The Arabian Nights


Just like fractals, there is a special allure to the stories of The Arabian Nights.

And also like fractals, I think that special quality that makes them attractive comes from their unique origin: fractals springing from a strange new area of mathematics; and The Arabian Nights, from the Middle East.

I’m not even a student of literature, or even much of a reader at all for that matter, but I’ve noticed that there are artistic differences between the folk tales of the British and the Europeans, and with those of The Arabian Nights.

What are they, you ask? Well, read the book and find out. It’s there, as curved and flowing as the arabic alphabet it was originally written in.

So I like fractals to be fractal-ish and The Arabian Nights to be Middle Eastern, retaining their Arab and Persian (Iran) origins.

How can fractals or Middle Eastern folktales be anything other than what they are?

Just as The Arabian Nights can be mistranslated or European-ized, fractals can be layered and “artist-ized”.

For example: one translation of The Arabian Nights I read told how Sindbad returned to Baghdad after another voyage into the uncharted world and out of thanks for surviving, gave a large donation to a “church”. Obviously it was a mosque, but why use a word which in 20th century English usage is never used to refer to a mosque? (And this was a version from the 1940’s.) Why not change Sindbad’s name to Sigfried or Samuel or Stephen, as well? Or substitute Basra with Vienna (not a good substitute for a busy ocean port) or Paris or London instead?

Anyhow, translation isn’t always so simple and sometimes there is more than one reasonable rendering and the final choice can come down to subjective, stylistic preferences that grow out of long, complicated scholarly arguments — the sort of things which I suspect bored Sindbad in Baghdad and drove him back out to sea… In fact, the Sindbad stories, although also of Middle Eastern origin, are not considered part of the Arabian Nights and were included by European publishers who regarded all Middle Eastern folktales as a single category, in the same way as “fractal” art includes, from time to time, imagery that isn’t strictly “fractal”, but looks like it.

I’m not arguing for a “pure” fractal genre, or even that such a category (is such a category even possible?) should have a special status; many of the stories in the “Arabian” Nights are very similar to those of Indian and Jewish origin. So in the literary arts as well as the visual arts, categories are a matter of degree because styles and methods are easily, even subconsciously, influenced and exchanged across (apparent) cultural boundaries. In such a context, purity has to be defined because very little is or can be isolated.

What I would say is: Don’t overlook the “natural” beauty of a simple fractal formula rendered in a fairly plain way in a program like Sterlingware. There is no natural or “pure” way to graphically render fractals, but it is possible to use simpler methods which allow the fractal algorithm to contribute more of the imagery instead of less. Like a translation that doesn’t attempt to embellish or transpose the cultural context of The Arabian Nights, sometimes fractal art can be more interesting by allowing it to retain its original “style” and making less adjustments to it.

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Why I don’t use Ultra Fractal

In a nutshell, it doesn’t do what Inkblot Kaos, Sterlingware, Tierazon or Xaos does. I want something that sprouts artwork after a couple of clicks. Ultra Fractal? It’s just too much work. Too many layers Too many moving parts. Too many moving parts that I have to move.

My first attempt at Ultra Fractal was three or so years ago. I don’t remember what version. I didn’t seem suited to it, but I didn’t think much about it at the time because I had plenty of other new fractal programs to work with. I didn’t know much about fractals in general, so I discounted my doubts about Ultra Fractal figuring I just didn’t understand it.

I picked it up again a year later because I had seen some really awesome artwork made by Paul DeCelle. I looked at Paul’s work and thought, “I want the machine that made that and I don’t care if I have to pay for it”. Well I downloaded some UF parameter files by Samuel Monnier (thanks, Sam) in hopes of getting some insight into the secrets of making these intriguing images. I have never seen anything take so long to render. It had something like 18 layers or parts to it.

Yes, some of you may be thinking, “Only 18?”. Well, I got Paul’s machine all right. What I didn’t realize at the time, but I have now come to understand, is the machine doesn’t make the artwork, the artist uses UF as a tool to make the artwork with. The program doesn’t come with an artist.

