Showing posts from November, 2005

Fractal Fossil

Minerals, the basic building blocks of rocks, form crystals.

Download parameter file rock.xpf

Whether made of a single molecule or billions, the shape of the crystal remains the same while it grows in size.

Thousands come together to make a large crystal which looks identical to the one made by a single member.

But don't take my word for it. I only took one course in geology and mineralogy was just a single chapter in the textbook.

But what if there was a crystal that was complex enough that when it grew it produced a typical mandelbrot shape?

Each new addition to the crystal was like the iteration of a fractal formula and produced the starting point where the next molecule was added to the crystal.

Like interlocking stone on a driveway. If the stones are curved, but the curvature is such that they never form exactly 360 degrees, never form a complete circle, then they would make a spiral, either inwards or outwards.

Anyhow, maybe such a mandlebrot fossil like the one pictured above i…

Seen any good kleenex boxes lately?

I saw one just the other day, it had an abstract, almost fractal pattern to it. The colors were deep, mysterious, and Chagall-like.

Download parameter file b29.xpf

But as I got closer to the kleenex box, I saw the fractal shape was just a big butterfly.

I never thought much of this kleenex box genre until I saw an amazing collection of six boxes for sale in the grocery store. Packaged together in clear wrap, a plastic carrying handle on top, just like the jumbo packs of toilet paper.

Each one could have been put in a glass case or flattened out and framed. And these were only the economy priced kleenex boxes.

You can find boutiques selling ritzy kleenex box covers made of metal, cloisonne or wood. But there are cheap paper board boxes made with material thinner than cereal boxes, made to be used and thrown away, that look better than the $50 dollar luxury models.

There are places in the world where poor people decorate their houses, or shanties with pictures from magazines and other th…

The Fleshy-Headed Microbe

If you switch from the first orbit counting method to the second, the arms turn springy.

Download parameter file squork09.loo

Which raises the question, just what can we expect to see in fractals?

I think fractal art is very similar to photography. We don't create the subject matter we create the way it is presented.

Everything you see in photographs you can expect to see in fractals. Fractals have the same potential as photography. That's quite a bit, isn't it?

Except for the wide range of expression made by human expressions, and of course reality in general, which has no equivalent in fractal imagery, since fractals are abstract, other than that, we should expect a lot from fractal art.

Well, maybe the absence of people and realism is a major limitation to fractal art. But are fractals really abstract?

The squork bugs here looks somewhat real, just stylized. Many fractals are named after real things because they have such a strong resemblance. Perhaps "abstract"…

The good, the bad and the mandelbrot

Bottlecap Boy, on the left. The Pull-tab Kid, upper right. Who will draw their guns first?

Download parameter file twomandels.xpf

We hear shots, we see smoke. It's Big & Dark vs. Small & Shiny.

Nothing happens. The shots came from somewhere else. The smoke is unexplained, maybe it was dust.

Close-up shots. The Kid is left-handed. Bottlecap Boy isn't used to that.

Still more close ups. Bottlecap Boy hasn't shaved for days. Just as well, it hides the scars. Man, he's ugly.

Why don't they shoot? Why?

Yes, the music isn't finished yet. They're waiting for Ennio Morricone's crescendo of trumpets.

Bottlecap Boy falls down. Even that takes a long time. Sergio Leone has rewritten the laws of physics just to make this scene.

No, just wounded. He's still alive, his gun has been shot conveniently out of his hand though.

Increased options for the screen writer. Dead gunslingers just get buried, but wounded ones can live on to spark a thousand flam…

Snowy, the ice pony

He's happy. The air is crisp, the snow's not too deep, and the bright sun makes the whole world shine like silver.

Download parameter file snow.xpf

So what could ruin his wonderful day? Ancient Mongols looking for fresh riding stock. Or something to hunt. Dead or alive, they want him.

Allow me to share some thoughts on Genghis Khan and his band of merry men.

People underestimated them because they were nomads. A bunch of goofs on horseback.

