Mandelbrot Story

z = z^2 + c

Who would have guessed that simple equation could have enslaved me so completely—mind, body and soul? Okay, I’ll admit it was just one of many puzzle-pieces that fell into place. But being the geek that I am, the Mathematician, I like to claim I was ensnared by an equation.

“Dude, you’ve got to try these out. I think I’ve finally got them working!”

Seth, my beautiful, lively, roommate was bouncing on my bed. Trying to return to whatever intoxicating dream he had pulled me out of, I pulled the comforter further over my head like a shield and rolled away from him. Despite the fact I suffered a deep crush on him, despite the fact that the object of my quiet unspoken yearnings was on my bed, straddling me, poking me through the blanket, despite the fact that he bore that intoxicating grin of excitement, I’ve never been one to wake from a slumber easily.

That was probably for the best, given that Seth was renowned for working night and day on his school projects. He was an Engineering major, and nobody doubted that someday he would be one of those rich, eccentric millionaires. It wasn’t enough to pass his classes with good grades. He was one of those nuts who actually loved being in school with access to professors and all of those Best and Brightest minds. Science was his playground.

After the requisite groaning and protesting, I eventually surrendered and poked my head out of the blankets. I couldn’t see my alarm clock from under the mess of papers that was my desk, but a look out our window and over to North Hall told me that only two other dorm rooms were lit. It had to be past 3 A.M. Seth was wearing these baggy heather-colored draw-string shorts and a huge, light blue long-sleeved t-shirt that over-emphasized his long, wiry frame. His straight, blond hair was sticking up a bit in back which suggested that he’d slept a little tonight, and—quite typically—woke up with some crazy idea he had to try out before he could get to sleep again.

While I sat like a statue, trying to shake the sleep out of my head, he was already busy strapping the huge visor to my head. “Is that comfortable?” He asked, gently tightening the straps around my head. I muttered something about campus policy regarding killing roommates, but I doubt it was coherent enough for him to hear. “Okay, hang on while I boot up the display.” He plugged a cable into the visor, and I could make out a familiar Linux operating system screen.

I was familiar enough with what he’d been working on all month. This “visor” covered your field of view completely with a gigantic computer display. That by itself wasn’t anything new, but Seth was working on a sensor that could detect where your eyeballs were looking. In theory, just by fixing your stare you should be able to control the pointer. Stare hard enough at a point and it would be like “clicking” on it.

My sense of foul, early-morning humor led me naturally to seek out the “shutdown” menu. Without realizing what I was doing I had willed the pointer to pull the menu down. It wasn’t until I was staring at the “Are you sure?” dialog box that I realized what I was doing.

“Seth, man, it works. I mean… it really works!”

I was beginning to really wake up now. I knew Seth had been working feverishly for a solid month on this project, but as far as I knew he wasn’t expecting to solve it until sometime next term, maybe longer. And even once he got the initial problems solved, it was supposed to take forever to refine the controls. But this was freaky. I mean, I could swear the helmet was reading my mind. Wherever I seemed to focus my attention the computer was instantly responsive. I could launch programs, move and resize windows, set controls, everything.

“The only thing you can’t do is type.” He confessed. “You’ve still got to use your hands for that.”

“Yeah, but pair that with some voice recognition and we’ve got an amazing tool for paraplegics.” I said. “I’m just amazed with how responsive these controls are. Wherever I look… whoop! there it is!”

“Actually, it gets a little intense after a while. There’s something to be said for being able to look away from the screen.”

I could see what he meant. For a moment I felt this small surge of panic like I couldn’t free my gaze from the controls—they kept following it—and then I realized I was being silly and simply closed my eyes.

“Hey, I’ve got an idea. Where’s a keyboard?” I asked, “I want to try something quick.”

“Hang on.” I felt as Seth leaned over me to grab the wireless keyboard from his desk. He placed it in my lap in front of me, and then he sat down on my bed right behind me, kind of turning himself into a temporary chair I could lean back against.

That kind of thing drove me completely crazy. Seth was one of those hyper “Peter Pan” types who is always so cheerful, so charismatic, and in some ways so damned blond that I couldn’t tell if he was oblivious to my crush on him, or if he sadistically played with me to bask in the attention. I could smell his distinct and pleasant scent. Oh, the number of nights I dreamed of simply burying my nose in his hair and breathing in his scent.

I tried to shake off the distraction and focus on the computer. I networked over to my own computer and pulled up a program I had been working on. It wasn’t hard to change the controls to accept input directly from this new ‘eyeball pointer’. Meanwhile, Seth just sat behind me, fiddling with the visor straps around my head and telling me how he’d solved his engineering problem.

