Friday, September 29, 2006

Retrospective (Part One)

It may seem trite to say that fractals have changed my life. I couldn't have imagined seven years ago, when I loaded up Fractint for the first time in years, what would arise from that act. It's been a strange journey for a guy who flunked math in high school, and who was later told that he had "no aptitude" for programming.

So, around Christmas of 1998 I bought my first printer and, looking for things to print, I loaded up Fractint (I'd known about Fractint since the early 90s: I have a dog-eared copy of the classic Fractal Creations, and even attempted a couple of formulas back then). I joined the Fractint mailing list and posted a few things there, with very little reaction. The talk on that list eventually led me to Ultra Fractal 2 and the Ultra Fractal mailing list.

I lurked there for awhile, and saw Ron Barnett post a couple of formulas based on things that I'd posted to the Fractint list. Now the formulas weren't anything new, because they were from The Beauty of Fractals, but I figured that I should be the one getting the credit. So I posted another couple of formulas from BOF, and I got a rather disparaging reply from Damien Jones. The point of that anecdote is that newbies can often be hurt by offhand comments from the "gurus", and that's something that we should all remember.

I guess my skin was reasonably thick, because eventually I started posting again. I'm not all that proud of my earliest images, but it's interesting that even though they weren't commented on at the time, some were later cited as favourites.

Perhaps my first real success came when I posted some swirly formulas, that again weren't really original , but were perhaps new to Ultra Fractal in that they ignored the need for a "bailout" condition. One of these swirly formulas: the "Popcorn" formula by Clifford Pickover ended up dominating my work for the next several months.

At about this time I had a good look over the Web site of Janet Parke, and I was thoroughly humbled. Janet's work changed the way I thought about fractals: from an interesting hobby to a long neglected urge for creative expression.

Thursday, September 28, 2006

Three Faces of Pi

Fractals aren’t just shapes; fractals can be numbers as well. A fractal sequence is one that, in some sense, contains infinite copies of itself. One example of a fractal sequence is the signature of an irrational number (a number that can’t be expressed as a fraction, like π or the square root of 2). To create a fractal signature sequence for a number x, create values of y, where y = i + jx and i and j are both integers. Create y values for i and j from 1 to infinity and order them from smallest to largest. If x is irrational, then every y value will be different and the sequence of the i’s and the sequence of the j’s are both fractal sequences.

Infinity is really big, so instead, let i and j both vary from 0 to 32. Then, draw a line from (0, 0) to (32, 32), going through each point in order of the y values. Different irrational numbers will create different graphs. Even though each graph is one continuous line, the angles of the zigs and zags change, giving the appearance of rectangular blocks of different shades of gray.

The above image is composed of three separate graphs, aligned so that the entire image is one continuous line. The graphs represent three different irrational numbers which are based on π: π/2 (~ 1.5708), the natural logarithm of π (~1.145), and the square root of π (~1.772).

Wednesday, September 27, 2006

Cult of the Microbe King

Who would have thought this humble pest would someday take a seat beside the likes of David Copperfield or Martin Chuzzlewit, as The King of the Microbes.

One of the most startling events for fans of Charles Dickens this past year has been the recent discovery of an unpublished manuscript, The King of the Microbes. It's authorship is still controversial, due to it's peculiar subject matter, but some scholars say it's nothing new, and argue that Dickens made numerous references to it in his diaries and letters although, until now, everyone assumed it never became more than just an idea.

Published for the first time after being written over a hundred years ago, Charles Dickens' strangest work has become an instant cult classic.

A noted scholar on Dickens' work has responded with total disbelief, "Charles Dickens never wrote anything remotely like this sort of science fiction novel. They didn't even know about microbes when he was alive. It's ridiculous, not even one of his contemporaries could have written it."

Tracing the life of Jim, a microbe, the novel describes his impoverished beginnings and subsequent separation from his family at the tender age of 8, when he's sent to a large industrial center to earn money to help support his family back home.

Exploited by the factory owners and earning nothing but a meager ration of gruel each day for his work, Jim uses his organizational talents and sincere charm to lead a labour revolt that eventually grows into something of a revolution ending with him being crowned as their king.

Standard Oliver Twistian fare, excusing the revolutionary theme, but this all takes place on the microscopic level and there's none of the happy, plump and playfully named humans which the readers of other works by Charles Dickens would expect. In fact, there aren't any people at all, and his best friend is named "Zorax."

Download parameter file ""

The prestigious Royal Institute for Victorian Literature said, "It's obviously Dickens' work. While he never actually quotes from it, he mentions a work, Microbe Town profusely in his diaries and letters, a few of which are to his publisher, who for some reason seems uninterested in it. Perhaps it wasn't finished, although most of Dickens' works were originally published as a continuous series of magazine installments. I rather suspect Dickens was uncomfortable with it and died before he could make up his mind to have it published."