You see, that’s the whole problem. There’s no digital Rumplestiltskin inside UF like there is in most other fractal programs. Stop me if I’m wrong, but UF is all about layers, and layers are chosen and positioned by a human mind and not a computer algorithm, although an algorithm may have made each layer, separately. This may explain why there is very little really “freaky” stuff made in UF: there’s too much artistic control.

To borrow an expression from the Bible: Freaky is begotten, not made. It comes from chaotic and mathematical algorithms, not from human hands, not even talented human hands. (And your own skill and talent is the key requirement for making good artwork in UF.)

Even Gertrude Stein agrees with me. Here’s what she had to say about UF; “Freaky is not as strange as we can imagine. Freaky is stranger than we can imagine.”

Tim Hodkinson

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From such simple seeds the image grows.

I can’t help but think of Sindbad and the rest of the Arabian Nights stories. Maybe it’s the tent-like arches. Maybe its the carved, honeycombed cielings.

I think of centipedes when I look at the fan-like fingery things. Ragged claws… silent seas…

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Do we invent fractals, make fractals, or do we discover them? Who can claim to have invented a formula? All the combinations and permutations are there already, somewhere out there, like fish in a dark sea, and we merely reel them in, unaware that it was they who were waiting for us.

Do we catch fish? Or do they decide amongst themselves, deep down where we can’t see them, who will be next?

No. Fractals are invented and fish are just fish. Sindbad never lived and the whole book was made up.

But our thoughts are real. And from such simple seeds all of these have grown.


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Or call it a fractal generator.

What is a fractal anyway? It’s something you look at.

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The math is interesting, but how often do you see a fractal formula with a frame around it?

Fractals are the fireworks of math. Just for show.

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The fractal images that have deep meaning, and are often displayed as diagrams, are ugly. They are never stolen or deep-linked.

Displayed for medicinal reasons. For anatomical study.

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Music is the better noise; art is the better trash. Art is the garbage we admire and take into our homes. We put a frame around it so no one will throw it out or ask, “Are you keeping this for something?”

Someday a flying saucer will land in the street and an alien will walk out into our house, and look at the art on the wall and say, “Wow! That is really something.”

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We change a formula. We generate the image. Art happens. We wonder why.

That’s all it does: make pictures.

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Computers are blind; they don’t know what they’re making. They don’t see what they’re doing. That’s where where we come in. If it were not for us, computers would throw everything away.

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We do their dirty work. We get into the garbage can and salvage the good stuff. “Whoa! Why’d you throw this one away? You Pentium pinhead!”

Brown Paper Fractals

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Doesn’t it make them even more incredible, that they were painted on such cheap material; built on such humble foundations, as brown paper?

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I’ve often wondered what fractal art would be like today if it had been introduced differently.

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What if the first fractal program was kept secret, known only to the programmer? And the programmer presented the images it produced, not as some new artform, but merely as his own personal artwork?

He’d be a household name by now, like Mr. Clean or Aunt Jemima. The ensuing scandal that would have erupted when it was discovered that all his artwork was made with a computer program, would only have enhanced his reputation by adding a dimension of intrigue and notoriety.

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Actually, come to think of it, that’s what Jackson Pollock did. Sort of, in a way.

I won’t get into all the details because I don’t know what they are, but I think he created a fractal or chaos machine with rope, cans and ink. He didn’t make the paintings, he made the apparatus and operated it.

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And look how famous he is. Lots of people have heard his name and don’t really know what he did. That’s the mark of being truly famous; people know your name and they don’t know why.

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So there you have it. It really did happen. Only the programmer didn’t even know he was a programmer.

Stranger than fiction.

Fractal Stiltskin

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I failed grade 11 Math, but I did alright in the other stuff. It’s funny because fractal formulas seem to be more about the other stuff than Math.

The trigonometry means nothing. Give the program a poem and it draws a picture.

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They’ve always wanted to do this. For centuries mathematics dreamed of the theater, the stage and the circus.

Who spotted the hidden talent of math? Who saw them trying to dig under the fencing of their cage and let them out?

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Bored with rocket science, math wanted to join the circus, or just run through the world.

