Tag Archives: Clouds are not spheres

Ethereal Visions

Posted on by
Reply

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.

fractal, ethereal, sky, Lianne Todd

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

Advertisement

An Archetypal Image

Posted on by
Reply

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″. Artist Lianne Todd. Private Collection.

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

New Fractals

Posted on by
Reply

I’m excited to have some new fractal art to show you in a week at the Oxford Studio Tour.

We have thirty-one artists at seventeen locations throughout Oxford County, Ontario, Canada in the heart of the southwestern part of this province.  It will be a fun day trip for anyone in the region – even those coming out from Toronto! (Wouldn’t it be nice to get out of the city for a day or two?)

Here is a preview of one of the fractals.  I have printed it (using Posterjack) on metal, 20×20″ and that is the only print I will do, so it is an original piece.  It is created digitally using the Mandelbulb 3D software.  As I find usual and striking for fractals, it looks very natural. It is pretty obvious what I thought it resembled!  I hope you’ll come and see it.  I think it would make a great piece to gaze at from anywhere in your house, while you consider nature and its mysteries, and it draws you in close, as well – as all fractals do with their self-similarity on smaller and smaller scales.

I call this one Ocean Floor:

Ocean Floor. Digital Fractal Art. Lianne Todd.

Ocean Floor. Digital Fractal Art. Lianne Todd.  This image has now been printed on metal as a single edition. 20×20″. $345.00

 

Following the Patterns of Nature

Posted on by
Reply

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″. Artist Lianne Todd.  SOLD.  Private Collection.

Show Reprisal!!

Posted on by
Reply

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

Biological Forms

Posted on by
Reply

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.
6×6″.
$175.00

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

Triad.
Lianne Todd. Watercolour on Paper.
20×20″.
$650.00

 

Physical Phenomena

Posted on by
1

If I am postulating that the universe is fractal in nature, it makes sense that structures formed by molecules behaving in their natural way should be recognizable as fractals.  Such is the case with frost, turbulence, and bubbles.  Just do a little Google search with each of those terms alongside fractal, and you’ll see what I mean.  Mandelbrot made groundbreaking progress modelling turbulence, which had confounded mathematicians before him, using fractal geometry.

It also makes sense that in my random wanderings through the fractal universes I create, I encounter images that remind me of these phenomena.  Such is the case with these two fractals which I chose to paint.  I especially like the way the bubbles in Turbulence & Bubbles look like they are in the process of being blown, sometimes from multiple locations, and melding together when they meet, just like real bubbles would.

Hot Frost. Watercolour on Aquabord. 6x6". $175.00 Lianne Todd

Hot Frost.
Watercolour on Aquabord.
6×6″.
$175.00
Lianne Todd

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

Turbulence & Bubbles.
Watercolour on Gessoed Paper.
20×20″.
$650.00.
Lianne Todd

The Experiment

Posted on by
Reply

This series of four paintings was an experiment.  Not a very scientific one but I did try to control variables and make predictions.  My hypothesis was that since all pigments are different in their molecule size, shape, and hydrophilic and hydrophobic qualities, they would all move differently through the medium of water, and as they interacted with each other, and that their movement would be fractal.  In other words, I expected them to appear, at the end, as if they were something like a cloud, or some other natural item that is already known to be able to be modelled using fractal geometry.  A coastline, for instance.

All four pieces were executed and controlled in the same way (I won’t give away all my secrets!), the only differences being the pigments I used and the order they were used in.  I tried to reduce the effects of gravity by levelling my table but it is kind of obvious there was a tiny bit of gravitational effect.  I changed the orientation of the final products so that when they were hung together, it would be aesthetically pleasing.  Other than that, the results you see here are basically the raw data.

I called them Negative Nebulae, because I looked at all the white space around them and imagined if it was black, and the colours were reversed, they would look a bit like those photos you see from NASA of distant nebulae.  In other words, these would be like the negatives of those photos.

Here they are – what do you think?:

Nebula Negative I Watercolour on Yupo 10x10" Lianne Todd

Nebula Negative I
Watercolour on Yupo
10×10″ (sold)
Lianne Todd

Nebula Negative II Watercolour on Yupo 10x10" Lianne Todd

Nebula Negative II
Watercolour on Yupo
10×10″ $125.00
Lianne Todd

Negative Nebula III Watercolour on Yupo 10x10" Lianne Todd

Negative Nebula III
Watercolour on Yupo
10×10″ (sold)
Lianne Todd

Negative Nebula IV Watercolour on Yupo 10x10" Lianne Todd

Negative Nebula IV
Watercolour on Yupo
10×10″ (sold)
Lianne Todd

Here is what they looked like at the exhibit:

KONICA MINOLTA DIGITAL CAMERA

 

 

Curious to know what they do really look like when you invert the colours?

Non Negative Nebula I (the inversion) Lianne Todd

Non Negative Nebula I
(the inversion)
Lianne Todd

Non Negative Nebula II (the Inversion) Lianne Todd

Non Negative Nebula II
(the Inversion)
Lianne Todd

Non Negative Nebula III (the inversion) Lianne Todd

Non Negative Nebula III
(the inversion)
Lianne Todd

Non Negative Nebula IV (the inversion) Lianne Todd

Non Negative Nebula IV
(the inversion)
Lianne Todd

 

The Photographs

Posted on by
1

It isn’t difficult to spot natural fractals all around you, if you know what you’re looking for.  It’s quite probable that you just don’t recognize them because you haven’t looked at enough computer generated fractals, at enough scales, to realize that even if something in nature doesn’t look like a whole fractal, i.e., you don’t really see the repetition of a pattern on smaller and smaller scales,  it will look like part of one.

Before Benoit Mandelbrot came along, nature was regarded as a rather chaotically influenced version of Euclidian geometry.  The artist Paul Cezanne said as instruction to young painters: “Everything in Nature can be viewed in terms of cones, cylinders, and spheres.”  But 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” contradicts this, and rings very true. 

Some mathematical experts are able to generate entire landscapes, or, small parts of nature like a fern leaf, just using fractal formulas.  Benoit Mandelbrot gave a few examples of these in his book, The Fractal Geometry of Nature.  Indeed, the generation of natural looking landscapes, textures, etc. using fractals is quite common, in video games.  Ever wondered how the game manages to keep up the appearance of the surrounding landscape the character is travelling through?  That’s how.  They are also used in movies, creating alien landscapes.

Some examples of fractals in nature are depicted in the photographs that were part of my exhibit this summer.  The patterns of ice crystal formation, mountain ranges, clouds, branching patterns of trees, growth patterns of mosses and lichens, flower structure, butterfly wings and their coloration, fur growth and patterning… on every scale you can recognize fractals, not just on earth but in the entire solar system and universe.  (More about that later).  For now, have a look at these, and look at the world in a new way the next time you go outside.

Top to Bottom, Left to Right: Freezing; Mountains & Vapour; Mossy Branches; Reiterated Beauty; Nature's Drapery; All the Markings of a Bandit. Digital Photography. 10x10" Prints, framed $125.00

Top to Bottom, Left to Right:
Freezing; Mountains & Vapour; Mossy Branches; Reiterated Beauty; Nature’s Drapery; All the Markings of a Bandit. Digital Photography. 10×10″ Prints, framed $125.00

As they appeared in the exhibit.

As they appeared in the exhibit at The ARTS Project.  Thanks again to the Ontario Arts Council!