The Fractal Murders Part 1

The Fractal Murders.

Mark Cohen.

For Tana.

Acknowledgments.

An author's first novel is necessarily a product of his life experiences. It is not possible to acknowledge every person that made an impact on my life, but I would like to recognize three that made me a better writer.

First, my father, an English teacher early in his career. He taught me the joy that comes from creating with words. Second, Walter Broman, a professor of English at Whitman College who gave me permission to ignore convention. He was an inspirational and gifted teacher. Finally, Colonel (Ret.) Al Rubin, my immediate supervisor during my time as a Judge Advocate. Whenever I thought I had drafted the perfect doc.u.ment, he would return it to me with red ink all over it and ask, "Isn't mine better?" It always was.

I also want to thank my agent, Sandra Bond. She believed in The Fractal Murders and never gave up. Equally important, she never let me give up. I want to remember Sara Ann Freed, the editor in chief at Mysterious Press when we were looking for a publisher. She took a chance on The Fractal Murders while others feared it was too unconventional. Tragically, Sara Ann died before The Fractal Murders. .h.i.t the bookstores.

Kristen Weber at Mysterious Press provided help with the plot and proved a worthy editor, while at the same time giving me the freedom to write "my way" and graciously tolerating my quirks.

Profressor James D. Meiss of the University of Colorado and Professor Alex Kasman of the College of Charleston both read the ma.n.u.script and offered insight concerning the mathematics of the story and the world of mathematicians. To make The Fractal Murders enjoyable for those not mathematically inclined I have greatly simplified some of the concepts presented as part of the story. Any errors resulting from that effort are mine alone.

Writing a mystery while practicing law is no easy task. I want to thank my a.s.sistant, Sandy Enke, for her help and encouragement. Her willingness to s.h.i.+ft from legal a.s.sistant to business manager to dog trainer while also serving as a general problem solver was a blessing.

My wife, Tana, provided love and encouragement while I was immersed in this project.

I want to say, "Woof" to Pepper and Sc.r.a.ppy up in heaven.

Finally, I want to thank Phoebe, Bear, and Wyatt. Their unselfish willingness to keep my tiny allotment of the bed warm while I was writing was critical to the success of The Fractal Murders.

1.

I WAS HAVING A BAD DAY. I had gotten behind Ma and Pa Kettle on the road down the mountain, and by the time I was able to pa.s.s them I was almost to Boulder. I blew past them, then blew my nose. I'd been fighting the Sinus Infection from h.e.l.l for a week. We were in the middle of round six and it was ahead on points.

The visitors' lots were full, so I parked my aging F-150 in a faculty lot. I ejected my Creedence tape, placed my "U.S. Government-Official Business" sign above the dash, and set out for the math building. I no longer worked for the government, but I'd paid enough taxes during my legal career to consider myself an honorary employee.

I had spent seven years at the university, but that was long ago and I'd taken great pains to avoid math cla.s.ses. Now I was a private eye in search of a math professor. Unable to find anything resembling a campus map, I finally asked for directions. The first kid wasn't much help. But for the safety pin fastened to his left eyebrow, he looked like a neo-n.a.z.i skinhead. He had no idea where the math building was and his surly demeanor suggested disgust at the notion that anyone would want to find it. I shook my head and said a prayer for the gene pool.

The next man I approached was a foreigner, probably Nigerian. Skin black as coal, trace of a British accent. He was polite and possessed a wonderful smile, but sent me on a trek that took me past the old field house-where I'd spent many an afternoon running sprints-and ended up at the alumni relations office. I could've sought directions there, but I hadn't contributed to my alma mater since changing occupations and I feared some eager a.s.sistant might strike up a conversation that would end with a plea for my time and/or money.

The third time was a charm. She was a studious-looking young woman with dark eyes who stared at her feet and talked to herself as she walked. She wore black jeans, a black vest over a gray T-s.h.i.+rt, and black shoes with crepe soles. Her hair was long, dark, and in need of conditioner. The lost daughter of Morticia Addams. She said she was a math major and gave me detailed directions.

It was the first Monday in May. Seventy-six degrees and not a cloud in the sky. Frisbees flew, stereos blasted, and leggy coeds abounded. I recalled the night Scott McCutcheon and I had sculpted a giant snow p.e.n.i.s in front of the administration building. Probably not the first college freshmen to engage in such foolery, but a fond memory nonetheless. It seemed like just yesterday, but more than twenty years had pa.s.sed. Time pa.s.ses more quickly as you age, but that's one of the disadvantages of growing up.

The math building, a three-story fortress, was right where dark eyes had said it would be. Not far from where I'd parked. I had expected it to be named the Chester Q. Hollingsworth Hall of Mathematics or some such thing, but the sign above the entrance read simply, MATHEMATICS BUILDING. It was a newer structure, but the design was consistent with that of most others on campus. Exterior walls consisting of long slabs of rough-cut Colorado sandstone, all capped with a red tile roof. This warm architectural style dominated the campus and created an atmosphere reminiscent of a rural Italian village.