No palaces, probably not even a garage for the ponies either. Did they have writing? Who knows. I mean, I don't know.

Somehow they got themselves organized. Cooperation allowed them to accomplish things their neighbours never expected.

They had the most advanced bows, which utilized a composite construction of wood with leather joints, shooting arrows like bullets. Their spare time was spent hunting tiny animals from horseback at a full gallop.

People, even soldiers, were much easier targets.

What he learned hunting rabbits, he applied…


Torn off, stuck on, tucked away. Framed by fingerprints. Legless, armless, torso of words. Stone among the ashes.

Download parameter file twohead.xpf

Home of the Two-Headed Mandelbrot: A subtitle I considered using for my blog.

This one really shows how easy it is to make good stuff with Xaos.

Recipe: Biomorphs in-coloring, squares out-coloring, edge detection #1 filter, anti-aliasing, palette emulator, magnet 1 formula, rotate so it's not lop-sided. Press the random palette generator hot-key, "p" until you see something worth saving.

Use a dirty cookie sheet and you won't have to grease it.

Cook 'em till they're burnt a little. The charcoal is good for you, it absorbs all sorts of intestinal junk.

It's a frustrating formula. This image is nice, but zoom in and all you see is the same stuff. If all fractals were this self-similar they're wouldn't be any fractal art.

It takes longer than your standard mandelbrot to calculate.

Why all the mandelbrot…

If you kick a fractal hard enough...

It swells up like a puffer fish and crackles with electrified rage.

Download parameter file soccer.xpf

So, only kick them once. The second time you'll get zapped.

Reminds me of the time I was bitten by a golden-haired ant in Mexico.

I was doing my regular rounds of collecting water samples from the four sites in this coastal dune area just north of Veracruz on the Gulf coast.

The last site was in an older, wooded area and when I was finished I decided to check out a semi-rotten stump I'd seen some strange ants in.

There's alot of strange bugs down there, but they're secretive and don't like people and you have to go looking for them.

Sure enough, just as I had thought, these big black ants had some sort of golden fuzz on the tops of their heads, middle and end parts. Feeling relatively safe, I began to poke around their hole with my walking/spider-web-clearing stick.

Pretty soon there were quite a few of these golden ants coming out of the hole and racing around. But th…

Fractal Morrisseau

Swimming to Mars

Download parameter file mars01.loo

For years a colorful painting of a fish hung on the wall in my parent's dining room. I grew up with this mysterious creature with colorful x-ray organs watching every meal.

I forget how they came to own it. My dad, one of the few doctors in the town of Dryden to make indian patients feel welcome, might have been given it as a gift from one of them.

It's painted and signed by Norval Morrisseau. People will make a big deal about him being an indian, or native, as they say today, but really he's just another great artist.

There's a nice slide show of some of his work at where you can judge for yourself if it has any resemblance to my fractal displayed here.

Yeah, they've got fancy little folk tales to go with all the paintings, but that's just for the tourists. Like most artists, he painted the things which interested him.

I remember reading in a Carlos Castaneda book where Don Juan was talking ab…

Glowing pyramid of power

Crashing surf of cosmic rays. Electro-frying crackling haze. Pounding pulsar shaking wave. It's full of stars, says Dave.

Download parameter file pyramid.xpf

I don't know if you've seen the garbage remake or sequel to 2001: A Space Odyssey. 2010, I think it is.

There's nothing good about the movie. Although, I should be careful, I saw it like 20 years ago and I'm famous for mixing up movies and creating recombinant memories.

It doesn't much matter since there's only one good scene to the movie. At the end, someone, or maybe more than one, goes over into the monolith, exclaiming, cryptically, "It's full of stars!"

Or something to that effect. Which brings me to my main point that at least the makers of the garbage sequel had the brains not to mess with Kubrick's surreal and cryptic utterance by Dave (or whoever the last guy left alive was called).

Arthur C. Clark wrote the original story? Someone like that, I guess.

