studios open on May 5 & 6 in Oxford County, and mine is one of them!  I am at Location #4.

This image you see here is a mere fraction of the size I have printed it – 24 x 24 inches.  As usual, I only have one print made of each fractal piece, on metal (or sometimes acrylic), so each is an original.  Although, I think this would make a great metal album cover don’t you?

Feast. Digital Fractal Art printed on metal, single edition print. 24×24″. Artist Lianne Todd. \$450.00

# A Matter of Scale

There exists a very old phrase, ‘as above, so below’.  Its meaning is interpreted in various ways, depending on where you look.  Its source is generally attributed to Hermes, though according to some, it is probably even older than that.

According to Wikipedia, the full quote translated from Hermes ‘ The Emerald Tablet of Hermes Trismegistus, as translated by Dennis W. Hauck, is “That which is Below corresponds to that which is Above, and that which is Above corresponds to that which is Below, to accomplish the miracle of the One Thing.”

Isaac Newton translated the Emerald Tablet’s passage as follows: ‘That which is below is like that which is above & that which is above is like that which is below to do the miracles of one only thing’  (according to Quora).

I don’t know exactly where I first heard the phrase, but it certainly popped into my head a lot as I began to explore fractal geometry.  The more I learn about fractals and about the cosmos, the more I see similarities between large scales, like the universe, and small scales, like an atom.  Perhaps an easier example to envision is the similarity between say, a river drainage pattern and the venation in a leaf.  After all, fractals are often self-similar on smaller and smaller scales.  It is one of the ways in which fractal geometry was discovered by Benoit Mandelbrot.  My cursory understanding of such things, as an artist whose education was mainly in biology, does not diminish my enthusiasm for humanity’s search to find a Theory of Everything.  Whenever I see a Physics article in my various news feeds, I am struck by either their use of illustrative images which I recognize from experience as being generated fractals, or how much the actual images generated by their physics experiments resemble generated fractals.  Maybe someday the ideas will all fit together.  Until then, I will continue to happily make my art and notice how in reality, sometimes it is tricky to know what the scale of an image is.

This piece will be on display in my gallery this weekend during ‘Welcome Back to Otterville’, our town’s 21st annual studio tour.  Please visit www.WelcomeBackToOtterville.ca for details of the tour, including maps and times.

A Matter of Scale. Digital Fractal Art, printed on metal. 20×20″. Single edition print. Artist Lianne Todd. \$345.00

# There is always a bridge.

We live in a very divided political landscape these days.  There are a great many vocal people on both the left and the right, and sometimes it is difficult to imagine we can find any common ground with each other.

I helped found, and am the publicity director for, the Canadian branch of the International Watercolor Society (IWS Canada).  Our mission is to “promote peace, harmony, love, understanding and acceptance of each others’ differences” through the medium of watercolour.   We recently held a contest in which we asked people all over the world to express ways in which they celebrate.  We asked what celebration meant to them.  Many interpreted the question as ‘what’ do you celebrate, rather than ‘how’. In a way, we were asking for participants to build a bridge for us so we could learn about their cultures.  It has meant we’ve interacted with 1450 people all over the world.  It may be a small contribution to peace, and love, but many small contributions add up!  The 150 finalists chosen by our four jurors can be seen on our website (thanks to the hard work of Ona Kingdon, Elizabeth Franchetto Irvine, and myself ;)), along with the videos in both English and French made by our president, Ona.  We recognize, of course, that all art forms “can bring people together despite differences in race, religion, culture and distance.” We just happen to especially love watercolour.

As you know, I also happen to love digital fractal art.

This piece of mine illustrates a landscape full of great divisions, but wherever there is a chasm, the fractal algorithm has built a natural bridge.

There is Always a Bridge. Digital Fractal Art printed on metal, single edition. 20×20″. Artist Lianne Todd. \$345.00

What if we did that?  What if each of us made it our business to build a small bridge wherever we see a chasm we can’t fill (like in that song by Sting!).  Our hearts can be open without compromising our ideals. We don’t have to have “fortresses” around them.

