I've just thrown away a previous draft of this post, in which I tried to make some overarching point about the interaction between technology and art, and tie that in to the current generation of 3D fractal art. That didn't work out so well, so maybe I'll just give a few impressions. All in my personal opinion, of course. I don't pretend to be an art connoisseur.
Early fractal art worked mainly as eye candy. A typical Mandelzoom was an assault of wild shapes and saturated colors, looking vaguely organic, or perhaps suggesting a paisley print, or maybe something you might see when you rubbed your eyes. Striking images. Trippy, beautiful, even.
As with any algorithmic art, there is a vital human element that gives them the claim to be called "art" -- whether good, or bad, whether your cup of tea or not. Someone took the time to search the infinity of the Mandelbrot set for an image to their liking, to frame and color it, and to present it. While not strictly fractal art, Electric sheep is an interesting example of this human-algorithm interplay, on two levels. On the one hand, someone (Scott Draves) came up with the idea and got it going. On the other hand, the actual curation is done collectively by thousands of people on the web. Very cool. I've got it as live wallpaper on my phone as I write.
But ... it's all sort of ... detached. It's cool, without a doubt, but it's also cool in the sense of "aloof". I get the impression of a mind at work, but an emotionless, alien mind. Maybe I'm biased by knowing too much of the mechanics behind it all. I'm sure others have warmer impressions, or more easily see familiar objects like trees or flowers, but to me, even when the images suggest some sort of life form, they look like something other. Which, I'm sure, is exactly the point to a lot of folks.
In 2009, after many not-quite-successful experiments by many people, Daniel White hit upon the Mandelbulb, a way to generalize the process behind the Mandelbrot set to three dimensions in a way that people generally agreed was as cool as the original 2D set. In 2010, Tom Lowe came up with a different way of generalizing to higher dimensions, called the Mandelbox, which was also deemed worthy. Strictly speaking, both the Mandelbulb and Mandelbox are actually families of shapes with infinitely many possible parameter settings, some cooler than others, of which the artist is free to pick the coolest, but they're generally referred to as single entities.
Being truly three-dimensional (in that they're embedded in three-dimensional space), these sets offer possibilities well beyond those of two-dimensional fractals. While some 2D fractals may suggest depth, these have it. A video rendering is truly a trip through an alien space. Technically, any fractal (or at least any non-linear fractal, where the structure doesn't simply repeat as you zoom in) has infinitely elaborate detail, but these 3D fractals somehow seem to have more infinitely elaborate detail.
They can also seem more organic, particularly if you play with the formula a bit. Note the images at the bottom. They look like they grew, rather than having been produced by a purely mechanical process. Even the more mechanical-looking images seem more made than found. In a normal Mandelzoom, it feels like a computer (or math itself) provided the image. Many of the 3D structures give the strong impression someone made them and the algorithmic process managed to stumble upon them -- see the intricacy of the design, the attention to detail, the exotic esthetic -- or even that they somehow made themselves.
If anything, the feeling of alien-ness is even stronger than for a 2D mathscape. Even the most organic-looking forms, though they may seem like they ought to be part of some coral reef or fungal growth, seem about as foreign as they could look and still seem familiar. No puppy dogs or Old Master still lifes here.
The artist has a fair bit of latitude in choosing the color palate, location, scale, viewing angle, lighting and so forth, but the underlying shape is still the underlying shape. Still, there's only so much you can do with a landscape so fundamentally bizarre, either to make it more familiar or more otherworldly [many 3D Mandelpictures have some sort of height map or similar manipulation that can impose a chosen shape on the underlying contours of the fractal. Old-fashioned texture mapping and other rendering techniques can be brought to bear as well, along with compositing and other image manipulation techniques. The artistic effect is to make the fractal more a technique than an end in itself, which seems overall like a good development -- D.H.]
What is it about these forms, both 2D and 3D, that resonates so strangely? What does it say about our brains that we should see these images the way we do?
It's not shocking that fractal forms should remind us of living things or other natural objects. Fractal geometry was invented in part to describe the wide variety of natural shapes that didn't fit into the regular categories of classical geometry.
The name "fractal" itself comes from the notion of a fractional dimension, which is ubiquitous in nature once you look for it. There are several definitions of dimensionality that can take fractional values, but the one usually used with fractals is the Hausdorff dimension. By that standard, the coastline of Great Britain, for example, has been measured to have a dimension of 1.25, the coastline of Norway 1.52. Galaxy clustering comes in around 2, cauliflower around 2.3, and the surface of the human brain around 2.8. Interestingly, the Mandelbrot set itself has a Hausdorff dimension of exactly 2 -- as does its boundary.
As odd as a fractional dimension may sound, it makes a certain kind of sense. A coastline certainly isn't 2-dimensional, but neither is it quite a straight line or smooth curve. Because we see these kinds of shapes all the time -- trees, clouds, veins in leaves, mountains, piles of pebbles, coral, broccoli ... it's not a great leap to think we would respond to something artificial with the same general property. And on the other hand, because they're not exactly like anything we naturally encounter, it's natural to think of them as alien.
In one sense that feeling of some of the 3D forms being organisms or artifacts themselves is a property of the sets themselves, but equally so is it in the eye (or the perceptual machinery behind it) of the beholder and of the artist selecting and rendering the scene. It would be interesting to show a bunch of people random images from the Mandlethingies and ask "Does that look natural, artificial, or other?"