I always liked that lin…

Crinkle Lips throws a party

He's an idiot, but his friends are just as stupid.

Download parameter file color03.loo

There's something comical about these images. The twitching, whip-like arms and goofy bodies.

Crinkle Lips is the big one in the middle. The ones above him have arrived together in the same raindrop which accidently splashed down on his head.

They think it's funny and one of them is laughing. He's a cousin of Crinkle Lips. You can see the family resemblance.

On the left side are a group of triplets who have walked in separately. They're not too bright and always like to stick out their tongues, like they're doing now.

Some of them will walk into a tree or trip over each other.

They don't eat anything, which is good, since a gas barbecue or even a plastic fork would leave at least a few of them with serious injuries.

On the other hand, take a closer look at Crinkle Lips' "feet." Claw-like and shaggy.

Kind of reminds you of... I should have been a pair of ragged …

Freezin' Fractals

Out of the south comes the whirlwind: and cold out of the north

Download parameter file whirlwind.xpf

Once again, a fractal that owes its interest entirely to the randomly generated palette. A subtle change to the palette created the contrasting areas of dark and light.

Perhaps "fractals" is a misleading name for these sorts of images. The word implies a basketfull of fruit or vegetables. A whole bunch of the same stuff.

The truth of the matter is that most fractal images have as much in common with each other as most photographs have with other photographs.

Fractalgraph. That sounds better. It implies something made by fractals and not the "fractals" themselves.

The similiarity to photography is good also since fractal programs merely produce fractal material which the user selects and frames-up just like a photographer.

What if photography was called "photos"? Sounds pretty limp and day-old, doesn't it?

Of course, if you take fractal images and do all…

What's shakin' with Ushiki?

When it comes to microbe-mania this guy's infected!

Download parameter file squork02.loo

I test every new color setting for the orbit counting renders with the number 7 formula, Ushiki Phoenix. If it's any good, Ushiki will show it.

It's a paradise for parasites.

Look at this one and his wacked-out buddies, flying around in epidemic formation.

This one is a Julia mode, which adds a freak factor to the usual harvest of microscopic mutants.

I'm so glad the fractals, or whatever these things really are, stay in the machine and never leak out.

What a strange twist to the Andromeda Strain: fractal infection.

Fractalia pestis. The Black Death of our time. Eventually the victims, loaded with parasites, begin to resemble the fractal formula encoded in the microbes' DNA. Just like some Serpinski's triangle inside you growing in reverse.

Freaky Ushiki: Fractal of Death.

Yeah, some of the microbes don't kill you because they have a different formula in their DNA. You don&#…

Attack of the Sky Spiders

...from outer space.

Imagine the horrible things that could happen. Think of the horrible things that have happened. Were they unimaginable?

Download parameter file 500_tidepool05.loo

Endless poisonous insects dropping from the sky.

I can imagine that. Don't unexplainable things happen all the time?

William Wordsworth once said that any reasonably developed technology was indistinguishable from magic.

In other words (no pun intended...) if you don't understand how something works, it may as well be supernatural.

The economy, for instance. How does it work? Why is there so much controversy over what should be done to improve it?

Since we don't understand so much that takes place today, why are we so sceptical about the horrors of the future? We ought to expect anything.

Why not civil war all over the place, in every country, all the time? Why does peace happen?

Aren't dinosaurs hard to believe? Many of the best monster movies are based on museum materials. Jurassic Park …

The cave-paintings of our time

Left on the walls of primitive dwellings. Anonymous, mysterious, depicting scenes of ancient slaughter.

Download parameter file xmas04b.loo

Hey, if you guessed, "What is Fractal Art?" you win!

Truly, these are the cave-paintings of our time.

I'm joking, of course. But just think: what if the only "artwork" to survive the coming nuclear destruction and be admired during the subsequent planet-of-the-apes phase of earth's history is graffitti?

Sure, all those Henry Moore sculptures will definitely survive thermonuclear destruction, but without signs or bronze plaques no one will know they're art.