Still only available in hard cover, and elaborately illustrated, The King of the Microbes has completely sold out it's first, and rather short, printing run. Copyright issues have blocked publication in the United States as the estate of Charles Dickens has said that since the manuscript was never published, it's not in the public domain yet, unlike the rest of Dickens' work, and therefore they still hold the copyright.

Borderbooks, a U.S. publishing house in New York, says it intends to publish the work since they say they have an exclusive contract with someone they claim to be the real, and currently "living" author. The real "Charles Dickens" who wrote the book they say is an american who uses "Charles Dickens" as a pen name and was something of a drifter who previously worked as a microbiologist and has been an avid fan of the original victorian writer all his life.

This american microbiologist apparently was intrigued by the references the original Dickens made to the unknown work, Microbe Town, and set out to write the novel that he thought the real Dickens would have made.

The mysterious writer has so far been unavailable for comment and, according to his publisher, was last seen "dressed up like the Ghost of Christmas Past on a motorcycle he bought with his advance money, seriously drunk, and intending to head out to California, with a surf board tied to the back rest of his motorcycle and promising to write a sequel along the way that he'd drop in the mail when he got there..."

Alright. That's too much. I should have stopped before I got to the motorcycle, or the drifter.

Anyhow, I thought these processed Inkblot Kaos images would fit in just perfectly with such a novel, The King of the Microbes. Should it ever be written. Or discovered. Or whatever.

Monday, September 25, 2006

Look into my eyes !

Hi all !

Isn't my little devil cute ? :-)

Maybe I can seize the occasion to try to answer Mark's last post about what one find appealing in fractal images. My apologizes if all the examples are taken among my works... it's just that they're the ones I know best.

I like some images because they combine simple elements to produce something rich and unexpected, maybe like what makes a fugue of Bach appealing (at a different level, of course...). For instance this one, or this one. In some others, it's the apparent complete disorder which still yields a global structure (this one). I think these two categories can be classified as "abstract".

Sometimes, like in the image above or in this one, it's the appearance of a face or the sketch of an easily recognizable object, appearing from the random encounters of shapes and patterns. The feeling coming from such images is closer to the one I could have in front of some "ethnographic" art, like african masks. Another example which looks like a totem to me.

It can be that I like the general atmosphere produced by the image, like a summer day in this one, a river flow in this one, a starry night here or a kind of technological allegory in this one. This one always made me think to some fresco escaped from the Atlantid... Sometimes it's a mix of the last two reasons, like in this one, which always made me think to Christmas, with a kind of very primitive christmas tree in the middle, and the triangles combining sometimes to make stars.

Sometimes it's just a painty effect, or a play with light, like in this one.... Writing this little text made me realize that if they were abundant among my old images, I'm not so fond anymore of realistic objects with textures and shades.

Not sure if I was completely exhaustive, but the images I like almost always fall into one or several of these categories, no matter whether they are mine or not. About dreams I'm not so sure... my dreams are in general too concrete to be realized as fractals.

It would be interesting if other people recognize these categories, and if they have more to offer.

Saturday, September 23, 2006

Tiffany Lamp Gone Bad

Tiffany Lamp Gone Bad

Tiffany Lamp Gone Bad (2001)

May West liked good salmon.
Her bedroom had dark panelling

and lava lamps. Over her tables hung
racks of critics behind the bar

where bad service is largely blamed
on Texas. Her rental limo

was toothless and made me think of
camp. Such dim jerky tastes

survivalist or maybe all the songs
about trendy green plots gas up

through hanging smoke. Her hip
inquisitor makes a great square

room addition. I hear her voice
calling me claw-footed.

Her old man gives off a soft glow
low and sexless. Victorian.

Well cut by Jack like shards
of sour cream on a white plate.


This is a "Google" poem -- a found text pieced together by search hit syntax snatches from a Google search of the phrase tiffany lamp gone bad.

Friday, September 22, 2006


Firstly, this picture is licensed under the attribution share-alike Creative Commons license. I think. I'm not sure who I should give the attribution to: Scott Draves or Ernst Haeckel. That's in Seahorse Valley, by the way, in case you didn't know.

It's often said that fractal art is an abstract art. After all it's heavily based on mathematics; the most abstract of human endeavors. However I think most fractal art is not abstract at all. Many of us are creating images of things: we give them form, we might manipulate a gradient to produce a three dimensional effect, or add a layer to produce a shadow. In our minds they are things and not simply relationships between line, shape and colour. But if they're not abstract, and they don't represent things in the "real world", then what do they represent?

Of course I can't answer that for everyone. The things in my pictures might be the things from my dreams: things I can't name; things that don't have a name.