Straw into gold. What else describes the transmutation of grey numbers into dreamlike fractal worlds?

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Anyone can do it. That’s strange, because up to a few years ago no one could. Artists copy, but fractals create.

Exponents are the exclamation marks of fractal poetry. Other than that, who knows what fantastic foliage will grow from the poetic engineering of fractal genes.

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I think fractals are old fashioned; they like formulas that rhyme:


Fractals are the rebellion of math. Math has grown up, done its military service and finished school. Now it wants to grow its hair long, ride a motorcycle and chase the horizon. When it runs out of money for gas it will join a commune, give itself a neon name and rediscover agriculture.

Victorian Florian Fractals

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For those of you who have just joined us, the blog is now anchored off Inkblot Kaos Island.

Old maps and rumours brought me here. As Long John Silver often said, “You’ll only find dirt, diggin’ where others have dug!”

Which for me raises a question, “Why after all these years, should fractal programs like Sterlingware, Xaos and now, Inkblot Kaos remain so relatively untouched that someone like me can find treasure after only an hour of coming ashore?”

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While fractal software has reached a state of advanced development, I think the artform is still in its frontier days or dark ages (frontier sounds more upbeat).

We ought to be driving down paved roads and looking at street signs and billboards, but instead we are more like conquistadors stumbling on cities of gold or explorers eating strange fruit.

I was reading some very enlightening information on the technical aspects of fractal programs by Damien Jones at his fractal website, I understand Ultra Fractal and Sterlingware much better now.

Stop me if I’m wrong, but Ultra Fractal is not really a fractal program at all, it’s a processor, an efficient, sleekly designed, platform which empowers or facilitates the instructions fed to it by the user.

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It comes with no built in formulas or rendering methods or coloring things (well, maybe it does, but not like other programs). It’s like what open architecture is to computers: modular and extensible.

It’s a facilitator, an enabler, a processor, an engine uniquely designed for fractal art, where creativity extends not just to making new images but also the formulas, rendering methods and coloring methods themselves. Users don’t just make imagery, they make the program too.

UF is just the hub that brings all these customizable inputs together and makes them happen. It’s a different way of making fractals, allowing the user to program the program.

The thing which allows you to input your own formulas, translates them, or something, into pentium assembler code which is like grafting or merging it right into the progam’s own flesh and bones allowing you to…

It’s like Frankenstein! Ultra Fractal is the torso of Frankenstein and the users stick on and swap legs, arms, feet and, and, and, brains even (formulas).

I’m not saying it’s a monster; smashing through walls, kicking down doors, setting fire to homes, terrifying whole villages, leaving the women and children shaking with fear while the men march off as an angry mob armed with pitchforks and torches to kill and destroy something they don’t understand and never asked to be born. That’s nuts.

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It’s a new category of fractal software design. UF is the screwdriver handle that the user sticks their own custom made bits into. Combinations and permutations unlimited! Or limited, rather, only by the user’s ability to craft new add-ons or aquire them from a growing public library.


I couldn’t get it to make stuff like this, so I’m sticking with Inkblot Kaos.

Fractal Orbits

Once in a while I like to walk up a tall hillside, sit down and reflect on what I see.

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Something that has puzzled me lately is the fractal art contest with Benoit Mandelbrot in Spain. It’s a great thing for the genre of Fractal Art, but it just isn’t my thing and I keep wondering why.

For starters, I wouldn’t even have heard about it if it wasn’t for an email from a friend about another fractal project. Why did something so big and bright not appear on my horizon?

Submissions to the contest ended May 1st. I never even thought of submitting anything. The required dimensions of the submissions seemed foreign and distant to me.

I’ve never made images that big even for the purpose of anti-aliasing. I’m not even sure if the programs I use will allow such sizes. I didn’t even try to find out, either.

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If that is Fractal Art, then what am I making? What does that make me? Where on their map is my little town?

Don’t get me wrong, I like Ultra Fractal stuff. It’s very rich and yes, it looks polished and professional. It’s the sort of stuff that really should be hanging in a gallery, winning contests and presented to the world as Fractal Art, or at least at the head of the parade.