What if graffiti becomes the sole influence on the next thousand years of art, just like all that busted pottery was to western art?

What sort of murals would you find in the palaces of the ape-kings? I can see it now, behind the throne, starting at the floor and reaching the ceiling, in chunky letters, "BossBoy rules!" The Bayeau Tapestry of their time.


They came, they saw, they squeaked

World domination just wasn't a realistic goal for the squiggle people.

Download parameter file squeaked01.loo

Sure, the entire voyage had been financed on conquering new lands. But the frenzy of excitement at the first sight of land...

Weeks later they were still running down the beach and tasting every new fruit they found. The ship's log hadn't been updated. The captain was last seen chasing a butterfly into the woods.

Eventually they had a meeting, for 5 minutes, while gathered under a tree to get out of the rain. They all began cheering, "Burn the ship!" and tore off in every direction.

Years later, a second expedition arrived. They set to work building houses and looking for commercially promising resources.

After several executions and the depletion of their funds, they returned to the old country and never came back.

The squiggles reached the other side of the continent, built rafts and floated out to sea, tired but optimistic.

Little remains today of this fi…

I like Christmas junk

Imagine an ICBM silo. Imagine a Christmas tree. Now, with your mental graphics program, start to morph them together and stop half way.

Download parameter file xmas01.loo

Well, you don't get this image, although it has a Christmassy look to it also.

I saw this cheesy, singing, 8-inch, ornamental Christmas tree for sale. You press the red button on the base and the top two-thirds of the tree starts to rise up, in missile silo fashion, revealing a miniature revolving Santa and reindeer underneath.

Syrupy music plays for a short time and is drowned out by a squeaky, child's voice exclaiming, "I LOVE YOU SANTA!!!!!! I LOVE YOU SANTA CLAUS!!!!"

More cheap music while Santa and the deer go once more around the tree. "I LOVE YOU SANTA!!!!!! I LOVE YOU SANTA CLAUS!!!!"

A blast of music, the sled grinds to a halt. Down comes the evergreen cone and the hidden party is silent and camouflaged waiting to be launched by the red button.

There are a few questions: What so…

Autumn in fractal land

With the last of the leaves, goes the memory of summer.
    -Shakespeare, Hamlet IV

Download parameter file spiral11.xpf

The sun, upper right quadrant. Just a distant glow, and in it's departing wake comes night and wind.

What are the seasons really? Are there just four? Maybe two?

Summer is the time of cold-seeking. Winter is the time of heat-seeking. In between is something different. But isn't spring just fall in reverse?

Winter comes in stages, like the approach of a large city as you drive down the highway.

Eventually there's a windy day, the trees are bare.

Leaves exist only for sunshine and in them is color and sugar, the beach toys of summer.

Like a president on a jet or a general in a helicopter, winter arrives from the air.

Square machine

I love the paintings by Chirico, or whatever his name is, the Italian surrealist painter. Why are there so few artists like him?

Download parameter file cubic.xpf

Sometimes the first edge detection filter in Xaos produces a chalkboard like style on dark backgrounds. It then takes on this handmade look. When the subject matter is square-ish, the result is a blueprint, drafting table-like image.

This is what is so exciting about fractals: the fractal structure is just the beginning, not the end of the process. There's so many ways to color it or otherwise process it that fractal art can become a strange way of drawing and very creative.

The sudden change of the palette makes something interesting out of something dull. A simple, repetitive image can be instantly reborn as something carefully drawn with a flawless eye for detail.

I think there are two kinds of fractal images: "faces" and "fingerprints." The big fractal images that show the whole formula are lik…

The humble Mandelbrot

I used to think it was cliche and juvenile, but after three and a half years I've never tired of seeing new variations of the classic mandelbrot man.

Download parameter file brot02.xpf

Maybe it's the shape: well balanced, curved, pointed, detailed edges, solid spaceous center.

Also, for reasons beyond my mathematical capabilities to explain, the mandelbrot guy appears in various places with slightly different characteristics.