Thursday, September 21, 2006

Sometimes a Cigar is NOT just a Cigar

I’ve been playing with Toby Marshall’s new coloring "Popcorn Plus Orbit Traps", and I got in the groove. I was making texture layers like crazy…. masking this, masking that… I was on a roll. Yeah, Baby, I might have something here!

Ever get just "too close" to an image? Like not being able to see the forest for the trees?

I decided to render this puppy – and with quite a few layers and not the fastest coloring in the world, it took quite a while. I changed some things and rendered again, and again…….

Ahhh….. now that’s more like it!

It was only after all these renders, and hours of work with this image, that I, er, noticed an "unfortunate" shape at the lower left. Good Lord! Has that thing been there all along?


I really liked the overall shape of this julia – thanks again to Toby on several levels- but now all I could focus on was THE THING.

I’ve taken Janet’s excellent courses – and in one she describes how we must make judgement calls on letting what we might like about a fractal go for the greater good.

I ended up cropping the image.

Lorena Bobbit would be proud.

Catch de wave mon

I was thinking of the chariot race in Ben Hur when they did the salute pass before the race proper. Side by side over the smooth sand. Hail Jupiter give me victory says Stephen Boyd, while Charleton Heston has a Star of David pinned on him by an admiring youth. Or maybe it's the wave in the original Poseidon adventure, where they had to climb the Christmas tree to be saved.

Boyd was from Ireland. He died of a heart attack while playing golf. The kid in the Poseidon adventure is now an electrical contractor in L.A.

Monday, September 18, 2006

He played the Balalaika

He played the Balalaika... then ate it!

I wasn't quite sure what to do, so I clapped.

He wasn't finished yet.

Everyone in the alien dinner theater scowled at me while he started again, from the beginning.

I couldn't see why this guy was such a big celebrity on this planet.

Until he started to sing. It was the most amazing performance I'd ever heard.

But the local aliens at my table weren't too impressed. "Anyone with two heads can sing harmony like that," they muttered.

Saturday, September 16, 2006

Who's That Tramping Over Our Blog?

Periodically, blog housekeeping issues arise that need to be clarified.

Orbit Trap is not an online community. We're a blog. In a very real sense, we are like a publishing house. We reserve the right to choose what we will and will not publish. We do not exclude public opinion. Comments are welcome, and we do not shy away from controversy, but we do expect all remarks to be civil and respectful. We will not tolerate trolls or hand our blog over to them for use as their private platform. Trolls, of course, have the freedom to set up their own blogs and rail away at us 24-7 if they wish.

glyph 1.0 released

(For more info, see my earlier post.)

Tuesday, September 12, 2006



Unattainable (1999)

An impossible self help question
will wait
check out
be home

unless you are a fan

of stupid networks. One of the tightest
going nuclear photographs cuts

waste and overlooks ad agency
ethics. To understand more

toast the Broadway stage with
handgun exits, silent designs

before clicking to play
shut the books
cool detachment
self protection

when the Coca Cola intelligentsia

stumble in household income
and brain drain your

favorite photos. Who is
that artist in the break room mirror

found in prison? I have a prop
like yours: a picture with problems.


This is a "Google poem" -- a found poem pieced together from syntax snatches uncovered in Google search results of the word unattainable.

Seeing Things in Things

I cannot forbear to mention among these precepts a new device for study which, although it may seem but trivial and almost ludicrous, is nevertheless extremely useful in arousing the mind to various inventions. And this is, when you look at a wall spotted with stains, or with a mixture of stones, if you have to devise some scene, you may discover a resemblance to various landscapes, beautified with mountains, rivers, rocks, trees, plains, wide valleys and hills in varied arrangement; or again you may see battles and figures in action; or strange faces and costumes, and an endless variety of objects, which you could reduce to complete and well drawn forms. And these appear on such walls confusedly, like the sound of bells in whose jangle you may find any name or word you choose to imagine.
-Leonardo Da Vinci

This facility to see things in other things is perhaps most potent in childhood, when the open door of a closet at night really does reveal a monster. As we grow older we realize that the monsters don't actually exist (although Ripley would have us believe otherwise), but the facility remains.

It's possible that the facility isn't limited to humans. This is supposedly an example of Neanderthal art. Personally I'm not convinced: not because I have a low estimation of Neanderthals (I don't know any), but in this case I'd ask the question: who is it that is seeing the face?

Neanderthal #1: This rock looks like a face!
Neanderthal #2: I don't see it.
Neanderthal #1: Wait, what if I shove a bone in here...and here.
Neanderthal #2: It still looks like a rock to me.

Maybe it isn't even limited to primates: the ability to resolve a lion in the shadows would certainly be a survival trait, even if the lion isn't always there. Anyone who owns a cat or a dog knows that they dream, and if they can construct a whole world to react to in their sleep, who's to say that they don't see things in other things (Turing's test might apply here: if they behave like us you have to give them the benefit of the doubt).