I entered unafraid. I was forty-four years old and n.o.body was going to ask me to bisect an angle or test my ability to solve a quadratic equation. That's one of the advantages of growing up. There aren't many, so I savored it.

The inside was about what you'd expect. The walls were covered with announcements and advertis.e.m.e.nts of every sort-typing services, bands in town, something about the Gay and Lesbian Student Alliance, a sign touting an upcoming lecture by a visiting professor, and so forth. One bulletin board was devoted exclusively to graduate programs at other universities. It was plastered with glossy posters and brochures. A young man wearing a pocket protector and carrying a beat-up briefcase studied them with interest. Probably the next Unabomber.

The lobby directory indicated the office of "Jayne Smyers, Ph.D., a.s.sociate Professor of Mathematics," was on level three. I took the stairs two at a time in my gray summer suit, hit the third floor, and started down a narrow hallway. It looked and sounded devoid of life. I glanced in each open office I pa.s.sed, but only one man looked up. Tall, blond, and in good shape. The nameplate on his door identified him as "Stephen Finn, Ph.D., a.s.sistant Professor of Mathematics." Papers covered his desk. He couldn't have been much older than twenty-seven, but his wire-rimmed gla.s.ses gave him a maturity beyond his years. "Can I help you?" he asked. Not hostile, but not friendly. My presence had broken his concentration.

"I'm looking for Professor Smyers," I said.

"Four doors down, on the right," he said with a forced smile. He pointed for me.

"Thanks," I replied. He did not immediately return to his work, and I felt his curious gaze as I continued down the hall.

I arrived at 3:20 P.M.-five minutes late. She was seated behind her desk and immersed in an academic journal of some sort.

"Dr. Smyers?"

"Yes."

"Pepper Keane." She rose from her chair and extended her right hand. I shook it. She was as tall as me and thin as a rail. Thirtyish. Luxurious dark hair-straight, full of body, and worn short, but not so short as to be butch. She'd been blessed with high cheekbones and white teeth. Bright blue eyes. Small, firm b.r.e.a.s.t.s. Smooth, milky skin. She wore designer jeans and a white cotton blouse. Except for pink lipstick, I detected no makeup.

"Thank you for coming on such short notice," she said.

"I'm sorry I'm late," I replied. "It took a while to find a parking s.p.a.ce."

"Yes," she agreed, "parking is a real problem here. Sometimes even the faculty lots are full." I smiled, said nothing. She motioned to two st.u.r.dy wooden chairs in front of her desk and said, "Please, sit down." Feeling liberal, I took the one on the left.

It was a typical faculty office. Small, equipped with an old metal desk and black filing cabinets. Linoleum floor tiles designed to resemble white marble were partially covered by a Navajo rug. Bookcases overflowing with textbooks and professional journals. She had made an effort to decorate it by placing cacti here and there. National Public Radio was barely audible on the small radio by the window behind her. There was one poster. It proclaimed: "A Woman Without a Man Is Like a Fish Without a Bicycle." I hadn't seen one of those in at least fifteen years.

"Would you like some coffee?" she asked. I noticed a small coffeemaker on one of the shelves to her right. The kind that brews only two cups at a time. There was also an electric grinder and a package of gourmet beans. She bought her coffee at Starbucks. I usually buy mine at the Texaco.

"No, thanks."

"You sound like you have a cold. Can I make you some tea?"

"Really," I said, "I'm fine." I had downed forty-four ounces of diet c.o.ke on the drive down and didn't figure to need liquids for a while.

She poured some coffee into a mug and said, "It's one of my few vices." The mug boasted a colorful Southwestern design featuring a coyote howling at the moon.

"Everyone needs a few vices," I said.

She forced a smile and sipped her coffee. "You're probably wondering what this is all about?"

"Well, Professor, I have to admit you've aroused my curiosity." She'd told me nothing on the phone, saying only that she would prefer to discuss it in person.

"I apologize for the secrecy," she said, "but I've never been involved in something like this." She paused. "Would you mind closing the door?" I reached back, gave it a good push, and listened as the latch found its place in the metal doorjamb. She took a deep breath, leaned forward, extended her long arms across the desk, and clasped her hands together. Her nails were short, but she wore polish and it matched her lipstick.

"Do you know much about mathematics?" she asked.

"Not much," I said. "I took calculus twenty-five years ago and it was the low point of my academic career."

She forced another smile. "My specialty," she said, "is fractal geometry. Do you know what a fractal is?"

"No."

"A fractal," she said, "is a type of geometric shape." She paused. "I don't know quite how to explain it to you." She tilted her head slightly, paused again, then said, "Picture a coastline."

"Okay." I didn't know much about geometry, but I'd been a marine officer for three years and I knew about coastlines.