“It was one of those total ‘eureka’ moments. These visors create a natural reflection that bounces light from the display off your cornea and it creates an annoying diffraction pattern. I was analyzing the reflection and working on countering it when I just remembered your motto: if you can’t fix it, feature it.” I could feel my face blush. Seth was always such a generous guy. He’s the type of person who constantly makes you feel like you’re the most incredible person in the world.

He continued, “It turns out that diffraction pattern was everything I ever needed! I could extrapolate your gaze to much higher precision. In the past two hours I figured out how to measure the ‘intensity’ of your gaze to simulate a mouse-click. I can even tell when your pupils are dilated.”

“Is that this ‘C3’ input I’m seeing here?” I asked. I continued typing. This was one of those miraculous moments when the code simply flowed and whatever I programmed ‘just worked’. Sadly, it’s a preciously rare experience. I willed the pointer over to the Project menu and hit the Build & Run button.”

My eyes were suddenly filled with an iridescent-green view of the Mandelbrot Set. It’s like this crazy, super complex spiral—eerily beautiful. It was a popular computer graphic back in the 1980’s when computers were just becoming interesting and Mathematicians were playing with Fractal Geometry and Chaos Theory. The Mandelbrot Set is a graph of the recursive equation z = z2 + c plotted on the complex number plane. That may sound complex, but in reality the meat of the algorithm takes up no more than about seven lines of computer code. The rest is all a matter of deciding how you want to color the results. The other thing about the Mandelbrot Set is that you can zoom in on any detail of it, magnify in and in and in, and you just get new and different, infinitely complex patterns. Spirals inside of spirals. Twenty years ago it would take a computer about an hour to generate a single snap-shot of the fractal. These days a computer could do it a fraction of a second.

And that’s exactly what I had done. I had a program that constantly zoomed in and in and in, 30 frames per second in full smooth-motion computer animation. I had done it as an exercise to teach myself some new graphics libraries. You would just move a mouse around the ‘movie’ and it would keep on zooming in on this infinitely complex spiral.

A quick disclaimer. I might sound like a really intelligent über-geek like Seth, but I’m nowhere in his class. I would classify myself as “a bit clever and really lazy”. I can scrap-together some tidbits of work other people have figured out, and often I’m mistaken for a genius. But I ain’t. I get to hang around with guys like Seth, and it’s the most amazing rush, but I’m just a man among giants. I just know how to keep being in the right place.

This was a good example. I just happened to have this silly little application, and I knew that just coincidentally I might be able to adapt it to Seth’s super-visor. I replaced the main input for the new gaze-pointer, and was even able to improvise so that if the viewer’s eyes started to dilate, the entire image would begin to spin as it zoomed-in. It was a lucky hack-job, but it sure got Seth excited.

“Oh man, it works! Hey, you’ve got to try this!” I pulled the visor off my head and handed it over to Seth. He looked at me with this quizzical grin, like he was savoring the anticipation of whatever surprise I had in store for him. “Set it for ‘full screen’ mode before you launch the program.” I told him.

“Whoa!” Obviously it had started. His muscled got tense for a moment and he reached out his hands for something to hold onto. “Dude, I feel like I’m falling!”

Seth started to slump over a bit, but I grabbed his shoulders and steadied him. “Seth, just lay back slowly onto the bed. Don’t worry, I’ve got you.” I said.

He giggled a little bit. His shoulders were tensed-up, and I could tell he had really lost his sense of balance. I cradled his head with the inside of my shoulder while guiding him into a horizontal position with my hands. I then went and gently picked his feet off the ground and placed them on the bed.

“OH DUDE! YOU DIDN’T!!” Seth was giggling again.

I guessed at what he’d discovered: “You found where the pupil dilation sets off the spinning effect?”

“Totally. Oh, that’s so cool. I’m completely floating. This is in-ten…” his voice trailed off.

I was worried that it might be too intense for him. His shoulders were still tensed up, and I suddenly realized that he was holding my hand tightly.

“Seth, try and relax if you can.” I was going to remind him that he could close his eyes any time that it got too intense for him, but instantly his body went slack. His hand was no longer squeezing mine so tightly. I was suddenly afraid he’s passed-out or was having a seizure or something.

“Seth! Seth can you hear me? Is everything okay?”

“Yeah,” his voice slurred, sounding distant, “Everything’s a-o-k.”

