Fractals

Joanne sits up without a word. It's as though my own inadvertent thoughts have triggered her. She turns to look at me, she leans right through the thing between us without even pausing, her face breaks through that invisible grin and replaces it with one of her own.

"If you wasn't livin' with a black woman," she says in her best Aunt Jemima drawl, "I'd say you was sho' 'nuff a racist honky sumbitch." She nips me on the nose. "As it is, I think you just need a good night's sleep." She settles back down with one arm draped over my chest.

We're alone again. In the next room, Sean coughs softly in her sleep.

My knuckles sting with faint remembrance.

I wonder if he had a family.

Whoever you were. I'm—

—sorry—

***

It's almost time to meet Roy Cheung. For two hours now I've been wandering downtown streets, watching morning traffic congeal in thin slushy snow. I've been counting invaders. They hurry past the rest of us, mixed but not mixing, heads down against the chill of this alien climate. Sometimes they speak to each other. Sometimes they even use our language. More often they say nothing at all.

They never look at me.

I didn't always feel this way. I'm almost sure of it. There was a time when we were all just people, and I knew exactly what racism looked like: it drove a Ford pickup with a gun rack in the rear window. It threw beer bottles out the window at stop signs, and it didn't think; it gibbered.

But now statistics and xenophobia are in bed together. Every day the planes touch down and the balance shifts a little more.

Asian wealth rises around us, flashing invisibly bank-to-bank, ricocheting down from comsats high over the Pacific rim.

Burying us. Who wouldn't be afraid? My whole world is listing to the east.

But nobody taught me to hate like this. It just happened.

Is this what it's like to discover you're a werewolf?

***

There's a poster commemorating the 1995 International Computer Graphics Conference hanging on one wall of Roy Cheung's office. Below it, a transistor radio emits country and western; it's partially eclipsed by a huge, luxuriant Boston fern in a hanging pot. I wonder how he does it. Every time I buy one of those bloody plants it's dead within a week.

His desk is barely visible under a mass of printouts and the biggest colour monitor I've ever seen. There is a spiral galaxy rotating on the screen. It seems to be made of iridescent soap bubbles, each arranged with unimaginable precision.

"That," says Cheung, "is a fractal. Beautiful, isn't it?"

He speaks without a trace of accent. He sounds just like I do.

Cheung sits down at the keyboard. "Watch closely. I'm increasing the magnification so we're only looking at one of these nodes. One star in the galaxy, if you will."

The image blurs, then refocusses. There is a spiral galaxy rotating on the screen.

"That's the same image," I say.

"Not quite. There are a number of differences, but overall it's pretty similar. Except, like I said, we're only looking at one star in the galaxy."

"But that's a whole—"

"Now let's zoom in on a single star in this galaxy."

There is a spiral galaxy rotating on the screen.

Something clicks. "Isn't this what you call infinite regression?"

He nods. "Actually, the term is scale-invariance. You can look at this thing with a microscope or a telescope, it doesn't matter; at every scale, the pattern is essentially the same."

"So at what scale do we get the nature scenes?" There isn't the slightest hint of tension in my voice. I even smile.

"All of them. This fractal comes from a very simple equation; the trick is it keeps repeating itself. Uses the output from one iteration as the input for the next. You don't have to store a complete image at all. You just store a few equations and let the computer draw the picture step-by-step. You get incredibly detailed output with hardly any memory cost."

"You're saying you can duplicate nature on a screen with a bunch of simple equations?"

"No. I'm saying nature is a bunch of simple equations."

"Prove it," I tell him, still smiling. For an instant I see him shrouded in darkness, arms thrown up in a vain attempt to ward off judgment, face bleeding and pulpy.

I shake my head to dislodge the image. It sticks.

"—shape of a tree," he's saying. "The trunk splits into branches. Then the branches split into smaller branches. Then those divide into twigs. And at each scale, the pattern is the same."

I imagine a tree. It doesn't seem very mathematical.

"Or your own lungs," Cheung continues. "Windpipe to bronchi to bronchioles to alveoli. Or your circulatory system. Or the growth of a crystal. Incrementally simple, the same thing happening at a dozen different scales simultaneously."

"So you're saying trees are fractal? Crystals are fractal?"