What perhaps is limited to humans (and their close cousins) is the ability (desire, need?) to alter their environment to resemble the things that they see in it. At some point we stopped simply seeing animals in the stains on walls and started tracing their lines.

If you start with a white thing, you are going to project things you already know. Make it dirty somehow and then you will start using hallucinations.
-Roberto Matta

I've said elsewhere that fractal art is what artists do with fractals. If you accept that (and I'm sure not everyone will) then we can claim some of the greatest artists of the 20th century into the ranks of fractal artists. The one who has had the most influence on me is Max Ernst. From the 1940s he used a process called decalcomania in many of his paintings, which entails pressing paint between two surfaces and pulling them apart. The result is what we would now call a fractal pattern.

Ernst used decalcomania to make his canvas "dirty" and, in Matta's words, started "using hallucinations", devising scenes stranger than Da Vinci's landscapes and battles.

Computer generated fractals can be viewed as just another way of making a dirty canvas. I believe that fractals have no value in themselves, no inherent beauty. They are simply a starting point for our "hallucinations".

Monday, September 11, 2006

in the spirit of the times

Electro Sine Trap Tentacles of Terror

It's been ages now since ants took over the Earth, but they still enjoy reliving the old battles.

"One small step for an ant, one giant leap for all insects." Conquering the humans was the defining moment in the civilization of the ants.

When they read what we wrote about them in textbooks, they weren't insulted. "Look how the mighty have fallen!" they roared with joy.

Every year on Veteran's Day (for ants) they re-enact the great battles and tell their children and grandchildren about the Revolution.

"Son, the history books will tell you that the 214th Leaf Cutter Division captured Washington. But by the time they got there it was just me and few other guys. Beat but not beaten."

"Just me, a few guys and our Electro Sine Trap Tentacles of Terror!"

"Boy, tell your children and your grandchildren, if the humans ever come back from their holes in the ground, just let 'em have it with the Electro Sine Trap Tentacles of Terror. Those babies will fry 'em where they stand!"

Sunday, September 10, 2006


Someone remarked to me the other day that there seems to be a renewed burst of creativity in things fractal-related. Mark has released Sprite; Dave Makin's got some new formulas he's brewing, and I hear rumors of other noted formula authors doing the same. And yes, I've got some new toys too. Toys that let me create images like the above. I did not use an image importer to create it; it's fully resolution-independent and can be rendered at any size. I think it needs some more polish and testing before I release it, though.

While it is very fulfilling to create art, I am one of those peculiar people who finds even more satisfaction in creating tools. Perhaps it's a cop-out; by making a tool, I side-step the inconvenience of having to be artistically creative. But knowing that something I've made can be used by many more artists to do things that I never thought of---well, that's just magical.

I'm going to sleep with a smile on my face tonight.

Saturday, September 09, 2006

Wishful Thinking/Old Man Describing an Umbrella

The first title is mine, the second is from the title generator suggested by commentator Sharkrey. I'd seen these for band names, didn't know they existed for artworks too. Thanks Sharkrey.

One theory I have about beauty in the arts is that it's a sensory overreaction. What would that be? Well, we are used to tuning out noise and mistakes to a certain degree. Our senses are compensatory mechanisms. But when the art comes, our senses which were all ready to spring into action fixing up things suddenly find themselves with nothing to do. The art is pure in some way our senses didn't expect. So they react like pulling at a tug-o-war when the other side lets go. There's surprise, overbalance, sometimes a knock out.

Thursday, September 07, 2006

Seeking for a New Space on Fractals

When Manet painted The Fifer a new kind of representation has been brought to visual perception of the space in our culture. There a flat space rendered without shadows appeared “like in a deck of playing cards”, as has been said by an art critic. This return to a pictorial space similar of the pre-Renaissance became one of the main interests of most of the 20th Century artists like Picasso, Braque, Matisse, Mondrian, Klee and Miro among many.

A key point for some of these artists has been the interest for the far cultures of Asia, like the Japanese, and other cultures from non-Éuropean world, like African and the cultures from the islands of Oceania, where the space relies basically on the integration of graphical elements on the plane of the picture. The image is created with simple shapes and basic color relationships. The perception matters on considering the whole space, the whole pictorial surface “at once”, as the dominant “thing” the viewer is going to see. If the graphic element is isolated than the image will lose its impact and power of persuation.

