雪花曲線


雪花的遞迴繪圖基本圖案如下圖左所示，進一步的構圖如下圖右所示：



這只是個大致的繪圖，說明雪花的基本架構，但並不是很精確，在遞迴時起始位置還需用上一些數學運算，才能使雪花繪圖接近自然，這個部份請自行觀看示範程式中的原始碼，如下所示：
  • SnowCurve.java 
package cc.openhome;

import java.awt.Color;
import java.awt.Graphics;
import javax.swing.JApplet;

import static java.lang.Math.*;

public class SnowCurve extends JApplet {
    private Turtle t = new Turtle();

    public void init() {
        setBackground(Color.black);
    }

    public void snow(double rad, double min, double ks) {
        if (rad > min) {
            double r = rad * (1 - ks) / (1 + ks);
            snow(r, min, ks);
            int n = (int) ceil(log(min / rad) / log(ks));
            for (int i = 0; i < 6; i++) {
                for (int j = 1; j < n; j++) {
                    t.warp(rad * (1 - pow(ks, j)));
                    snow(r * pow(ks, j), min, ks);
                    t.warp(-rad * (1 - pow(ks, j)));
                }
                t.turn(60.0);
            }
        } else {
            t.pset(t.getCurrentX(), t.getCurrentY());
        }
    }

    public void paint(Graphics g) {
        g.setColor(Color.yellow);

        t.setGraphics(g);
        t.window(0, 0, getWidth(), getHeight());
        t.view(0, 0, getWidth(), getHeight());
        t.setPoint(300, 50);
        t.setAngle(90.0);

        int d = getHeight() / 8;
        for (int i = 0; i < 20; i++) {
            double x = d + (getWidth() - 2 * d) * random();
            double y = d + 5 * d * random();
            double r = 0.1 * d + 0.9 * d * random();
            t.setPoint(x, y);
            t.setAngle(90.0);
            snow(r, 0.1, 0.5);
        }
    }
}

以下是使用HTML5 Canvas的方式（如果瀏覽器支援HTML5 Canvas，例如最新版的Firexfox、Chrome、IE9等，可以直接將下面的內容存為HTML或按下檔名連結，直接載入瀏覽器執行觀看結果：
<!DOCTYPE html>
<html>
    <head>
        <meta content="text/html; charset=Big5" http-equiv="content-type">
        <script type="text/javascript" src="js/turtle.js"></script>
        <script type="text/javascript">
            window.onload = function() {
                function snow(rad, min, ks) {
                    if (rad > min) {
                        var r = rad * (1 - ks) / (1 + ks);
                        snow(r, min, ks);
                        var n = Math.ceil(
                                  Math.log(min / rad) / Math.log(ks));
                        for(var i = 0; i < 6; i++) {
                            for(var j = 1; j < n; j++) {
                                turtle.warp(rad * (1 - Math.pow(ks, j)));
                                snow(r * Math.pow(ks, j), min, ks);
                                turtle.warp(-rad * (1 - Math.pow(ks, j)));
                            }
                            turtle.turn(60.0);
                        }
                    } else {
                        turtle.pset(turtle.currentX, turtle.currentY);
                    }
                }
            
                var canvas1 = document.getElementById('canvas1');
                var context = canvas1.getContext('2d');
                var turtle = new Turtle(context);
                
                turtle.window(0, 0, canvas1.width, canvas1.height);
                
                turtle.view(0, 0, canvas1.width, canvas1.height);
                turtle.setPoint(300, 50);
                turtle.setAngle(90);
                
                var d = canvas1.height / 8;
                for(var i = 0; i < 20; i++) {
                    var x = d + (canvas1.width - 2 * d) * Math.random();
                    var y = d + 5 * d * Math.random();
                    var r = 0.1 * d + 0.9 * d * Math.random();
                    turtle.setPoint(x, y);
                    turtle.setAngle(90);
                    snow(r, 0.1, 0.5);
                }
            };
        </script>
    </head>
    <body>       
        <canvas id="canvas1" width="600" height="400"></canvas>
    </body>
</html>

以下是Firefox下看到的結果：