"I never would have got out," Frank said.

"The law would have lost a brilliant attorney, and for what? So I can get the right change in the supermarket?"

"I can't always do that," Mike said.

"But you would have got out. If you had known without a doubt that math was required, you would have mastered it exactly as you mastered whatever it is that lawyers have to study."

Frank laughed.

"Law. The Const.i.tution. Civics. His tory."

"Give me a quadratic equation any day."

Frank came to the table and poured himself a gla.s.s of wine.

"What's so great about chaos? Barbara showed me the pictures, and I said, "So what?" She didn't really know so what."

"We're finding out so what at a pretty good clip," Mike said.

"We have tools we never had before to measure and predict aspects of nature that were out of bounds for centuries." Barbara had put candles on the table; he picked up the matches she had put down and lighted one.

"Watch the smoke," he said. A column of silvery smoke rose straight up, then started to swirl around and disappeared.

"Turbulence," Mike said and blew out the candle.

"We've always known it was there, in smoke, in the flow of water, in the heart, the brain, but we couldn't do anything with it. We didn't have the tools. Now we do. We know now that it's not incremental, but catastrophic in nature. Turbulence arrives all at once, the way a pot of water boils all at once. Or the smoke breaks out of the smooth column Frank sipped his wine, listening with a careful expression.

"You say predictions, but I read that no one can predict the weather any more than my grandfather could."

"That's right," Mike said cheerfully.

"But that's an important thing to know, you see. What we know now is how sensitive systems are to initial conditions, and we know we can't always^ predict those initial conditions, therefore no guaranteed weather predictions. But do you have any idea how much money has gone into research of weather with the goal of perfect predictions?"

" No," Frank growled.

"Me neither. But gobs and gobs. Now a lot of it can go into something more productive."

"How do those pretty pictures figure in all this?" Frank took his wine back to the working half of the kitchen and began to stir something in a pot.

"Those Mandelbrot images are derived from one of the simplest algorithms ever discovered " He stopped when Frank groaned very loudly.

"Anyway, from this very simple instruction those sets are derived; they have fractal properties, that is, they are self-similar, no matter what the scale is, and they are infinite. From the simple comes the most complex. And that describes just about every natural object that exists, they all have fractal properties.

The most complex dynamic systems can be described by another equation that is equally simple, and it has a universal application. That means it can be applied to all turbulent systems up and down the line. We used to think each one had to be considered independently and painstakingly worked out. Now there is a universal algorithm to use. What we're learning is that under the most chaotic-appearing systems, there is order and simplicity. And from order arises chaos. And the world is not what it seemed to be just a few years ago."

Frank put the lid back on the pot and looked at Mike directly.

"Can you see any way any of that could pose a threat to someone? Would anyone kill for any of that?"

"No," Mike said.

"I can't see anything like that. Not yet, anyway." He looked apologetically at Barbara, who shrugged.

"Frobisher was a minor-league player," he said.

"I looked up what he published, and it's not really much.

Of course, he started before there were any clear indications where any of this would lead. He was one of the pioneers, but unfortunately he seemed to have a knack for dead ends instead of the mainstream."

"Wasn't any of his work any good?" Barbara asked.

"Why did Schumaker invite him to collaborate then? And Brandy wine? They seemed to think he had something."

Mike pulled out a folded paper and glanced at it. He folded it again and wrote down a few figures.

"Look, you have to understand something basic or nothing else will make any sense. This is the algorithum for the Mandelbrot sets. You take one number, C, and a.s.sign it a value. Say one and a half. Z is an imaginary number with a value of zero. You simply add Z to C and feed the result back in over and over and over. It's the iteration that creates the set. You don't even need a computer--that just makes it go faster, but they can be plotted by hand on a grid. An ordinary grid with a horizontal and a vertical axis. Each time you iterate the formula you put down a dot, and eventually you have a pattern. But sometimes the formula will give you a result that flies right off the grid, out to infinity, and that's what fascinated Frobisher. Not the sets, but the ones that sent the attractor into infinity. And he believed and was attempting to prove that there were visual cues that would lead a good perceptive observer to antic.i.p.ate which sets would end that way. Remember that this was in the infancy of the research, no guidelines yet, no mentors to ask questions of, d.a.m.n little in print, and a half dozen people who were obsessed by the whole field. All of them were interested in the transition zone, the phase s.p.a.ce, where one thing becomes another. If Frobisher had been able to come up with an equation that would eliminate the ones that didn't work, he would have made his name. That's why Schumaker got interested in his work, I guess. He's an operator, an opportunist. He's worked with nearly everyone in the field at one time or another, just to keep his name up there, and now he's on the lecture circuit, the big bucks circuit. I think he's pretty much dropped out."

"And Brandywine? She was into juvenile schizophrenia. How could that tie in?"

Mike shook his head.

"I just don't know. No way that I can see." He glanced at Frank, who was standing immobile with a woodea spoon in his hand.