Among the best examples of graphics are characteres and other forms of writing like we see in those “not to far alive” cultures of the North America (Navajo and many “prairie´s cultures” ,to the Canadian Northwest coast´s cultures, where today is the British Columbia); at Middle America, like the Youcatan´s cultures (the Maya Empire) and at South America (Inca´s Empire and some people of the forests). These cultures demonstrate how graphics have been intensively used. They also show how rich and varied basic shapes can be and how these variations of simple geometric repeatitions effect how we receive the meaning and mainly, how form and presentation come together. Could not be different if we consider that these works weren´t “art” in the same sense of today. Mostly they were related with the magic proprieties of lines and colors and the patterns were transmited to initiates from a generation to another.

Here we must to make a stop to remind that we are dealing with a long tradition of making marks that carry meanings. In this sense the recent destruction and smugglering of thousands of Mesopotamic clay tablets at the Bagda Archeological Museum must be complaint due they are among the earliest examples of mankind writings.

Where can we get themes and ideas for our modern graphics with meanings? I would say that everywhere in the history of visual culture “written” with images made out of strokes and filling. For us today, the “inspiration” is not limited to comics, cartoons and publicity. Sources extend from the graphic art of the cave´s men about 50,000 (guessing) years ago to contemporary street graffitis. Just a detail brought by the Italian writter Italo Calvino on a text in his book “Sand´s Collection” : the walls of the ancient Rome were fully covered with pornographic grafittis. The whole city was nastily “written”. Very inspiring!

But the list still continues: experimental typographic poems of the Dadaism to the numbers and letters in paintings, drawings and prints of pop artists like Frank Stella and Jasper Johns.

These are some few examples I can remember now. And these examples are comming to my mind after viewing some new works done with Mark Townsend’s recent project. I prefer to leave the commentary with Ron Barnett:

“In a related matter, Mark's Sprite program is integrating a whole world of images into fractal art. Kerry did some work along these lines a number of years ago, and Mark Hammond's BringItIn was another step in this direction. I think we are entering an expanded era for algorithmic art with the integration of several algorithmic types (traditional, IFS, raytracing, etc).”

Without going to far with my thoughts, I would say that the swirling eyes Mark is showing here appears to be the beginning of something new, perhaps a synthesis of fractals embodied by facts and matters of life and the merging inside a long cultural tradition. Let us see what we´re going to do with so many of that.

Wednesday, September 06, 2006

Fractals and Spam


I’ve always had trouble coming up with titles for my images. Often, it seems that I’ve spent as much time trying to think up a name for an image as I’ve spent creating the piece. When title inspiration eludes me, I resort to simply naming them by the date and sequence – 20060905-01, for example, and tell myself that I’ll work out a decent name for the thing later.

As a result, my parameter folders are filled with whole blocks of unmemorable numeric titles. This make for a mess when I browse through saved parameter files because my visual memory processes are geared toward associating images with descriptive names, not strings of numbers.

A partial solution came to me from an unlikely source - Spam. My spam filter dumps all e-mails from non-approved senders into a special quarantined folder, but I still have to skim through them every day or so to make sure I’m not missing any legit messages. That’s when I noticed that a lot of spammers use made-up nonsensical names in the “From” or “Subject” lines.

Most of them don’t get much consideration – “Pr0n”, “PHmdARMA” and “AMvBBtEN” don’t really work as image titles for me (But one never knows..). Every now and then I do find a real gem. A few that I’ve either used lately or have filed away for future reference include “Zed Thill”, “Sang Bourgeois”, “Xhobitol”, “Freddy Kruger wears Rolex”, and my current favorite, “Grunting Strontium”.

So you see, I’ve found a use for spam after all..

Tuesday, September 05, 2006

Nebula and Julia

I've noticed a new type of fractal that has been imerging on the Internet. It is typically called the Buddha Mandelbrot and Buddha Julia images. You can find several web sites that have galleries of them by searching the Internet. These images have probably been around for about a year or two, but I'm, just start starting to take notice.

I'm also still dabbling with the IFS flame type fractal by Scott Draves from several years ago. The flame algorithm has been converted to several programming languages, one of which is Java language which is my current preferred software development language. Delphi and C++ just seem to be too overly complicatated these days, but that is another story.

The Buddhabrot / BuddhaJulia and the Flame fractal type are the new types of fractals that have emerged recently and I find them very interesting.


Monday, September 04, 2006

I walked with Warhol

Hey, how about it? Is this the Campbell Soup Cans of fractals or what?

Anyhow, Andy told me, and no one else knows this, that he's taken all his talent and everything he's ever learned about art and put it into a single photoshop filter.

And he gave it to me, on a diskette.

I'd post it for download, but I promised I wouldn't, or else I'd lose all my super-powers.

A long time ago when I was in university I wanted to learn Spanish because I was going to go to Mexico for two months in the summer. Being exceptionally lazy when it comes to learning languages, or anything else mathematical, I checked out, started to study, and gave up on, a number of Spanish grammars.