Most of the great fractal artists choose Ultra Fractal to work with and I think it’s because the program allows them to compose complex, stereophonic symphonies of fractal imagery. I’ve seen many of these concert hall images and some of them are my all-time favorites.

Download parameter file “orange03.zar”

I think this contest will, among other things, produce a fine showcase of Fractal Art to attract the attention of the public and give them a high class introduction to the artform.


Although all fractal art revolves around the same thing: fractal math; it doesn’t all follow the same orbit. Some of us are on Mars.

We use Martian programs, Martian dimensions, Martian colors and do Martian things with our alien pictures.

We don’t do contests and there’s not enough of us to form a committee or even a webring. In fact, come to think of it, I could be the only one on this planet.

Or asteroid. Maybe I’m way out on an asteroid

Fractal Oddities

I’m not talking people. I mean the sort of, “Oh, isn’t that interesting” type of image that otherwise might just get deleted.

Clouds can look like animals and a fractal can look like….

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…a chair.

You’ve probably already looked at the next picture and are reading this afterwards. That’s what I always do when I’m “reading” a blog with illustrations.

This Chinese vase or ceramic container raises some interesting questions about fractals and artistic design.

Download parameter file “ming01.zar”

It’s kind of freaky isn’t it? It even has handles in the right place and a chinese-looking roof-lid on the top.

The bottom has this sort of snakey or scaly dragon-shaped leg and foot thing to it. The handles on the side near the top appear to have rings dangling from a dragon’s mouth.

If you notice the reddish patches on the sides of the vase, they suggest the “object” is eight-sided, which is not too far off from many authentic chinese designs.

If at this point you think I’m lying, I suggest you load the parameter file into Tiera-Zon 2.7 and see for yourself. Try a different formula and you may discover another ceramic or cloisonne wonder.

Or maybe something more serious with less of a side-show freak appeal.

But back to the serious fractal questions. How could this fractal generated thing look so much like a chinese vase?

I think it’s because many naturally occuring organic shapes have a fractal related mechanism in their growth. Probably something like the shape of a common protien which is “iterated” by being linked into strands or combined to form a crystal like form. These in turn have been incorporated by artisans into their man-made creations.

The vase is not too far off from a coconut (with the husk) with lizard legs. Or a large corn (maise) seed cradled by a snake (and wearing the roof of a pagoda as a hat).

I think this means that the more complex fractal generators get and the futher they go by incorporating chaotic variables (to imitate real world environments), the more fractal imagery will resemble the art we’ve seen as well as producing artistic variations we could never have imagined: surreal; more than natural; or “hyper-natural.”

Hypernatural. I’ve just coined a new universe… on a Friday afternoon…


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Think of it as fractal froth. Something skimmed off and tossed. adj. 1. of no direct relevance; a by-product of mathematical calculation; a far-out domain, eg.(OE) “let’s go to sudzy-ville”.

In Xaos, the Barnsley formulas when done in Mandelbrot mode using squares in-coloring and the edge detection filter, would produce this shattered, fish-net sky that when zoomed into had all sorts of interesting currents and eddies of what is really not part of the fractal formula at all but is just something produced by the rendering method of the program, artificial and un-fractual and should have been rendered as empty space.

Download parameter file “sudz02.zar”

I’m not really interested in fractals, I’m just looking around for interesting things.

What is a fractal? To me it’s the seeds that grow into wild digital domains. Jack’s digital beanstalk -and you get to keep the cow.

We came up here to ponder mathematics? I came up here to plunder mathematics.

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I started to read about fractals and chaos in a book by James Gleick. Very interesting, although somewhat challenging intellectually. However, not really important for the making of fractal art.

Fractals are unique in digital art because they have such freaky, theoretical foundations. Fractal programs do more than make pretty pictures. Mathematical theory made flesh. Not too long ago this was the exclusive domain of dreams and visions.

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Infinity in a grain of sand, or something like that. Only the mathematicians see that. We just see a pretty picture, overflowing here and there, with sudz.