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.

microcosm or macrocosm?

A Matter of Scale. Digital Fractal Art, printed on metal. 20×20″. Single edition print. Artist Lianne Todd. $325.00



Halls Creek Festival

September 10 & 11 is the Halls Creek Festival of Creativity in Ingersoll, and I will be participating again!

This festival was good fun last year and I kind of wished I was one of the attendees rather than an exhibitor – lots of learning and creating going on all over the place, and great live music most of the time.

I plan to have some of my fractals there – last year I ONLY brought the fractal metal prints – but I think I will also bring some paintings of fractals this year and some other paintings as well.  I also hope to do some painting while I’m there.

Check out the website for details.


An Archetypal Image

I think I have mentioned before how I see many fractals as somewhat archetypal in nature.  We have, in our decorative past, incorporated many motifs that turn out to be quite common in fractal geometry.  The swirls and whorls, the spirals and branches, the radiating patterns… it is like we knew about fractals before we knew about fractals.  But of course we did, didn’t we?  Because fractals are the shapes of nature, and we are a part of nature ourselves, and surrounded by it.  We noticed the regular and irregular natural patterns around us and we appreciated them.  We began to find them beautiful. Then we began to associate them with ideas, and some of them became symbolic.

This particular fractal is one of those ones that seems to be archetypal.  Of course the cross shape, as a symbol, is much more ancient than the Christian religion.  This is more complicated than a simple cross, though.  What other associations does your mind bring to this image?

Symbol.  Digital fractal art on metal.  Single edition print. 16x16". Lianne Todd

Symbol. Digital fractal art on metal. Single edition print. 16×16″. Lianne Todd

I hope you’ll come out to my studio this coming weekend during the Oxford Studio Tour to see this piece and more.

Rough Waters

A little over a month ago, my mind was in turmoil and I spent some time creating this image.  The process of creating is always calming and even though none of the problems turning circles in my head were solved by it, it was a way for me to get through that time.  The piece is called “No Port in Sight”. Since then, things have gradually become better.  The waters have calmed.

No Port in Sight.  Digital fractal image.  Lianne Todd.  Unprinted as yet - only one print will be made.  If you wish to own this please contact me to discuss format, size, etc.

No Port in Sight. Digital fractal image. Lianne Todd. Unprinted as yet – only one print will be made. If you wish to own this please contact me to discuss format, size, etc.

Unbeknownst to me, at the same time, another artist, a photographer named Dave Sandford, was capturing the real thing from my favourite beach, Port Stanley!  I hope he won’t mind if I link to his photos here.  I don’t know him but apparently he lives in my “hometown” of London, Ontario.  They are absolutely awesome, would have been difficult to capture, and really exemplify the turbulence and fury our Great Lakes are capable of.  I hope the fractal nature of these is as obvious to you as it it is to me, especially after seeing the image above created entirely using fractal software (Mandelbulb 3D this time – a new (to me) application I’ve been learning to use).

On that note, I’d like to wish you all a Happy New Year – and may you always have a port in sight!

November News

I am very pleased to announce that some of my fractal art will now be available at the Art Gallery of Lambeth!  I grew up in that area so it is really nice to be able to display my art there.

I still have many pieces at my home studio/gallery though, and that’s a good thing, because this weekend is Welcome Back to Otterville, our 19th annual Studio Tour.

For details, please see my previous post. As always, I have a few things left to do before morning so I will keep this short!

You could also visit my other site, liannetodd.wordpress.com, to see a couple of new pieces I will have on display.


Following the Patterns of Nature

It is an absolutely beautiful day today in Otterville, full of colour and the patterns of nature, so I plan to spend some time outside.  It was during another beautiful day a few years back, hiking in the woods at Awenda Provincial Park, that I came across many kinds of fungus.  I took a number of photos, and an edited version of one of them ended up as part of this image I am presenting to you today.

On another completely separate occasion, I was creating fractal images and found that, as is often the case, there were distinctly natural and vegetative features recognizable in one.  I saved it, and later on when looking through all of my photos, I noticed how well the features in it mimicked and extrapolated the patterns of growth I had noticed in the fungal photo.  I had even just happened, by whim, to have edited the photo so that its colours matched the ones I had, by chance, used in the fractal creation.

What you see below is a digital collage of the natural and the generated fractal patterns, printed on metal.  Once again nature shows how it is a manifestation of the fractal patterns of the universe.

Following the Patterns.  Digital Fractal Art printed on metal, single edition.   16x16".  Lianne Todd.  $225.00.

Following the Patterns. Digital Fractal Art printed on metal, single edition. 16×16″. Lianne Todd. $225.00.

Turbulence Revisited

Big whorls have little whorls
Which feed on their velocity,
And little whorls have lesser whorls
And so on to viscosity.
-Lewis F. Richardson

In the book I reviewed in my last post, Chaos: The Making of a New Science, by James Gleick, this quote begins one of the chapters.  And in the first paragraph of that chapter, another quote is mentioned which is in the description of this interesting video about the unexpected math in Van Gogh’s Starry Night.

James Gleick makes no reference to that painting, but goes on to describe the stories of past mathematicians and physicists trying and failing to solve the problem of turbulence.  Finally, along came Chaos Theory and Fractal Geometry, and things started to make some sense.  It is easy to understand why, when you look at the self-similarity and the complex patterns of a turbulent system.

I wonder what was going through Van Gogh’s mind when he was painting Starry Night.  According to the video, it was during one of his “periods of psychotic agitation”.  Perhaps the patterns approaching chaos happening in the electrical signals of his brain were translated to his expression with paint?  It’s an interesting point to ponder when you consider all of the systems in our bodies that involve fractal patterns.