Then follow up with "If this looks artificial to you, who do you think made it?"
And why?
Early fractal art worked mainly as eye candy. A typical Mandelzoom was an assault of wild shapes and saturated colors, looking vaguely organic, or perhaps suggesting a paisley print, or maybe something you might see when you rubbed your eyes. Striking images. Trippy, beautiful, even.
As with any algorithmic art, there is a vital human element that gives them the claim to be called "art" -- whether good, or bad, whether your cup of tea or not. Someone took the time to search the infinity of the Mandelbrot set for an image to their liking, to frame and color it, and to present it. While not strictly fractal art, Electric sheep is an interesting example of this human-algorithm interplay, on two levels. On the one hand, someone (Scott Draves) came up with the idea and got it going. On the other hand, the actual curation is done collectively by thousands of people on the web. Very cool. I've got it as live wallpaper on my phone as I write.
But ... it's all sort of ... detached. It's cool, without a doubt, but it's also cool in the sense of "aloof". I get the impression of a mind at work, but an emotionless, alien mind. Maybe I'm biased by knowing too much of the mechanics behind it all. I'm sure others have warmer impressions, or more easily see familiar objects like trees or flowers, but to me, even when the images suggest some sort of life form, they look like something other. Which, I'm sure, is exactly the point to a lot of folks.
In 2009, after many not-quite-successful experiments by many people, Daniel White hit upon the Mandelbulb, a way to generalize the process behind the Mandelbrot set to three dimensions in a way that people generally agreed was as cool as the original 2D set. In 2010, Tom Lowe came up with a different way of generalizing to higher dimensions, called the Mandelbox, which was also deemed worthy. Strictly speaking, both the Mandelbulb and Mandelbox are actually families of shapes with infinitely many possible parameter settings, some cooler than others, of which the artist is free to pick the coolest, but they're generally referred to as single entities.
Being truly three-dimensional (in that they're embedded in three-dimensional space), these sets offer possibilities well beyond those of two-dimensional fractals. While some 2D fractals may suggest depth, these have it. A video rendering is truly a trip through an alien space. Technically, any fractal (or at least any non-linear fractal, where the structure doesn't simply repeat as you zoom in) has infinitely elaborate detail, but these 3D fractals somehow seem to have more infinitely elaborate detail.
They can also seem more organic, particularly if you play with the formula a bit. Note the images at the bottom. They look like they grew, rather than having been produced by a purely mechanical process. Even the more mechanical-looking images seem more made than found. In a normal Mandelzoom, it feels like a computer (or math itself) provided the image. Many of the 3D structures give the strong impression someone made them and the algorithmic process managed to stumble upon them -- see the intricacy of the design, the attention to detail, the exotic esthetic -- or even that they somehow made themselves.
If anything, the feeling of alien-ness is even stronger than for a 2D mathscape. Even the most organic-looking forms, though they may seem like they ought to be part of some coral reef or fungal growth, seem about as foreign as they could look and still seem familiar. No puppy dogs or Old Master still lifes here.
The artist has a fair bit of latitude in choosing the color palate, location, scale, viewing angle, lighting and so forth, but the underlying shape is still the underlying shape. Still, there's only so much you can do with a landscape so fundamentally bizarre, either to make it more familiar or more otherworldly [many 3D Mandelpictures have some sort of height map or similar manipulation that can impose a chosen shape on the underlying contours of the fractal. Old-fashioned texture mapping and other rendering techniques can be brought to bear as well, along with compositing and other image manipulation techniques. The artistic effect is to make the fractal more a technique than an end in itself, which seems overall like a good development -- D.H.]
What is it about these forms, both 2D and 3D, that resonates so strangely? What does it say about our brains that we should see these images the way we do?
It's not shocking that fractal forms should remind us of living things or other natural objects. Fractal geometry was invented in part to describe the wide variety of natural shapes that didn't fit into the regular categories of classical geometry.
The name "fractal" itself comes from the notion of a fractional dimension, which is ubiquitous in nature once you look for it. There are several definitions of dimensionality that can take fractional values, but the one usually used with fractals is the Hausdorff dimension. By that standard, the coastline of Great Britain, for example, has been measured to have a dimension of 1.25, the coastline of Norway 1.52. Galaxy clustering comes in around 2, cauliflower around 2.3, and the surface of the human brain around 2.8. Interestingly, the Mandelbrot set itself has a Hausdorff dimension of exactly 2 -- as does its boundary.
As odd as a fractional dimension may sound, it makes a certain kind of sense. A coastline certainly isn't 2-dimensional, but neither is it quite a straight line or smooth curve. Because we see these kinds of shapes all the time -- trees, clouds, veins in leaves, mountains, piles of pebbles, coral, broccoli ... it's not a great leap to think we would respond to something artificial with the same general property. And on the other hand, because they're not exactly like anything we naturally encounter, it's natural to think of them as alien.
In one sense that feeling of some of the 3D forms being organisms or artifacts themselves is a property of the sets themselves, but equally so is it in the eye (or the perceptual machinery behind it) of the beholder and of the artist selecting and rendering the scene. It would be interesting to show a bunch of people random images from the Mandlethingies and ask "Does that look natural, artificial, or other?"
Then follow up with "If this looks artificial to you, who do you think made it?"
And why?