He reminds me of Alfred Hitchcock. Also a Geography professor I used to know with a big paunch who wore his pants halfway up his stomach.

But you know, why does everyone assume it's a man?

Well, on second thought, let's not go there. It could just be that since it's named after the mathematician Benoit Mandelbrot, that it got its gender that way.

Back to the math. The inside of the mandelbrot is uh, the inside part. It's separate from the outside part. Well, forget the math...

I've used the squares in-coloring method here and the biomorph…

Zippy, the happy fractal giant

Aw shucks, everybody loves Zippy.

Download parameter file zippy.xpf

Where does he come from, and what does he do?

He just walks around whistling a cheerful tune and smiling at everyone he meets.

You're in the kitchen, working away, you hear a noise, turn around... it's Zippy! He's just popping in to say hello and get back on his way.

I know you're all familiar with the theme song to the Australian TV show, Skippy the kangaroo. Try singing this: "Zippy, Zippy. Zippy the fractal..." Darn, it doesn't work.

That's okay. Zippy will write his own theme song. He's the Uncle Remus of fractal land.

But you know, and maybe I'm paranoid, or just mean spirited, but I'm not sure Zippy is always a nice guy. Sometimes I see stuff smashed or whole trees uprooted and thrown hundreds of feet away.

It's got to be Zippy. Who else can do that? Sure, maybe a tornado, but I think I would have noticed a tornado if there was one.

I've never actually seen …

Die Fractelung

Supposed to be German. I think it's close enough.

Download parameter file shadow.xpf

Once upon a time, back in university, down a remote and rarely used hallway was an art gallery. It was always closed when I walked past it. The whole campus was generally in a state of semi-hibernation.

Twice in the four years I was there, it was open. I always went in (no charge) and looked around.

There was a display made up of old photographs blown up and put onto laminated styrofoam sign-board material. The photos were grainy and of low quality, the kind I like.

I don't know who was behind the exhibit because there wasn't really any artwork around, just this photo display that could have been set up in a shopping mall. But I used to browse through the library on a Saturday night for fun, so I wasn't going to leave just yet.

The photos were of turn of the century Wagnerian stage sets with titles like, "Klingor's Keep" and "Tristan and Isolde" or something lik…

Radio, live transmission

It's a detail of a detail. The pattern reminded me of the speaker covers on a portable radio or the metal mesh of an old fashioned satellite dish. Can satellite dishes be old-fashioned?

Download parameter file radio.xpf

Or maybe a tiny part of a towering antenna. Far from the ground, alone in the air.

The sun sets. Moonlight reflects on the mesh and the antenna merges with the endless night sky.

Still and empty, electrified and alive, silent transmission.

Named with numbers and secret signs, made by math and radiating lines, anonymous tree of technology.

Routine maintenance, a single truck with hard-hat priest, performing the technical ritual.

Still the same reliable radio, the perfect echo, adding nothing.

Relaying, repeating, no heartbeat, no breathing.

Corroded with age and growing with beauty, humming the symphonies of the glowing cities.


What hath Xaos wrought?

I checked the spelling on that last word and it's correct. I was sure some of those letters had to go since they're clearly vestigial.

Download parameter file spiral30.xpf

If you try out the parameter file, I suggest you start by just pressing the random palette hotkey "P" a few times to see what radical transformations the palette can make.

Color is such a mysterious thing. I can always tell when it's just right, but I can't do anything to improve it when it's wrong.

That's the beauty of the Xaos fractal program: it harnesses the power of computing to present you with endless color choices. Imagine an enormous box of pencil crayons with a high-bypass turbojet engine strapped to them.

Yeah, now you understand.

Some people make their own color palettes or whatever they call them. They do it color by color and sometimes by candlelight. That's admirable and lends a gentle human touch to a technology-laden artform. But the random palette algorithm in …


It used to really bug me to see an image on a fractal site and hear how the artist really liked it because it looked like something real, like a flower or animal. It bothered me because fractals don't have to impersonate or represent "real things" to have artistic value.