"If we take a small section of that coastline, we can use a straight line to represent it on a map. But if we look closely at that section, we will see that it is made up of many small inlets and peninsulas, right?"

"Sure, and each inlet and peninsula has its own smaller bays and headlands."

"Yes," she said, "that's exactly right." She sipped her coffee. "And if we continue to look at smaller and smaller sections of the coastline, we'll find that this pattern is always present."

"Right down to the last grain of sand."

"Yes. That's the interesting thing about fractal objects: Their pattern remains more or less the same no matter how closely you examine them."

"So a fractal is just a shape with a random pattern?" I took the white handkerchief from my pants pocket, blew my nose, folded it gently, and placed it back in my trousers.

"Not a random pattern," she said, "an irregular pattern. Strictly speaking, there's no such thing as a random pattern. The two words are inconsistent. It's an oxymoron, like military intelligence." I let that pa.s.s without comment, though my high and tight haircut should've suggested I had once served in uniform.

"You're saying the shape of a coastline is not random?"

"Not in a mathematical sense," she said. "Each point on a coastline is linked with the points next door. If it were truly random, one point would have no relations.h.i.+p to the next. Instead of gradual curves, you'd see lines going all over the place. One point might be up here, the next might be way down there."

"Okay," I said, "I'll buy that." I waited for her to continue, confident that sooner or later the reason for my presence would become apparent.

"Did you study geometry in high school?"

"Tenth grade." I wondered what Mrs. Clagett was doing these days. Probably in the Aspen Siesta nursing home suffering recurring nightmares about McCutcheon and me.

"The problem with traditional geometry," she continued, "is that triangles, squares, and circles are abstract concepts. You can't use them to describe the shape of things like mountains, clouds, or trees."

"Or a coastline."

"Or a coastline," she agreed. She was becoming more animated; she clearly enjoyed the subject. "Traditional geometry-what we call Euclidean geometry-has to ignore the crinkles and swirls of the real world because they are irregular and can't be described by standard mathematical formulas. Then, about twenty years ago, a man named Mandelbrot invented something we call fractal geometry."

"Fractal geometry," I repeated. I sensed the lesson was nearing its conclusion.

"Mandelbrot realized that although many natural phenomena appear to be chaotic, there is frequently a hidden order in them. In fact, he called fractal geometry the geometry of nature." Another sip of coffee. "No two coastlines are identical, yet they all possess the same general shape, so there is a certain order there. Do you follow me?"

"I think so."

"Fractal geometry provides a way to identify patterns where there appears to be disorder. It allows us to model and predict the behavior of complex systems. It's a language," she said. "Once you speak it, you can describe the shape of a coastline as precisely as an architect can describe a house."

I doubted that. "Give me an example," I said.

"Certainly," she replied, eager for the invitation. "One of the tools we use to compare fractal objects is the concept of fractal dimension. For example, the coastline of Great Britain has a fractal dimension of approximately one point two-five, but the more rugged coastline of Norway has a fractal dimension of better than one point five-six."

"I'll take your word for it."

"I'm sorry." She sighed. "I've probably told you more than you need to know. I hope I haven't bored you."

"No, it's interesting." Not as interesting as the way her delicate bra straps traversed her bony shoulders, but interesting nonetheless.

"This will all make sense in a minute. I promise." She sipped her coffee, and I noticed a silver Navajo bracelet on her right arm. No wedding ring on either hand.

"Take your time," I urged. Despite my strong preference that people get right to the point, experience had taught me that the best way to conduct an interview was to shut up and listen.

"As I said," she continued, "my specialty is fractal geometry." I noted the Ph.D. from Harvard on the wall to my right. "Last year I began working on a paper I intended to present at a conference this fall. It's publish or perish, you know."

"So I've heard."

"When I completed my draft, I wanted someone else to critique it." She finished her coffee and set the mug to one side. "The last thing you want to do is publish a paper that contains a flaw."

"So you have your colleagues read it in advance to see if they can poke holes in it?"

"Yes, but my colleagues here wouldn't be much help. Fractal geometry is a rather narrow specialty, so I compiled a list of five of the most respected people in the field and attempted to contact them to see if they would be willing to critique it." Her slender neck became visibly tense and I thought she might be having trouble breathing.

"Are you all right?" I asked. She took a deep breath and nodded affirmatively.

"Mr. Keane," she continued, "when I attempted to contact these people, I learned that two had been murdered and a third had committed suicide."

"Over what span of time?"

"All within six months of each other," she said. "Do you know the odds against that?" It was a rhetorical question, but I had a hunch she could tell me the odds right down to the decimal point if she wanted to.

"And you want me to find out if these deaths were related?"

"Yes."

"Did you report this to anyone?" I asked.

"I called the police."

"And they said it wasn't their problem?"

"Yes, because none of the deaths had taken place in Boulder. They suggested I call the FBI."

"Did you?"

"Yes."