Process V Outcome

My Grandparents were true Victorians. Indeed, you could say that in some ways they were more Victorian than the good queen herself. Not unnaturally, therefore, their taste in art ("pictures", they would have said) was Victorian. "Every picture tells a story" was a phrase I grew up with. They meant, of course, "Every picture should tell a story". Certainly, their pictures had narratives, usually a moral, which could be deduced from the work itself, often with the aid of the title.

Some days ago, surfing on the net, I came upon a blog extolling the primacy of process in all things art. I thought little of it at the time, and surfed on, but later thought more about it. Back a decade or two (or three) there was a vogue for process, not only in art, but in other fields also. (There may still be, for all I know.) In Education, for example, this translated as "How a person learns is what matters, not what s/he learns". "Process, not outcome," became the dictum. In other words, it is what happens to a person during the learning process that matters in the long run, that will decide what sort of a person s/he will become.

Following this dictum in art, the story is no longer told by the work, but of it. So what at first sight appeared to me to be a ventilation grill well overdue for cleaning, having layers of fluff adhering to its bars, became, when I was given its credentials, an object of vastly different kind: it was Idris Khan's photograph of the Qur'an'. He had scanned every page - nearly 2000 in all -into his computer and then digitally layered them to form a composite image. some say the result is beautiful. I do not go that far, but would say that knowing the story behind it, changes the emotional charge.

Cornelia Parker, you may recall, blew up a shed - or had it blown up, hopefully by someone who knew what s/he was doing. She presented the result as an installation, and intriguing it was, too. But knowing the means by which it was achieved added enormously to its impact. Simon Starling's boat seemed nothing extraordinary - until you were told that it was an ex-shed, and would be one again. It was said that his Shedboatshed was instrumental in gaining for him The Turner Prize.

There is in fact a whole genre called Process Art, has been since the 1960's. It was originally a reaction against minimalism. Its exponents chose transient materials, such as ice, wax, sand, fat, yeast. The artist would devise and set in motion a process by which the chosen materials would be changed, often repeating the process over and over. I think I see similarities here with the way in which fractals are produced, but here we have something physical, an artifact, if only fleetingly, not an image of something virtually conceived.

Like to find out more? Try these links.

General

The Guggenheim Collection

The Tate Collection

Artists you might like to look at are: Hans Haacke, Jannis Kounellis and Richard Serra.

Haacker

Kounellis

Serra

Fractal Zoom

I have had another flood of emails asking about fractals, both of them raising the same two questions. (Hey, what about using the comment facility, fellahs, so's others can join in and help me out?) However, I will do my humble best. Before that, though, a word of warning: both emailers seem to have scooted off to my website expecting some sort of enlightenment there. Far be it from me to dissuade anyone from visiting my website or to suggest that enlightenment is not to be found there, but I feel I ought to point out that enlightenment on fractals is conspicuous by its absence. Much else you may find in the way of spiritual insight, but not that.

The first point raised was that it is difficult, when presented with a series of individual plots, to see the relationship between them. I don't think I actually presented a series in that sense with that intention, but here's one which I hope will help. You will see that I have marked on each the area to be magnified for the next plot.



The other query is of a rather more technical nature. I realised, reading the emails, that I had not explained - or not explained clearly enough - the process by which a fractal is produced. Fractals are produced naturally or artificially - in a computer. In either case (matter in the first instance, data in the second) becomes the input for a process which wreaks a small change in it. The slightly modified data or matter (the output from the process) then becomes the new input. It is fed back into the process and modified again in the same manner, before becoming output once more. The new output is fed back in... the process being repeated, usually thousands of times without variation, to produce the fractal, which may be either of two types: self-repeating or self-similar.

Post Script

Following my recent post I received a couple of emails (via my website - and no, there are no fractals there and I have no plans to include any) seeking further information on the business of mapping fractals. I thought it might be more useful to answer them in the form of a further post.
The maps below represent a sequence of Mandelbrot Plots, each one being a magnification of a fragment from the previous one. The section to be magnified is indicated with a small rectangle. They show, I think, the process of investigation.
These maps, unlike those in my last post, are the product of a generator, The Mandelbrot Explorer, which I have since downloaded. You can obtain it, free, by clicking on the title to this post or by popping Mandelbrot Explorer into Google.

The Most Beautiful Piece of Prose Ever - Probably.

Where the world ceases to be the stage
for personal hopes and desires,where we, as free beings,
behold it in wonder, to question and to contemplate,
there we enter the realm of art and science.
If we trace out what we behold and experience
through the language of logic, we are doing science;
if we show it in forms whose interrelationships are not
accessible to our conscious thought but are
intuitively recognized as meaningful, we are doing art.
Common to both is the devotion to something
beyond the personal, removed from the arbitrary.

I came upon the piece of prose upon which I still lavish superlatives, must have been twenty years ago. Perhaps more. It was in a book called "The Beauty of Fractals" by H.-O. Peitgen and P.H.Richter, a book which for some years became a sort of Bible to me. There was back then a bit of a fad for fractals. They were cool. Made possible by the advent of the computer in home and school, it was not long before every teenager had one on his bedroom wall. Or so it seemed. They were part of our fascination with Chaos Theory and the intriguing idea that a butterfly flapping its wings in Hong Kong might cause a hurricane to hit the Florida coast. For me, fractals and everything about them are as fascinating now as they were back then. They have not lost their magic. They bring together art, science, mathematics, technology and music (There is such a thing as fractal music.)and represent a form of geometry we had not seen before. Some had intuited it, but no one could see it before computers opened their window on it. It was as unbelievable as much that was happening elsewhere in science and had already happened in the arts.

The geometry they taught me at school was Euclid's. It was about shapes in two and three dimensions. They had sides and areas that we could measure and/or calculate. (That was the point of it all.) Fractals possess none of that. They have neither sides nor areas that are measurable. The perimeter of a fractal is infinite. Incalculable. A computer allows you to zoom in on your chosen fragment and to see it as under a magnifying glass, a microscope if you will, even an electron microscope. And however much you magnify it, it is as if you were still looking at the original, your starting point - except that its spirals, whorls, folds, spikes and vortices have become ever more complex. In places it may appear to be disintegrating into dust, but the detail is infinite. You will never get to the end of it.

Example: Take an equilateral triangle and place centrally on each of its three sides, another, similar, but with sides one third the length. You now have a Star of David. In the center of each of the new star's twelve sides place another equilateral triangle, its sides again reduced to one third of the previous triangle's. You get the idea. You now have 48 sides requiring triangles with sides again reduced by two thirds. And again on each of the resulting 192 sides. And on through all eternity. The length of the shape's perimeter expands infinitely, yet the triangles you keep adding will never collide with each other. Furthermore, if you were to draw a circle around the first triangle, to touch all three points, your fractal will never stray outside that circle - and you will never draw the complete fractal, not this one nor any other you might attempt by whatever method.

The fractals I have drawn here were all produced by an on-line fractal generator, of which there are many. There are also down-loadable versions. There is much experimenting to be done, and anyone can do it. You do not need to be a mathematician. I have chosen fractals from what is known as The Mandelbrot Plot. For the mathematicians among you, they are fragments from the graph of Xn+1=f{Xn} - but, as I say, you do not need to understand that. The variety of results is - you've guessed it! - infinite, the product of where on the plot you decide to search and the parameters you choose. (The fractal generator pages will lead you by the hand.) Happy hunting - oh, and whose pen was it crafted my opening lines? Albert Einstein's.