Anyone who knows me knows I love to argue (not fight), just for argument’s sake.  So it may seem odd to them – me talking about building bridges.  But my arguments are never meant to hurt or cause strife – they are meant to bring more understanding, both for me and for the other person.  It really saddens me when that isn’t the outcome, as is sometimes the case.  There is always a bridge that can be built or found.  We can’t/won’t always cross the bridges, and can’t expect others to cross over to us either, but at least we may get a little closer to seeing the others’ point of view, and sometimes we can meet in the middle.

# Ethereal Visions

Before I begin to introduce this new piece, I would like to thank all of the nice people who visited my studio/gallery this past weekend for the Oxford Studio Tour, and showed such fascinated interest in my fractal art.  You really do help me keep the inspiration fresh!

As you may know, clouds exhibit fractal geometry.  Mandelbrot’s famous quote:

# “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”

is certainly a confirmation of that if you needed it.  That quote is from the very first paragraph of his book The Fractal Geometry of Nature and he discusses the topic in several places throughout it.

I took the photo of these clouds at sunset one evening here in Otterville.  Living down close to the historic mill in this little town, we don’t always get the best view of sunsets, but every now and then there is a spectacular one that must be photographed.  And of course since I am interested in the cloud geometry, I also like the way it is highlighted by the colours.

It seemed like a very natural place for this fractal, created in Oxidizer, to occupy.  The shape immediately brought to mind something happening in the sky, perhaps a place Zeus would be.  There was an obvious (to me) song title that came to mind too, and perhaps you can guess what it was, or maybe not.  But it didn’t quite interpret this the way I wanted, and I was stumped for a while trying to think of a title.  I liked the little spirals and the curved shapes reminded me of somersaults, and I still felt there was a musical component.

After having it printed on acrylic, and hanging it on my gallery wall, I showed it to my son, and asked him what he thought I should call it.  It didn’t take him very long to say “Aerials” and although the word on its own is ideal, I immediately knew he was referring to the song by System of a Down.  It is on their Toxicity album.  I confess I only know it (and all the other metal that I like) because of my son, but it is truly one of my favourite songs of all, and I hope they don’t mind me naming this piece of art after their music.  I agreed with him that it is the perfect title.  I don’t know why I didn’t think of it myself.  My suggestion is that you first go find and read the lyrics.  Then listen to the song.  I think you might agree too.

Aerials. Digital fractal art printed on acrylic, single edition. 20×20″. Artist Lianne Todd. \$375.00

# New designs…

It came to my attention recently that my site was not terribly friendly for those who are unaccustomed to reading blogs, and that I should make the images of my work more accessible to the attention span of the casual visitor.  So, I spent a little time the other day doing just that.  The home page is now a static gallery of my fractal work, and the blog has its own new page on the menu.  Please have a look at the newly designed site – is there anything that you as a viewer would suggest to improve it?  I am open to suggestion – although there are of course limits to what I can do since I am using a template.

Now, it’s time for me to introduce another fractal that you may not have seen yet.  I’ve exhibited it already but you may have missed it.  This one was difficult to title.  What I saw in it first, changed for me, until I was seeing it a number of different ways.  Perhaps that is why it appeals to me so much.  I decided it deserved a name fitting its ‘behaviour’, one that would allow the viewer to perceive it their own way as well.  So, I called it “Indeterminate”.  This image is a small watermarked version of the digital image used to create the piece of art, as photographing the final art printed on acrylic proves difficult with all the reflections.  If you’d like to tell me what you see in it, I would love to hear – but please do it in a private message using the contact page.  I would like all viewers to see it with fresh eyes uninfluenced by the perceptions of others!

Indeterminate. Fractal Digital Image. Available as an original single edition print on acrylic, 20×20″. Artist Lianne Todd. \$375.00