# 17.3 復雜性理論 下面要介紹的程序的前身是由Larry O'Brien原創的一些代碼，并以由Craig Reynolds于1986年編制的“Boids”程序為基礎，當時是為了演示復雜性理論的一個特殊問題，名為“凸顯”（Emergence）。 這兒要達到的目標是通過為每種動物都規定少許簡單的規則，從而逼真地再現動物的群聚行為。每個動物都能看到看到整個環境以及環境中的其他動物，但它只與一系列附近的“群聚伙伴”打交道。動物的移動基于三個簡單的引導行為： (1) 分隔：避免本地群聚伙伴過于擁擠。 (2) 方向：遵從本地群聚伙伴的普遍方向。 (3) 聚合：朝本地群聚伙伴組的中心移動。 更復雜的模型甚至可以包括障礙物的因素，動物能預知和避免與障礙沖突的能力，所以它們能圍繞環境中的固定物體自由活動。除此以外，動物也可能有自己的特殊目標，這也許會造成群體按特定的路徑前進。為簡化討論，避免障礙以及目標搜尋的因素并未包括到這里建立的模型中。 盡管計算機本身比較簡陋，而且采用的規則也相當簡單，但結果看起來是真實的。也就是說，相當逼真的行為從這個簡單的模型中“凸顯”出來了。 程序以組合到一起的應用程序／程序片的形式提供： ``` //: FieldOBeasts.java // Demonstration of complexity theory; simulates // herding behavior in animals. Adapted from // a program by Larry O'Brien lobrien@msn.com import java.awt.*; import java.awt.event.*; import java.applet.*; import java.util.*; class Beast { int x, y, // Screen position currentSpeed; // Pixels per second float currentDirection; // Radians Color color; // Fill color FieldOBeasts field; // Where the Beast roams static final int GSIZE = 10; // Graphic size public Beast(FieldOBeasts f, int x, int y, float cD, int cS, Color c) { field = f; this.x = x; this.y = y; currentDirection = cD; currentSpeed = cS; color = c; } public void step() { // You move based on those within your sight: Vector seen = field.beastListInSector(this); // If you're not out in front if(seen.size() > 0) { // Gather data on those you see int totalSpeed = 0; float totalBearing = 0.0f; float distanceToNearest = 100000.0f; Beast nearestBeast = (Beast)seen.elementAt(0); Enumeration e = seen.elements(); while(e.hasMoreElements()) { Beast aBeast = (Beast) e.nextElement(); totalSpeed += aBeast.currentSpeed; float bearing = aBeast.bearingFromPointAlongAxis( x, y, currentDirection); totalBearing += bearing; float distanceToBeast = aBeast.distanceFromPoint(x, y); if(distanceToBeast < distanceToNearest) { nearestBeast = aBeast; distanceToNearest = distanceToBeast; } } // Rule 1: Match average speed of those // in the list: currentSpeed = totalSpeed / seen.size(); // Rule 2: Move towards the perceived // center of gravity of the herd: currentDirection = totalBearing / seen.size(); // Rule 3: Maintain a minimum distance // from those around you: if(distanceToNearest <= field.minimumDistance) { currentDirection = nearestBeast.currentDirection; currentSpeed = nearestBeast.currentSpeed; if(currentSpeed > field.maxSpeed) { currentSpeed = field.maxSpeed; } } } else { // You are in front, so slow down currentSpeed = (int)(currentSpeed * field.decayRate); } // Make the beast move: x += (int)(Math.cos(currentDirection) * currentSpeed); y += (int)(Math.sin(currentDirection) * currentSpeed); x %= field.xExtent; y %= field.yExtent; if(x < 0) x += field.xExtent; if(y < 0) y += field.yExtent; } public float bearingFromPointAlongAxis ( int originX, int originY, float axis) { // Returns bearing angle of the current Beast // in the world coordiante system try { double bearingInRadians = Math.atan( (this.y - originY) / (this.x - originX)); // Inverse tan has two solutions, so you // have to correct for other quarters: if(x < originX) { if(y < originY) { bearingInRadians += - (float)Math.PI; } else { bearingInRadians = (float)Math.PI - bearingInRadians; } } // Just subtract the axis (in radians): return (float) (axis - bearingInRadians); } catch(ArithmeticException aE) { // Divide by 0 error possible on this if(x > originX) { return 0; } else return (float) Math.PI; } } public float distanceFromPoint(int x1, int y1){ return (float) Math.sqrt( Math.pow(x1 - x, 2) + Math.pow(y1 - y, 2)); } public Point position() { return new Point(x, y); } // Beasts know how to draw themselves: public void draw(Graphics g) { g.setColor(color); int directionInDegrees = (int)( (currentDirection * 360) / (2 * Math.PI)); int startAngle = directionInDegrees - FieldOBeasts.halfFieldOfView; int endAngle = 90; g.fillArc(x, y, GSIZE, GSIZE, startAngle, endAngle); } } public class FieldOBeasts extends Applet implements Runnable { private Vector beasts; static float fieldOfView = (float) (Math.PI / 4), // In radians // Deceleration % per second: decayRate = 1.0f, minimumDistance = 10f; // In pixels static int halfFieldOfView = (int)( (fieldOfView * 360) / (2 * Math.PI)), xExtent = 0, yExtent = 0, numBeasts = 50, maxSpeed = 20; // Pixels/second boolean uniqueColors = true; Thread thisThread; int delay = 25; public void init() { if (xExtent == 0 && yExtent == 0) { xExtent = Integer.parseInt( getParameter("xExtent")); yExtent = Integer.parseInt( getParameter("yExtent")); } beasts = makeBeastVector(numBeasts, uniqueColors); // Now start the beasts a-rovin': thisThread = new Thread(this); thisThread.start(); } public void run() { while(true) { for(int i = 0; i < beasts.size(); i++){ Beast b = (Beast) beasts.elementAt(i); b.step(); } try { thisThread.sleep(delay); } catch(InterruptedException ex){} repaint(); // Otherwise it won't update } } Vector makeBeastVector( int quantity, boolean uniqueColors) { Vector newBeasts = new Vector(); Random generator = new Random(); // Used only if uniqueColors is on: double cubeRootOfBeastNumber = Math.pow((double)numBeasts, 1.0 / 3.0); float colorCubeStepSize = (float) (1.0 / cubeRootOfBeastNumber); float r = 0.0f; float g = 0.0f; float b = 0.0f; for(int i = 0; i < quantity; i++) { int x = (int) (generator.nextFloat() * xExtent); if(x > xExtent - Beast.GSIZE) x -= Beast.GSIZE; int y = (int) (generator.nextFloat() * yExtent); if(y > yExtent - Beast.GSIZE) y -= Beast.GSIZE; float direction = (float)( generator.nextFloat() * 2 * Math.PI); int speed = (int)( generator.nextFloat() * (float)maxSpeed); if(uniqueColors) { r += colorCubeStepSize; if(r > 1.0) { r -= 1.0f; g += colorCubeStepSize; if( g > 1.0) { g -= 1.0f; b += colorCubeStepSize; if(b > 1.0) b -= 1.0f; } } } newBeasts.addElement( new Beast(this, x, y, direction, speed, new Color(r,g,b))); } return newBeasts; } public Vector beastListInSector(Beast viewer) { Vector output = new Vector(); Enumeration e = beasts.elements(); Beast aBeast = (Beast)beasts.elementAt(0); int counter = 0; while(e.hasMoreElements()) { aBeast = (Beast) e.nextElement(); if(aBeast != viewer) { Point p = aBeast.position(); Point v = viewer.position(); float bearing = aBeast.bearingFromPointAlongAxis( v.x, v.y, viewer.currentDirection); if(Math.abs(bearing) < fieldOfView / 2) output.addElement(aBeast); } } return output; } public void paint(Graphics g) { Enumeration e = beasts.elements(); while(e.hasMoreElements()) { ((Beast)e.nextElement()).draw(g); } } public static void main(String[] args) { FieldOBeasts field = new FieldOBeasts(); field.xExtent = 640; field.yExtent = 480; Frame frame = new Frame("Field 'O Beasts"); // Optionally use a command-line argument // for the sleep time: if(args.length >= 1) field.delay = Integer.parseInt(args[0]); frame.addWindowListener( new WindowAdapter() { public void windowClosing(WindowEvent e) { System.exit(0); } }); frame.add(field, BorderLayout.CENTER); frame.setSize(640,480); field.init(); field.start(); frame.setVisible(true); } } ///:~ ``` 盡管這并非對Craig Reynold的“Boids”例子中的行為完美重現，但它卻展現出了自己獨有的迷人之外。通過對數字進行調整，即可進行全面的修改。至于與這種群聚行為有關的更多的情況，大家可以訪問Craig Reynold的主頁——在那個地方，甚至還提供了Boids一個公開的3D展示版本： http://www.hmt.com/cwr/boids.html 為了將這個程序作為一個程序片運行，請在HTML文件中設置下述程序片標志： ``` <applet code=FieldOBeasts width=640 height=480> <param name=xExtent value = "640"> <param name=yExtent value = "480"> </applet> ```