I was worried, so I told him I was gradually going to turn down the brightness knob on the visor. I didn’t want to do anything jarring. I slowly turned it off and removed the visor from his head.

“Seth, are you okay? You look so relaxed!” I was a little confused. A visual experience as intense as that struck me as anything but a calming experience. “You remember everything, right? Your body just seemed to release every bit of tension all of a sudden!”

“Release… all… tension.”

“Hey, snap out of it. Okay? Why don’t you go splash some cold water on your face. Wake yourself up.” I suggested, “Just be careful not to get up too quickly.”

Seth looked up at me with those big dammed blue eyes and again I could feel myself blush. I helped him sit up, and he went over to our water-cooler and splashed some cold water in his face.

“Dude, you’ve got to try that!” He had that mischievous smile on his face again. “It’s so intense. I totally felt like I was floating. And then when my eyes must have dilated and the thing started spinning… That’s just an amazing program. You’re a total God.”

I muttered something about just being lucky—well, you just heard my whole spiel a minute ago. I guess I don’t take compliments well. Seth was busy fastening the visor’s straps to just the right amount of tension on my forehead. He was so excited about having me go through the exact same experience.

“In fact, don’t lay down at first. Sit on the edge of the bed. When you feel weightless tell me and I’ll help you lay back. Are you ready?”

I nodded. Seth jumped over and sat behind me again on the bed. He put his hands on my shoulders and told me to start. I launched the program, set it to full screen mode and watched. My entire field of vision filled with this delicate figure with it’s tendrils of infinite spiraling complexity. I fixed my gaze along the graceful curve of one of the inner black circles and the figure rushed out at me, zooming in on that curve until I could see that it wasn’t a smooth curve but instead a union of infinite self-replicating spirals.

Seth was gently rubbing my shoulders. “How’s it feel?”

“That’s neat!”

“I love how if you try to look intensely at some piece of detail it just starts zooming in faster.” Seth said behind me. “Try it. Look at one point really hard and notice how fast you start to fall in!” he suggested. “Notice how you can never quite fix on any point? I love that.”

It was beginning to get really intense for me. My shoulders started to tense up, and I started feeling like I was falling.

“Oh, I’m beginning to feel the vertigo.” Something in the back of my mind was starting to panic.

“You know what I found intense?” Seth said, “When I felt that happening I decided not to close my eyes. I just kept looking to see how intense it would get. Try the same thing. Try not closing your eyes. You can blink, but keep your gaze fixed. Now lean back. I’ve got you.”

I couldn’t look away. Every now and then my gaze would just drift over to an edge of my field of view, but the spiral would follow it, thanks to Seth’s nifty new sensor. I fell gently back into Seth’s arms and he lowered me down into the bed. I could feel him lift my legs and place them on the bed. He must have felt how tense my legs were because he said, “Relax. Relax your muscles. You can calm yourself if you try.”

My pupils must have started to dilate because the fractal image was beginning to spin on its axis. It was getting faster and faster and all I could do was say “Whoa!”

I felt Seth pick up my right arm a couple inches and drop it back onto the bed.

“You’re helpless, aren’t you? You couldn’t move your muscles even if you wanted to?” He asked.

It was so true. I tried to speak, to answer him, but I could feel my tongue, thick in my mouth. Too relaxed to make sound. Actually, it felt like this was someone else’s body I was feeling from a great distance. My soul was elsewhere, endlessly falling into the Mandelbrot Set.

“Hey, Zach, can you talk? Tell me you’re okay.”

My mouth closed, my throat swallowed lightly and my lips moved. I could feel my larynx generate a soft voice, “I’m okay. I can talk.” It was like someone else was controlling the various muscles in my body. Someone else made that voice. Someone else answered the question.

There was silence. I guess Seth was thinking something out. All I could focus on was the spiral image.

“Zach, you’re really enjoying this, aren’t you?”

“Yes,” I answered.

“You’re really, really relaxed right now. Your body is tingling, isn’t it?”

“Uh huh.”

“You like feeling this way, don’t you. You like floating inside these beautiful images.”

“I like feeling this way.” It was true. It was so true. At first the experience had been a bit intense and unnerving, but the memory of it ever being unpleasant quickly faded from my memory.

I could hear Seth typing on the computer. He must have remotely logged on via the other computer on my desk and was looking at the program data.

“Wow, it says here you’re pupils are dilated to a full 7.3 millimeters. That image must really be spinning fast. Hey Zach, do you think you can will it to spin even faster? Relax your mind and maybe you can… oh wow, it’s working! 7.8 millimeters… Whoa! 8.8!”