I was in the public library looking for a different kind of Spanish textbook when I found a hardcover one with no dust jacket from the 1950's illustrated with small line art drawings. Each little ink sketch was signed, "A. Warhola."

I laughed. It had to be Andy Warhol. In fact, I figured he was a little embarassed with putting his real name on these trivial illustrations so he contemptously wrote his last name "Warhola."

Years later, when I began to read about things, I was surprised to find out that Warhola was actually his real name from the beginning, and he dropped the "a" off the end later on so it wouldn't sound so...

I never finished reading the book about Andy Warhol. I don't know what the reason was. A lot of people have altered their names to make them sound more or less of something. I'll bet there's even been someone with the last name Warhol who's added an "a" and changed it to Warhola.

Here's the original before "warholization" occurred, made in Inkblot Kaos.

Download parameter file ""

Which is better? The Warhol or the Warhola?

Actually, the effect is just the uscomic.8bf thing with the darkness slider moved to the lighter end of the range, the image inverted and the hue moved about half way around the spectrum. But maybe that's all Andy Warhol ever did when he made his famous stuff.

Of course he would have had to do it the hard, old-fashioned way.

The Fossil Whale (Moby-Dick, Chapter 104)

The Fossil Whale (Moby-Dick, Chapter 104)

There’s room there, and it could go either way. Faith just doesn’t have anything to do with what I’m doing as a scientist. It’s nice if you can believe in God, because then you see more of a purpose in things. Even if you don’t, though, I think that there’s a virtue in being good in and of itself. It doesn’t mean that there’s no purpose. It doesn’t mean that there’s no goodness. I
think that one can work with the world we have. So I probably don’t believe in God. This will earn me a lot of enemies probably, but—in some ways, it’s more moral. If you do something for a religious reason, you do it because you’ll be rewarded in an afterlife or in this world. That’s not quite as good as something you do for purely generous reasons. I think it’s a problem that people are considered immoral if they’re not religious. That’s just not true.

Lisa Randall, from Discover magazine interview

I heard about this Felonious guy—he's some kinda nut. He'll come in a club and stare at a wall. I mean, he's not like Erroll Garner or Oscar Peterson—he can't sit down and play you a regular show. Besides which, I hear he never gets out of New Jersey somewheres.

owner of the Black Hawk Jazz Club, circa 1958

Readers may remember how the U.S. military blared Van Halen and others at the Panamanian dictator Manuel Noriega, when he took refuge in the Vatican Embassy in Panama City during our invasion of Panama years ago. This method of rousting the wicked proved so successful that it was repeated during the recent Afghan experience, when heavy metal chart-busters were unleashed on caves thought to be sheltering Taliban and al-Qaeda fighters. The English Guardian newspaper reported last year that we were breaking the wills of captured terrorists, or suspected terrorists, by assaulting them first with heavy metal followed by "happy-smiley children's songs." The real spirit cruncher turns out to be the "Barney, I Love You" song played for hours on end. Even the most hardened, sadistic killers buckle under "that kind of hell," or so asserted a reliable source. But if that fails to work, I suggest a round-the-clock tape of Garrison Keillor reading poems on his daily Writer's Almanac show.

August Kleinzahler, Poetry magazine

Is it a fractal?

I often see this question in forums or galleries, or as a rule for a contest or challenge. This is mostly because forums, galleries and contests usually have some categories, and some are thematic and others are for specific software, so there isn't a neat fit. So how do we answer?

As an artist or a program developer, it doesn't matter to me; fractals are merely tools. But since you asked...

One reaction to the question is that it is a false dichotomy to assume that a picture is a fractal or not. By analogy, it's like saying that a picture is or is not a spiral, and by extension, spiral art is a category that contains all spiral pictures, created by spiral enthusiasts... which would obviously be a strawman argument in the absence of extreme examples. Sometimes collages are acknowledged as a crossover category, allowing for elements that either are or are not fractals, but this has not addressed the underlying assumption. To escape from the dichotomy, we might encourage people to treat fractal as an adjective instead, that applies to structure or process. A picture or object may have fractal structure in shape, coloring, texture. Or tools may use fractal processes to create shapes or coloring, whether evident in the end result or not.
Having divided the picture into various aspects, each of them can have multiple parts, and each might be categorized, for example, as 1. arbitrary or 2. algorithmic but not fractal or 3. having genuinely fractal aspects. Some of them might be further subdivided until the analysis itself seems both recursive and chaotic.
But it may be "too much information."

Some fractal structures have already been assimilated into mainstream computer art/illustration without question - fractal terrains, and many procedural textures use fractal noises - and nobody says the resulting art 'is a fractal'. So if you consider making an arbitrary shape and using a fractal texture in Maya or Photoshop, or doing the same in UltraFractal or XenoDream, what is the difference? Practically, the steps in each program may be different, but the viewer's (and often the artist's) perception is likely to be shaped by expectations of what the programs are for.