Download parameter file ice.xpf

But here I am, doing the same thing, so forget all that.

First the serious stuff. It's a plain mandelbrot; default plane, "mu"; edge detection, although it doesn't look like it; iteration outcoloring; iterations lowered from 170 to 70.

None of that explains this arctic snow drift formed from sea ice, broken and pushed up. Or the blowing snow and ice crystals that swirl about and merge into the starry sky...

If you've never experienced winter, and most people on earth haven't, think of it as a sand dune and ignore the bit about blowing crystals.

Strangely enough, the file size of this image is large (115k) for the sort of stuff that I usually make. B…

Needlepoint fractals

Long before electronic computing, Grandma Mandelbrot made this simple needlepoint image.

Download parameter file needlepoint.xpf

Pillows, quilts, tea-cosies and table cloths: everything in the old homestead was decorated with her unique designs.

Book covers; curtains; table napkins; shirt collars: she was quite a prolific needlepointer.

Dresses; gloves; winter coats; canvas shoes; horse blankets; socks; bed sheets; coverings for the piano legs; doll clothes: she was nuts, obsessed, out-of-her-head; needlepoint all day, needlepoint all night...

She ran out of fabric. Her daughter burnt the wooden frame thing and took a hammer and drove all her needles into a piece of firewood.

She had extras, hidden for just such an occasion. She stole more fabric.

Back then there was no psychiatry or stuff like that so they just pleaded with her to stop and tried to keep visitors away from the house out of embarrassment.

Until she sold one.

Then it was dear mother this, and dear mother that. Get mom some mo…

Brave New Fractal World

"Fractals make the Sistine Chapel look like cave paintings" -Walter Merton, World Museum of Art

Download parameter file image_8.loo

Just what could the future look like if serious and hardworking artists discover the creative power of fractals?

In the year 2025, not too long from now, fractal imagery is everywhere. The restoration of great masterpieces, like that of the ceiling of the Sistine Chapel have been abandoned. According to a leading restoration expert in 2025, "Why should we spend millions of dollars and years of effort when I can make something better with my computer in a few seconds?"

In schools of the future, the same attitude prevails. I open my son's university textbook on Art History: It doesn't start with Greek pottery and busted figurines. Chapter one, Origins of Art, is a biography of Benoit Mandelbrot.

"If you want to see what we used to call 'the old masters' today," says Vito, a retired gallery curator, "you h…

Color Town

I just can't get over the goldmine of color that's been liberated by the orbit counting render methods. Until this happened, I'd come to accept the earthy and subtle colors of Sterlingware as just one of the characteristics of the program.

Download parameter file color01a.loo

It's truly a program that can produce a great range of fractal imagery.

This image uses the "03) orbit counting" render setting, although the 02 one works well also. 04 and 05 don't give quite the same results.

The only other parameters of note are the Stalks and Bubbles radius that has been upped from 0.05 to 0.50, and the iterations, which has been decreased to 10 from 30. The iterations value doesn't much matter so I lowered it to increase the processing speed.

But it's the color that's most important. The color number is 11. Never before have I seen anything look good with this number. In fact, all the colors below number 13, I considered a waste of time to experimen…

Take off your shoes, worm!

And grovel before the King of Sterlingware.

Download parameter file keepontruckin.loo

I'm joking, ha ha, keep your shoes on. But I just can't get over having all this blogging power at my fingertips. And for free too.

I remember reading a book about the difficulties of getting a book published. It was really depressing how hard it is for good authors to find a publisher.

Of course, from the publisher's point of view it's not easy to find works that will be profitable. Printing books is expensive and it seems fewer people read these days... and it's just that sort of depressing dilemma.

But look at all this. Blogger gives you unlimited blog space for free. No ads, simple to use templates.

Who's paying for all this? Well actually, it's all rather cheap to start with. Publishing blogs, or any other online content is nowhere near as costly as the old book method. And Blogger belongs to Google and Google is the friendly giant of the internet with a great big c…