Chaos Game inspired from https://www.youtube.com/watch?v=kbKtFN71Lfs&t=1s. It generates Sierpiński triangle, when points = 3 and moving by half the length to each point with same probability. Try to tune different number of points and change the amount of length you can move from 1/2 to 1/3 (in lines 57 and 58) for different patterns.

chaosGame.java

/**
 * Generates various fractals of geometries using chaos game as 
 * mentioned in https://www.youtube.com/watch?v=kbKtFN71Lfs&t=1s
 */

import java.awt.*;
import javax.swing.*;
import java.util.*;
import java.lang.Math;


/**
 * @author Sasi Kiran Gaddipati
 *
 */

public class chaosGame extends JPanel{
	
	private int iterations = 150000;
	private int upperbound = 500;
	private int radius = 200;
	private static int points = 3;
	
	public void randomPoint(Graphics g, int iter, int num_points) {
		
		Graphics2D g2d = (Graphics2D) g;
		Random rand = new Random();
		
		// To save the points 
		HashMap<Integer, Point> points = new HashMap<Integer, Point>();
		
		// Generating the points on the window
		for (int i = 0; i < num_points; i++) {
			int x = (int) (radius * Math.cos((2*Math.PI*i)/num_points) + 250);
			int y = (int) (radius * Math.sin((2*Math.PI*i)/num_points) + 250);
			
			points.put(i+1, new Point(x, y));
			g2d.fillOval(x, y, 5, 5);	
			
		}
		
		
		// starting random position
		int cur_x = 5 * rand.nextInt(upperbound);
		int cur_y = 5 * rand.nextInt(upperbound);		
		g2d.drawOval(cur_x, cur_y, 5, 5);
		
		Point point =  new Point();
		
		// Iterating to reach each point
		for (int i=0; i< iter; i++) {
			
			int num = rand.nextInt(num_points) + 1;
			
			point = points.get(num);
			
			cur_x = (cur_x + point.x)/2;
			cur_y = (cur_y + point.y)/2;

			
			g2d.fillOval(cur_x, cur_y, 5, 5);
			
		}		
		
	}
	
	public void paintComponent(Graphics g) {
		super.paintComponent(g);
		randomPoint(g, iterations, points);
	}
	
	public static void main(String[] args) {
		chaosGame cg = new chaosGame();		
		JFrame window = new JFrame("Pyramid");
		window.setSize(500,500);
		window.add(cg);
		window.setVisible(true);
	}

}

choasGame_100points_by3.PNG

choasGame_5points_by2.png

choasGame_8points_by3.PNG

choasGame_sierpinski_fractal.png