We could simply choose one of Yes/No/Partly/Sort of. we could sometimes say that it is a fractal in principle but all the coefficients that would make it look like a fractal are zero. But all this assumes an informed artist. Many would have to admit "I have no idea but I made it with program X". I haven't yet received any requests to automatically generate an answer along with the picture.

Changing the subject slightly, here is the Blogofractal.

Sunday, September 03, 2006

ICM Exhibition Photos & Thoughts

It's amazing to me how quickly all the day-to-day stuff I do can get backlogged just by being gone for a week. I took a short trip to Madrid for ICM and when I get back I have two thousand emails waiting. Half of those turn out to be junk (easily identified, but that spam filter needs tuning again) but still, it takes some time to get caught up.

Now it's the weekend, and I think I've managed to catch up. Catch up enough that I was able to sift through the photos that I took in Madrid, stitch together some panoramic photos of the fractal art exhibition there, and post them. And maybe think a little bit about the exhibition and fractal art.

Sometimes fractal art gets no respect from the "art crowd," but I've usually found that the public seems very receptive. Conde Duque in Madrid has a three-part exhibit about mathematics and art. One part is about why mathematics is important, and has some hands-on ways to experiment with some of the questions and ideas currently being explored in mathematics. One part is "demoscene", using computers to rendering images and music in real time using mathematics. And one part is the fractal art exhibition, using some images selected from the recently-held contest. This exhibition had people lined up to see it. An amazing thing, really; laypeople lined up, waiting patiently to see an exhibition about mathematics. Positively wonderful.

This same collection of fractal art was also on display at ICM, the International Congress of Mathematicians, a collection of math geeks of the highest caliber. This is a very different sort of audience, but Benoit Mandelbrot himself was there, and was impressed with the quality of the artwork. His perspective was interesting. While you cannot prove anything with a pretty picture, what you can do is bridge the gap between the common perception of math as difficult or boring and the reality that math can be wonderfully expressive and endlessly fascinating. Fractal art serves a useful purpose quite aside from merely being art.

I also had the opportunity to have dinner with Prof. Mandelbrot while I was in Spain. It was amazing to listen to him talk about Gaston Julia, not as a figure of mathematical legend, but someone that he knew. This is of course to be expected, and yet it still seems strange. We never think of "great" people as being normal, but greatness in one area of life does not describe a complete person. It reminded me that real history is not just a sequence of emotionless facts, but actions conducted by real people with real motivations, peppered with moments of outstanding significance. If you were to chart mundaneness of someone's life, it would probably be fractal, although for some people it might have a higher fractal dimension than for others.

Mandelbrot Among the Gypsies

Mandelbrot Among the Gypsies

Mandelbrot Among the Gypsies (2001)

Gaston Julia, recovering from injuries caused by a hospital, was named king of the gypsies in 1917. He had darned some socks for corpses and driven a hawthorn stake through his soon-to-be famous set. Much of his initial groundwork was spent decapitating computers on a finite area of the X-Y plane. Female vampires might have been more helpful in seducing his theory, but Pierre Fatou was a familiar who was missing a finger. He used melons to free up computer time. Of course, they dripped blood. To ward off vampires, gypsies used computer-generated cremation grounds. In 1979, Benoit Mandelbrot himself could reproduce after he made noises and calculated Kali. The goddess drank his image -- all his blood was drained but none was spilled, thereby the “Mandelbrot Set.” The values of IBM went from C to mullo (one nomadic perimeter of a large, complex ghoul). The discrete boundary of this formula is very loyal to dead relatives, both inside and out. In 1982, Mandelbrot’s soul re-entered the world, and he published a book similar to ours only very different. It was called In the Fractal There Is No Death. His soul, kept crated in wooden boxes, stayed more around his publisher than his body. This was actually seminal, for undead followers soon generated and sprang out of the ground. They believed only in dendrites and Slavic primacy. Later, after deep zooming and (re)animating irregular shapes, interesting patterns like animal appendages emerged and wandered the countryside. These beautiful images were a surprise, and intestines and a skull combined to make an apparition that drank only coloring gradients. So, yes, Bram Stoker spread his work at high magnification. By 1000 AD, computer artists with their powerful PCs had settled in Turkey. All culture and contemporary simulation seemed to stop shortly afterward.


Using the "cut-up" composition method popularized by William S. Burroughs, two blocks of text were run through a virtual cut-up machine. The result: a randomly scrambled "found" text mirroring chaos theory and yielding new meanings.

The two texts used here and merged were:
1) an article about the beginnings of fractal art--
2) an article on gypsy vampire superstitions--


I sometimes try to write poetry using similar steps to the way I make fractal images.

