Snapshots from the Fourth Dimension

The sine-trap 01 and 02 render methods in Sterlingware have always captivated me. They have a real vintage sci-fi look to them.

Download parameter file rocket02.loo

It was only natural then to spend some time trying to find new color settings for them. Diamond shaped bean strings/ long tails with shark fin collars/ and then tangled masses of both, produce a rich forest of imagery to be captured.

But they can also be repetitive and boring at times. That’s why you have to get off the beaten trail, so to speak, and zoom into the tangled underbrush.

I’ve got alot of images based on this render setting, and next to the fractal dimension option this one has been the most productive.

Add in Julia Mode and you’ve got the ingredients for some very exciting stuff. Julia Modes will mutate the simple sine-trap plant growth and produce contorted forms.

I used to read about the “fourth” dimension in comic books. It was something like the proverbial “parallel” universe. It could be anything the author wanted it to be, but it was usually a big, space-age city with insect-like people rushing around acting serious.

I think it was meant to be threatening: To suggest that right under our noses was a burgeoning empire ready to overwhelm and incorporate us into their army of slaves: silent, anonymous, then move on to other conquests.

Hmmmn…makes you wonder. Just what is underneath the floor of the universe? Or behind its walls?

October 25, 2005

Mandel with its head blown off

Finally, a fractal program that saves in PNG format and also supports the use of high explosives. It’s called “perturbation,” which is, I assume, a standard mathematical term since I’m sure no one would deliberately give that name to anything.

Download parameter file mandel.xpf

It’s free, it’s fun, and if you’ve ever experienced the joy of blowing up your toys with firecrackers, you’ll love this.

I’m not sure what it does mathematically, but the result is a fractal that looks like it’s been flash-frozen and carefully dropped on a concrete floor.

Or, imagine a fractal image painted on a lovely china plate then whipped out of a car travelling 70 mph as it passes a brick wall.

That’s not quite it. When you press the hotkey, “b” and hover the mouse cursor over an area, the image is almost instantly transformed just as if the cursor detonated a charge of dynamite.

I’ll bet Ultrafractal doesn’t do this. This is not a serious fractal function. It’s built for the “true enthusiast” who demands the freedom to blow up his work at any moment.

It does create some interesting images when combined with the edge detection filter. Xaos is short on formulas and this helps to spice up the plain mandelbrot sandwiches.

What would really be cool is to add an explosion sound effect to the mouse-click, or to change the cursor to a hammer whenever the perturbation function is used.

They’ll probably just laugh at me if I suggest that. Nobody designs software for nutcases like me.

Maybe it could have therapeutic value; the smashing and everything. How about some of you fractal folks with problems, like say, excessive anger or paranoia, trying it out for a few weeks and letting me know if it helps.

October 24, 2005

Printmaking made easy

By now it may be obvious that my approach to Fractal Art is somewhat lazy. My creativity is limited to photographing fractals rather than developing them into more complex works.

Download parameter file orangevilla02.loo

We all have individual preferences, not just in style or artistic taste, but in the tools of art. I like to keep it simple and concentrate on the capabilities of the fractal generator, despite creative limitations.

But there’s so many things you can do with a fractal image in a graphics program like Photoshop. And with all the added effects and filters from a graphics program your fractal artwork may become more creative. I say “may” because it takes time to get a feel for, and become creative when you use more complex tools.

I’ve always liked art, that is, looking at art. Way back in high school art class we were forced to work with a wide range of mediums. I didn’t like any of them. Drawing, painting, pastels, bas relief, sculpture, etc… My accomplishments with these tools were discouraging.

I liked printmaking and silkscreening, but even that was alot of work. Planning, sketching, multiple layers… The traditional ways of making art are hard. Just like learning to play a musical instrument.

It’s been twenty-some years since then but I’ve finally found my thing: art machines. Algorithmic, generated: the computer does the work and I just coach it, and put my name on the results.

I’m excited about the fractals from Sterlingware that have a “printed” or silkscreened look. I can’t change the image the way a painter could, but like a photographer I can frame up an interesting piece of it and save it. It’s like cutting out pieces of a great Japanese print.

I always knew there would be an easier way.

October 23, 2005

Fluffy, the cat who loved rabbits

Everyday I get hundreds of emails asking me to write about animals and the warm and fuzzy things they do.

So at long last I bring to you the true story of Schwartz and how he came to earn his new name, “Fluffy.”