I can assure you I was perfectly calm and sane during the painting of Turbulence and Bubbles – I was just letting my own hands and brain interpret the patterns that arose from an external fractal formula.  When I first started I had a completely different title in my mind, but then as I was painting it, I realized the black whorls reminded me of turbulence, and it looked like the yellow parts were bubbles emerging from some unknown source within it, and merging with each other when they touched.  We know turbulent systems do produce bubbles… (think boiling water)… I doubt this is how, but still!   I know I’ve introduced it before but here it is again:

Turbulence & Bubbles. Watercolour on Gessoed Paper. 20x20". $625.00. Lianne Todd

Turbulence & Bubbles.
Watercolour on Gessoed Paper.
Lianne Todd

Here is a raw fractal which, to me, looks like a cross section of a wave crashing in.  A detail, below it, shows the patterns present within.  I haven’t quite decided what I’m doing with this one yet, but thought I would show it to you as it relates to this post so well.  It’s not exactly turbulence, as there aren’t any true whorls, but you can see how fractal geometry would lend itself to the study of turbulent systems.




In the mind’s eye, a fractal is a way of seeing infinity. – James Gleick

I just finished reading a really good book called “Chaos – Making a New Science” by James Gleick.  It was recommended to me by the London Free Press photographer who took photos at my The Fractal Nature of Our Universe exhibit last summer.  (Don’t forget the reprisal of that show, A Fractal Universe, is currently at the Station Arts Centre in Tillsonburg until April 7!)

It was a really interesting read, full of insight into the difficulties scientists and mathematicians have had in the past, with certain problems they encountered.  Most of them involved non-linear dynamical systems – the kind you often find in nature.  They were so troublesome that these problems would be put aside, ignored, deemed unsolvable.  So many different kinds of scientists and mathematicians in the late 1960s and 1970s were separately converging on the same theories to solve these problems at the same time, while the tools (computers) to more freely explore these theories were also developing, one can truly say it was a science whose time had come.  That didn’t mean that it didn’t meet with resistance!  Sometimes even those who were essentially promoting the same ideas refused to acknowledge each other.

Fractals are a large part of Chaos Theory.

Wherever chaos led, Mandelbrot had some basis to claim that he had been there first. – James Gleick

However, there was much to discover even after Mandelbrot had provided this language for describing nature.  Scientists wanted to know the “why” – and they still do.  I am not sure how many scientists today are attempting to use chaos theory and the language of fractals to interpret systems from the smallest to the largest of scales.  Certainly many ecologists, medical researchers, economists, meteorologists, and some astronomers are.  But there is still some resistance.

Will those who are looking to complete a Grand Unified Theory give full consideration to Chaos Theory and Fractal Geometry?  I hope so.  Time will tell, and these are exciting times indeed.



Patterns of humanity

I have mentioned a few times in previous posts about fractal images often being archetypal.  I’m not really sure I was correct in describing them that way, but what I will say is that they often look familiar in a way that transcends their immediate translation into a real object.  For instance, when I first looked at this fractal image, I immediately thought of the Aztecs and the patterns they incorporated into their art forms.  Having now looked at some Aztec art in more depth, I’m not even sure why I thought of them, other than the  feather motif and the colours.  That’s just what immediately came to mind.  And I have other fractal images created (not shown here) which really speak to me of Native American blanket patterns.  Others might look at this piece and be more immediately aware of the hourglass shape.  Maybe you will look at it and see something else entirely.

My point is, from near the beginning of humanity, we have been making patterns, whether or not they were drawn with a stick in the sand, sculpted along the edge of a stone building’s rooftop, painted on a cathedral ceiling, or digitally on a tablet.  Possibly for 60,000 years, we have been making patterns!  And if you look at all the patterns we have been making, you may notice that many of them are self-similar on smaller and smaller scales.  We were making fractals and we didn’t have a name for what was common to them all.  And we didn’t have a concept of the way fractals were involved in the geometry of nature – not consciously, anyway.  Maybe we were consciously inspired by nature, but didn’t recognize that specific aspect of it.  Only for the last 30-40 years have we, thanks to Mandelbrot, come to an awareness of this common denominator.  I like the way fractals connect all of humanity over time, and the way they connect us to nature.   I’m really looking forward to exploring this with future pieces!

Aztec Gold. Watercolour on Gessoed Paper.  20x20".   $625.00.   Lianne Todd

Aztec Gold.
Watercolour on Gessoed Paper.
Lianne Todd

Biological Forms

Examples of fractals in biology are not difficult to find, and indeed if the universe is fractal, there should be a fractal component to all biological forms.  In the post entitled The Photographs, in which I have captured some natural fractal forms, there are at least five forms which are biological.  In the post entitled Butterflies and Moths, there were several digitally generated fractals which just happened to look biological.  Anyone who has looked up the word fractal has probably been given the example of the fern, or the romanesco, or even the tree.  In fact, people can create extremely realistic looking plants using software that takes advantage of fractal geometry.  Our lungs, and our vascular systems are obviously fractal in nature.  Ever looked at a sea slug?  Beautiful little fractals.

When I create my fractal digital art, and sometimes watercolours, I don’t try to make things that are biological, but I recognize natural forms when I see them and they pop up on their own all the time.  The fact that I’m not making them on purpose somehow speaks to my scientific side, and relates them to evolutionary theory.  I talked about this a little bit in The rose and the creation process as well.

These two pieces are examples which are maybe not as obvious as the butterflies but do remind me of biology just the same.

Cell Division.   Lianne Todd. Watercolour on Aquabord.  6x6".  $175.00

Cell Division.
Lianne Todd.
Watercolour on Aquabord.

Triad.   Lianne Todd. Watercolour on Paper.  20x20".   $625.00

Lianne Todd. Watercolour on Paper.