"Remember the time element," Mike said.

"You're talking about seven or eight years ago, maybe ten or even twelve years ago. There just wasn't any money for chaos research. Schumaker swung a lot of weight and could have got funded for just about anything he wanted to do, but Frobisher and Brandywine? I don't think so. And if they were onto something big and important, something that could have brought fame and fortune the way it's happened to a few of the early researchers, if that was the case, why didn't they publish?

Why did they all stop? And apparently they did stop what ever they were doing. Brandywine is back into her juvenile studies, as far as I can tell. And Schumaker hasn't done anything real for years. The other one, Margolis, he's into artificial intelligence, in computers, nothing at all to do with chaos."

Frank had too much sense to say I told you so, but the unspoken words were in the air, and Barbara could feel only a deep frustration. She had learned that a strange attractor was not simply a point but could also be a pattern that repeated over and over, always similar, never exactly the same, and she felt that the pattern of those scientists circling around Lucas, the dead boy and the dead Probisher, all made up a strange attractor. It was all of a piece, and without that piece she had no case for Nell Kendricks.

She, Barbara, was part of the pattern, she acknowledged, although she could not say how or why. But she was part of it and had to see it through to wherever it took her.

A strange b.u.t.terfly in Brazil had awakened, had floated off a leaf somewhere in a jungle, and she had been set in motion. So far, she felt almost certain, she had made the right movements, but with each new choice, each new decision, each new bit of information, there was the danger that she would be flung off the grid, out to infinity. If that happened, she followed the line of thought, she would not be able to finish something she had started, something important--not only for Nell, but for her, also.

EIGHTEEN..

on friday frank, Barbara, and Nell had a final conference before the trial. They were in the living room of his house, before a fire muttering to itself, as, outside, a cold wind drove fir needles against the windows. Frank had insisted on the topic that headed his list of priorities for discussion.

He watched Nell closely over the rims of his gla.s.ses when he started. "You still have the option to change your plea. You know that, don't you?"

She nodded. She was wearing an oversized sweater that accentuated her diminutive body; she had lost weight in the past months, and she appeared more frail and more vulnerable than ever.

"Right," Frank said.

"You can opt out right up to the time the case goes to the jury. You know what Tony's offering manslaughter he wouldn't fight self-defense and a probable sentence of two to four years."

"I know," she said.

"But I can't do that. I didn't do it."

"Okay. So we go all the way." He leaned back in his chair and let Barbara have the floor, but he was troubled.

Every line on his face, his posture, his voice all attested to his concern.

Barbara began to outline the procedure.

"First, they will establish that the cause of death was a gunshot wound to the head. There will be the sheriff's men who responded to the call, the search for the body, autopsy, all of that.

And it will be ugly." She paused.

"Do you ever take tranquilizers? Would they help?"

Nell shook her head.

"I don't react very well to most drugs. Tranquilizers do funny things to my system and even make me hyper. Doc says I should leave them alone."

Doc. Barbara wanted to find him and give him a swift kick, but she did not comment. No one had commented about the forlorn look that had come to lodge on Nell's face. Barbara continued to prepare her client for the ordeal to begin the following week.

"Next, there will be evidence about the location, who had access, things of that sort, and the weapon itself, your abilities as a marksman.

I'm afraid he'll call various neighbors of yours to add to the details, and that might get hard to take."

Nell nodded, white-faced, her eyes too large.

"The next part will be motive. I doubt that they will try to do much with that, but what little they do will again rely on neighbors and your in-laws. About all they can establish is that you were an abandoned wife. The problem is that they won't need much more than that for a motive, if they can establish that you were the only one with opportunity because most murders are within families. Tony is certain to concentrate on that fact in his summation.

That and the fact that circ.u.mstantial evidence is sufficient.

In your case that means opportunity, being in the place at the time; weapon, probably your rifle, or one exactly like it; and the ability to use the weapon, which I think they will more than substantiate. Now, I can't deny any of those bits, no one can. All we can hope for is to demonstrate that another person had equal opportunity and took advantage of it."

Nell looked almost wildly to Frank, who appeared even more grim than he had before. He shook his head.

Very slowly Barbara said, "Nell, if the case were confined to the points Dad made a while ago, I would tell you to pay close attention to what he advised. Tony will fight to keep the past out of it, to limit everything to what happened on that ledge that Sat.u.r.day, and I'll fight just as hard to expand our playing field to the utmost. The judge will decide finally what will or won't be admitted as relevant.

And right now I can't guess what that decision will be."

Now the jury was in place and Judge Kendall Lundgren was on the bench. He was an ascetic intellectual, pale-faced, with thin, sandy hair, in his early forties; he would have looked at home in a monastery. According to Frank's summary, he had no sense of humor and little patience with theatrics in court or with stupidity. He had talked very briefly to the jury about the gravity of a murder case, about reasonable doubt, and mandatory sentencing guides.