Download parameter file spiral10.xpf

Once upon a time Schwartz, my younger brother’s white and tan cat, went out to the hay fields around our farm to seek adventure. The hay had just been cut, and for some unknown reason he seemed to be heading out to the hay fields alot. Also, he hadn’t been eating much of his catfood.

Some time later, on this bright summer day, he returned with something small and furry hanging from his mouth. It was making a faint screeching and screaming noise.

Schwartz, friendly as usual, sat down beside the sandbox where my niece and nephew were playing. He began to chew on the baby rabbit in his mouth.

It wasn’t exactly a rabbit, but a “hare.” It seems that “hares” are different from “rabbits” in that they live in nests above ground and not in holes. The cutting of the hay field had disturbed and revealed to every creature around, many nests of baby hares.

My niece and nephew ran into the house crying. By now there was a considerable amount of blood on the grass, enough to give any Walt Disney movie an Restricted rating.

It gets worse. My mom found quite a few little bunny bodies on the lawn during that period. She said they hadn’t been eaten, but all the heads were missing. Sometimes just the top of the head was gone. It seems Schwartz, just like the zombies in Night of the Living Dead, was only after the sweet, fatty tissue of the brain.

I always called him Fluffy after that.

October 22, 2005

Layered fractals: Images math never intended

“There are no natural fractal images, only post-processed ones.”
      – Plato

Alright then, the so-called “post-processing” is okay, and the debate has been laid to rest. But what about layering?

Download parameter file flatblue.loo

No way. It’s unnatural. Some layered “fractals” don’t even look like fractals.

And it’s hard work too. When you layer an image it takes all sorts of adjustments to get it to look good. Organically grown fractals are easy to make: the generator does everything and you just save whatever looks good.

People who layer fractals just want to make their lives hard. It’s almost like traditional brush and canvas art that took ages to make and required plenty of talent and training.

That’s why I prefer to hunt, gather and scavenge my fractals from off the ground. It’s so much simpler just to pull one off your boot and frame it. In the words of Laika, the first dog in outer space, “Bad artists borrow, good artists steal.”

Well, maybe Laika never said anything like that, and certainly not in English, but if he (she?) were smart he probably would have.

A quotation from a dog? Great. Now no one’s ever going to believe anything they read here.

The parameter files never lie. That much you can trust.

October 21, 2005

Why post-processing is evil

I know it’s a dead issue, but I’ve never had a chance to speak on the matter and I feel like talking.

Like a master geometrician allow me to solve this question in a few simple steps and then quietly sit down.

Download parameter file evil2.loo

First, stop me if I’m wrong, but the beginning of all fractal images is the calculation of a series of two-dimensional (horizontal/vertical or x/y coodinates) points by carring out the instructions of the fractal formula (ie iterating it). This just creates alot of information, you can’t see anything yet, it doesn’t produce anything visual.

It’s similar to a magnetic field. Imagine a magnet under a piece of paper. You don’t see anything until you sprinkle some metal filings on the paper and the metal filings reveal the invisible pattern of the magnetic field. A magnetic field, alone, cannot be seen.

There, I’m done.

Okay, there’s more. You can’t see the output of a fractal formula: the millions of coodinate points. Our fractal, pure, serene and still living in the divine realm of mathematics has no clothes and looks just like the Invisible Man without his wrappings.

The next step, only the second one, is to “render” the huge map of x/y points. This is the same as deciding what we would like the invisible man to wear.

Just as we only see the clothes the Invisible Man wears; we only see the “clothes” the programmer dresses the fractal in.

It’s that simple. But let me explain things another way.

Have you ever noticed how the same fractal formula with the same settings always looks different in every program? Well, why is that?

How a fractal is rendered to make it visible (that is to render it “graphically”) is 100% artificial and arbitrary. It’s entirely the decision of the programmer and is the style or method they’ve chosen. This of course is why there is more than one fractal program and why some are more popular than others. Making fractal programs, even simple ones, is a creative and not a mechanical activity.

In other words, all fractal images are artificial. We don’t normally call them “post” processed because the processing is done in the fractal generator. But it’s all post-processing. Which is to say, it’s not determined by the fractal formula, it’s independent of it. It isn’t the generation of the fractal that produces the image but rather the arbitrary, artistic preferences of the programmer. What you see is never the math, only the artistic embellishment of the math.

Even if the calculation of a fractal formula was graphically rendered with a drafting plotter in the math department of a university it would still be a post-processed fractal image, just a very plain and uninteresting one.

Well, there you have it class. There are no natural fractal images, only post-processed ones.