My process for creating a fractal-like poetry begins with the “cut-up” theory of writing popularized by the late Beat writer William S. Burroughs. It's probably written by elves Wikipedia describes cut-up composition as follows:

Cut-up is performed by taking a finished and fully linear text (printed on paper) and cutting it in pieces with a few or single words on each piece. The resulting pieces are then rearranged into a new text. The rearranging work often result in surprisingly innovative new phrases. A common way is to cut a sheet in four rectangular sections, rearranging them, and then typing down the mingled prose while compensating for the haphazard word breaks by improvising and innovating along the way.

I then try to add two new dimensions to cut-up composition: 1) collage software and 2) bits of fractal theory.

My compositions begin by pasting two existing text excerpts into a virtual cut-up machine. This is software designed to scramble and splice texts to make new, “found” texts. But I use the software in a very specific way -- and for a very specific end: to create a kind of “fractal poetry.” There are, indeed, some connections. Chopping and rearranging (layering?) the same two “set” texts means subsequent cut-up(s) will always be “self-similar.” The field of available words never changes and syntax replicates but is altered with each iteration. In theory, the cut-up text could be infinite -- if I could live forever and constantly keep mashing up the same two select texts. Fractals are also infinite in theory, but a graphic viewer capable of a never-ending deep zoom has (to my knowledge) not yet been created. Moreover, by placing all of the cut-up machine’s settings on “random,” chaos theory comes into play. So, the resulting cut-up texts do have some fractal characteristics -- computer generation, self-similarity, theoretical infinity, and influence of chaos theory.

I am not the only writer to link fractals and poetry. Poet Alice Fulton has discussed “fractal poetics” in her book Feeling as a Foreign Language (Graywolf Press, 1999). She writes:

Science’s insights concerning turbulence might help us to describe traits common to the poetry of volatile (rather than fixed) form…Just as fractal science analyzed the ground between chaos and Euclidean order, fractal poetics could explore the field between gibberish and traditional forms. It could describe and make visible a third space: the non-binary in-between.

Naturally, Fulton has her detractors. Michael Theune disses her ideas in an issue of Pleaides:

At first, Fulton’s theory sounds promising. A real departure from organic theories of poetry, it could help to privilege a new kind of poetry, a hyper-repetitive or incremental poetry perhaps analogous to the fugue -- a structure Fulton mentions in her essay, “To Organize a Waterfall” -- that might approximate the not-quite and both chaotic and self-similar -- “[a] self-similar mechanism is, formally speaking, a kind of cascade, with each stage creating details smaller than those of the preceding stages” -- aspects of the fractal. The fractal, one could say, replaces the paradigm of the musical score with the paradigm of the loop.


The trouble with Fulton’s theory is that none of this happens. Instead, Fulton makes a mess of things, bleeding her potentially interesting theory dry by turning it into at best a lightweight surrealism or at worst a trite descriptive tool.

Fulton applies fractal theory to existing free verse patterns in hopes of discovering a middle ground of exciting expression poised between sense and nonsense and for extracting (deep zooming?) new meanings. Fulton is less interested in generating poetry based on fractal components than she is concerned with applying fractal theory as a critical tool to decode and validate what she sees as super-charged free verse poetry. In contrast, I am more attracted to using pieces of fractal theory as a mirror and a map to generate new “found texts” that are somewhat fractal in both compositional method and structural design. Ideally, such new texts can truly inhabit Fulton’s “third space.”

And that's where I want to be. In that third space suspended between chaos and order.

Fulton goes on to say is poem is not a fractal because poems aren't "complex adaptive systems." True enough -- but if a poem can be spliced and diced to embed at least some fractal characteristics, and each subsequent stage of that cut-up is a new iteration, doesn't that evolving new text demonstrate traces of complex adaptation? Or is the inclusion of deliberate randomness in my cut-up process an adaptation buzz killer?

Saturday, September 02, 2006

In Praise of Chaos...

This could be a sort of metaphorical portrait of my dining room table. Or my bedroom. Or my cubicle at work. So maybe I am just a clutter junky. I find myself drawn inexorably to the irregular, the unsymmetric, the disorderly, the "ugly" side of algorithmic art.

I remember corresponding with someone, perhaps Carol Walske, about chaos and fractal art and how so much of the fractal art one sees seems to attempt to eliminate the chaotic, to neaten it up, confine it to order. Like the artist is afraid of chaos.

I have been either actively or philosophically involved in fractals for almost 20 years now, and a biologist of sorts for most of my life. I have been entranced with the higher order that looks like chaos -- the "empty" field that is ecologically much more stable than the plowed and planted field next to it. It partakes of a higher that is not as easily apparent to the casual observer as the straight rows planted with a single species. But the order is there, to be sensed if not completely understood.

Let's hear if for chaos!