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| Brenton Fletcher |
 Posted: Sun Aug 10, 2003 9:01 pm |
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Sierspinki Triangle
A Sierspinki Triangle is generated in five steps:
First plot the vertices of a triangle on the screen.
1: Randomly pick a point within the triangle (we'll call it a)
2: Randomly pick one of the vertices (we'll call it b).
3: Plot the midpoint of a and b (we'll call this c).
4: set a to c.
5: repeat steps two to five.
Algorithm sourced from "Math Projects For Young Scientists" pp.99-100
I implemented this in Java: The part that is bold is the main implementation of the algorithm:
import java.applet.Applet;
import java.awt.*;
import java.awt.geom.*;
import java.util.ArrayList;
import java.util.Random;
//applet that draws a Seirspinki Triangle
public class TriangularFractalGenerator extends Applet
{
private int MAXIMUM_ITERATIONS;
private int MAX_X, MAX_Y;
///store the vertices for drawing
private ArrayList vertices = new ArrayList();
private Polygon triangle;
public void init()
{
MAXIMUM_ITERATIONS = Integer.parseInt(getParameter("iterations"));
MAX_X = Integer.parseInt(getParameter("width"));
MAX_Y = Integer.parseInt(getParameter("height"));
//////add the vertices of the invisible triangle
vertices.add(new Point2D.Double(MAX_X / 2.00, 50)); //add top vertice
vertices.add(new Point2D.Double(50, MAX_Y - 50)); //add left vertice
vertices.add(new Point2D.Double(MAX_X - 50, MAX_Y - 50)); //add right vertice
//////nessacery setup for creating a triangle Polygon
Point2D.Double topVertice = (Point2D.Double)vertices.get(0);
Point2D.Double leftVertice = (Point2D.Double)vertices.get(1);
Point2D.Double rightVertice = (Point2D.Double)vertices.get(2);
int[] triangleX = {(int)topVertice.getX(), (int)leftVertice.getX(),
//first line
(int)leftVertice.getX(), (int)rightVertice.getX()}; //second line; third
//line is automatically added
int[] triangleY = {(int)topVertice.getY(), (int)leftVertice.getY(),
//first line
(int)leftVertice.getY(),(int)rightVertice.getY()}; //second line; third
//line is automatically added
//////declare triangle; this i used to check wather or not a random point is
//////within the triangle
triangle = new Polygon(triangleX, triangleY, 3);
//////step 1: create a random point within the triangle
Point2D.Double a = randomPoint(triangle, MAX_X, MAX_Y);
//////random number generator
Random randomGenerator = new Random();
//////iterate to produce the triangle
for(int i = 0; i < MAXIMUM_ITERATIONS;="MAXIMUM_ITERATIONS;" i++)
{
//step 2 randomly select one of the vertices of the triangle
Point2D.Double b = (Point2D.Double)vertices.get(
randomGenerator.nextInt(3));
//step 3: get the midpoint of a and b, then add
//midpoint to list of points to draw
Point2D.Double c = midpoint(a, b);
vertices.add(c);
//step 4: set a to c
a = c;
}
}
public void paint(Graphics g)
{
Graphics2D g2 = (Graphics2D)g;
//////iterate
for(int i = 0; i < vertices.size();="vertices.size();" i++)
{
/////////get a new element
Point2D.Double point = (Point2D.Double)vertices.get(i);
/////////create a pixel out of point
Rectangle2D.Double pixel = new Rectangle2D.Double(point.getX(),
point.getY(), 1, 1);
/////////draw the current element
g2.draw(pixel);
}
}
///get the midpoint of a and b
public static Point2D.Double midpoint(Point2D.Double a, Point2D.Double b)
{
double x = (a.getX() + b.getX()) / 2.0;
double y = (a.getY() + b.getY()) / 2.0;
return new Point2D.Double(x, y);
}
///make a new random point outside shape, mumimum(0, 0), maximum(maxX, maxY)
public static Point2D.Double randomPoint(Shape shape, int maxX, int maxY)
{
Random randomGenerator = new Random();
Point2D.Double randomPoint;
//////loop until a random point is found that is outside shape
do
{
//create random point that is at most the bottom-right corner of shape
randomPoint = new Point2D.Double(
randomGenerator.nextInt(maxX + 1),
randomGenerator.nextInt(maxY + 1));
}
//while randomPoint is inside shape
while(shape.contains(randomPoint));
return randomPoint;
}
}
A compiled version of this applet is at http://themaster5000.netfirms.com/Applets/page5.htm
I would greatly appreaciate comment for this program.
B. |
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