I could hear him move back over to the bed. I felt him sit down next to me.

“Zach. Zach can I ask you a question? Do mind if I ask you a personal…” Seth’s voice trailed off for a moment.

“Zach, you feel very relaxed and safe and content right now, don’t you?”

“Uh huh.”

“I’m going to ask you a question, and nothing about the question will make you nervous. In fact, after you answer the question it’ll all fade quickly from your mind. You won’t even remember that I asked it. You’ll just remember how wonderful you’re feeling right now. Do you understand?”

“I understand. I’ll answer and I just feel wonderful.” Again, something else was working my mouth. The words were coming from far away.

“You’ll feel very comfortable answering questions that I ask you. They will never make you uncomfortable. You’ll never be hesitant in answering. You’ll only feel better when you answer my questions. Do you understand.”

“Yep. I understand.”

“Zach, are you in love with me?”

I was swimming in a sea of bliss and light. “I think so! I don’t know if ‘love’ is the right word. I’ve thought about it a lot though. I think about you a lot. I feel good when you’re around. My heart beats faster, and sometimes I get nervous. Is that love? I dunno.”

Seth put his hand lightly on my chest.

“Thanks for answering that, Zach. It felt so good to answer the question, didn’t it? Not uncomfortable at all?”

“Not at all.”

“In fact, you can’t even remember what I asked you just then. You can’t remember what you answered. All you remember is that you answered, and how good it felt. Everything else fades from your memory.” Seth was rubbing my chest lightly.

He continued, “Zach, I want to see just how effective this hypnosis is. Over the next few days I think we’re going to do this quite a few times. Zach, every time you wake from these sessions you wont remember anything. You’ll just remember that you were very relaxed and very happy. If I suggest doing this again you’ll be very agreeable. You have fun falling into this trance, and you trust me completely. Right?”

“I love doing this. I trust you.”

“And before this ends, I’m going to plant a suggestion in your mind. You will be unaware that I’ve done this. You won’t remember the particulars of our sessions, just that you enjoy them. Here’s your suggestion: whenever we’re together, here in our room, whether or not anyone else is around, you are going to feel very natural wearing very little clothing. It’s completely natural to be almost naked. In fact, it’s very natural and relaxing to be naked. You won’t be worried about what I think about it. You know our friendship is completely safe. The less clothing you wear, the less you worry, the more relaxed you feel, the better you can concentrate. Do you understand?”

“I understand.”

“One other thing. You are going to start taking better care of your body. Your body is a temple. You like your body; it’s a really good looking body. But if you’re going to show it off, you’re going to want to build it up. Whether you’re going to the gym or swimming laps, you feel good when you know you’re improving your body. Same goes for diet. Doesn’t your body feel good right now?”

“Yes.”

“Can you feeling your entire skin tingling?”

“Yes.”

“You like that feeling, and you know that taking care of your body, exercising it, will just make it feel better.”

“Better.”

“Okay, now I want you to make the image in the visor slow down. I want you to do it on your own. You are going to relax you gaze. You are going to stop the spinning. You are going to relax your eyes, look around a bit. There. That looks good. Okay, take a few deep breaths, and then deactivate the full-screen mode and shut down the program.”

It took a bit of effort figuring out how to climb out of the deep mental fog. It was like somehow finding my body again and taking control of it. I took a deep breath and felt my lungs fill with air. The sensation was something I could hold on to. I focused on the feeling of my lungs, then opened and closed my hand a few times. There! I could feel my body. The Mandelbrot image in front of me has slowed considerably. It wasn’t spinning anymore, just slowly zooming farther and farther in.

I was able to disengage the full screen mode and turn off the program. I felt my entire body again. It felt nice, like every millimeter of my skin was tingling. I took a few more deep breaths. Seth was loosening the straps of the visor and gently taking it off my head.

“How are you feeling?” he asked.

“A little dizzy, but good. Really good. Really really good!” I giggled a little bit. Then I asked if he could get me a glass of water. He brought one over and as I drank it he had this funny expression on his face as he looked at me. It was like he was studying me or trying to figure something out. It was a little unnerving.

“It’s time to go to sleep, isn’t it?” He said.

“You don’t have to tell me twice! I walked over, flipped off the light switch, and as I walked back over to my bed I yanked off my shirt. Then I stepped out of my shorts and decided I would sleep in the buff. I climbed into the welcoming blankets of my bed and immediately zonked out cold.