It had been so brief that Barbara had begun to worry that he might have a date in Hawaii, a hanging maybe, or more likely a burning; he could be itching to get on a plane.

She knew he was considered to be a fair judge, but still she worried, exactly as she always did. Tony was finishing his opening statement. "What the state will prove is that Nell Kendricks deliberately shot to death her husband, that no one else could have done it, that no one else had cause to do it. Her rifle was the instrument of death, and no one else had access to that rifle. We will prove that no one else could have entered her house that Sat.u.r.day in June, no one could have taken the rifle. And in fact no one else knew that her husband would arrive that day or any other day."

When Tony concluded and resumed his seat, he did not look at the defense table. He had not looked at Barbara a single time yet. He had nodded in her direction, but his eyes had focused on a spot just over her shoulder. She and Nell were alone at the defense table. Her father had chuck led when she said that that was how she wanted it. He was seated directly behind her, one of the law clerks from his office on one side of him, and John and Amy Kendricks on the other. Clive was in the scant audience not directly behind the defense table, but off to one side where he could see Nell's profile. Mike planned to come by between cla.s.ses; curiosity, he said. When Mike asked if she would wear her three-hundreddollar suit, she had said no emphatically She wore a skirt and jacket, a very simple blouse, nothing fancy, nothing expensive, just in very good taste. Nell was in a dark dress, low heels. Barbara had told her to wear low heels every day, and she had been bewildered but compliant. Barbara knew that when they stood together the jury would notice and remember how very small Nell was. Barbara was seven inches taller than Nell, wider in the shoulders; she felt gargantuan when they stood together.

She got to her feet unhurriedly and approached the jury.

"Ladies and gentlemen," she said, "the defense does not have to prove anything except that there is not simply a reasonable doubt, but in this case a great doubt, that Nell Kendricks killed her husband." Tony had been declamatory; she was conversational. Go for the contrasts, one of her instructors had said, and treat the jury as if you really believe they have a brain among them. Sometimes they may even have one.

"It is the duty of the state to investigate every lead, to pursue every bit of evidence, to actively search out those who have testimony concerning the crime being investigated. If the state fails to discharge that duty, there is a basis for reasonable doubt. The state has vast resources at its disposal manpower, subpoena power to gather testimony, financial resources to carry the investigation to wherever the evidence leads and if the state misuses those resources, or fails to use them, there is basis for a reasonable doubt. The state would have you believe a murder was committed in isolation, and that it does not matter where Lucas Kendricks was for the past seven years, and yet, you and I, ladies and gentlemen, know that human acts of such violence do not take place in isolation.

The defense will demonstrate that Lucas Kendricks had powerful enemies who were actively pursuing him, that those enemies performed illegal acts in the course of that pursuit, and that Lucas Kendricks knew he was being followed, pursued, and he was fearful because of it. And that, ladies and gentlemen, is a basis for a reasonable doubt. Nell Kendricks did not shoot her husband, the father of her two children. She did not know where he was.

She did not know when or if he would visit her. The defense will demonstrate that his enemies knew those things, and that provides a basis for a reasonable doubt. The state, with all its power and all its resources, has brought the wrong person to trial."

Tony was whispering to one of his a.s.sistants, who got up and left the courtroom. When Barbara took her chair, Frank's hand pressed her shoulder briefly, and he pa.s.sed her a slip of paper. You 're walking a thin line. Keep an eye on KL's face.

Judge Kendall Lundgren ignored her and said to Tony, "Let us begin, if you please." He, Barbara thought, was part of the state. She nodded slightly to let Frank know she understood.

Tony efficiently led his first witness through his testimony. Sheriff Bernard Gray established that murder had been done, when, and where.

"Sheriff Gray," Barbara said when Tony concluded, "I have a map also. Will you look at it, please, to make certain it is essentially like your own?" It was much bigger in greater detail; it showed, as did the one already introduced, the trail from Old Halleck Hill Road to the waterfall, the bifurcation there, the dead end side, and the continuation that led down to Nell's property. The sheriff agreed that it was the same.

"Will you examine these photographs, please, to make certain they are comparable to the ones you took." Like the map, the photographs were enlarged conspicuously.

When they were accepted, Barbara put one on an easel before the sheriff.

"Where would you place the mark in the rocks where the bullet struck? Please, indicate it on the photograph."

He looked from his picture back to hers and finally touched a spot. Barbara marked it with a red pen.

"Thank you. You said in your testimony that it is about four feet high, is that right?"

"Yes, Ma'am."

"And you testified that you did not find a spent sh.e.l.l casing, is that right?"

"Yes, Ma'am."

"Where did you look?"

"All over the place."

"Show us on the ^photograph, will you? All over where?"

Sheriff Gray looked patient and long-suffering as he pointed at the photograph.

"Four of my men searched every inch of that ledge," he said, pointing to the section on Nell's side of the gorge.

"How about below the ledge?" Barbara asked.

"There, too."