October 20, 2005


On an island in the Pacific somewhere there are trees that have very smooth but thick bark similar to beech, baobob, or fig trees (depending on what you’re familiar with). They have been known to live for 600 to 800 years, but once they are more than a hundred the inner wood disintegrates and the trees become hollow.

Download parameter file skyhole.xpf

As long as the island has been inhabited the people there have lived in these hollow, but still living trees.

Inside, on the inner walls of the tree are deposits of sap or resin. This material dries to form a hard, glassy material with a slight bluish tinge. It gives the inside of the “house” a jewelled look.

From time to time, due to age or insect damage, openings form in the ceiling of the house. Since there’s very little rain there’s no reason to fix these holes and they perform the practical function of letting in light or letting out smoke from cooking fires.

There are no windows as we know them or even doors for that matter since the wood is extremely hard and difficult to cut through. Everything comes in or out through these holes in the ceiling. The native word for these natural chimneys or skylights is literally translated as “skyhole.”

October 19, 2005

Who cares what the name is?

A good name is at least a meaningful label. Like a magnet it attracts the right things and repels the wrong ones.

Download parameter file glob.xpf

Names I didn’t choose: Fractal Safari; Fractal Mine; Fractal Voyage; Fractal Journey; Fractal Tales; Fractal Caravan.

I wouldn’t call this an art gallery, so I avoided anything artsy. It’s not a technical discussion either.

I wanted a name that conveyed that special quality that makes fractals exciting: The math is interesting and the artwork that comes from it can be good, but there’s something more.

I don’t know, a fractal program like Sterlingware or Xaos is like a magic beanstalk and here’s some of the things I’ve found. And an electronic trail of bread crumbs so you can go right back to the same place, if you’re curious, or sceptical.

That’s good enough, who cares about the name?

October 18, 2005

The glory of fractals

When I first discovered fractals I was sceptical and disbelieving. I was curious, but I sensed that they were being hyped and promoted by some group of fanatics trying to make their little thing into something big.

Download parameter file cutout.loo

Then it was like falling down the rabbit hole, so to speak. Everything I saw was incredible and endless. I saved thousands of images because I felt they were all unique and I would never find my way back to that place again.

I would go to bed late, not quite sure that what I had seen was real. Occasionally I stared at the image on my monitor and wondered, “what is this!”

I couldn’t relate fractals to anything else I knew. They seemed to be a strange new world separate and unconnected. I had seen things no mortal was meant to see.

Well, as it turns out, they’re just fractals. Very down to earth and natural. Mathematics made flesh.

Previously, they had been known only in theory, dreamed of by mathematicians. The written formulas they had discovered were the seeds. Computers contributed the environment where they could grow.

But for me, there’s still an element of the fantastic or the unbelievable to them. It’s just like in the fairy tale of Jack and the Beanstalk. The magic beans grow into a towering plant that leads to a world above the clouds, separate and strange.

October 17, 2005

The fractal that dripped blood

Or better yet: The mandelbrot that ate people.

It’s because of chance discoveries like this that I keep experimenting with Sterlingware. I’ve never seen this sort of Jackson Pollock, paint all over the place look before. The color worked out well and has a number of variations that look just as good.

Download parameter file blood2.loo

It uses the “x/y; y/x; stalks” rendering method which is generally pretty frustrating and one I give up on quickly. You have to enjoy the hunting and gathering process to work with fractals.

Hmmmn… what else? I never saw the movie, The House that Dripped Blood. But it’s not necessary to see movies, or even read books for that matter, to talk about them. I saw the title, I talk about the title.

I don’t like Jackson Pollock’s artwork either. It’s very interesting that he may have actually generated fractal or chaotic graphics with his swinging paint cans, but I don’t find them interesting artistically. And they’re big! That’s one good thing about fractals, and digital art in general, it’s easy to handle.

In case you’re trying out these parameter files, you might like to know that almost all my images are anti-aliased 4:1. You make an image four times the size you want and click on “anti-alias 4:1” in the drop-down “image” menu. Anti-aliasing is just a wacked-out, funky, jargonic label for smoothing. It’s just like using sand paper when working with wood: it makes the final result look polished.

The man who invented the term “anti-aliasing” is still in therapy. Coining the term was enough to convince a judge to give his wife power of attorney over him. If there were a Nobel Prize for sociopathic contributions to confusing terminology he would have gotten the first one. He didn’t live long after that. The stoneworker who engraved his tombstone made the lettering as rough and jagged as possible and didn’t complain when his estate refused to pay him.

October 16, 2005