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.
20×20″.
$650.00.
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.

waveeditsmwaveeditcrop

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Chaos

Quote

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.