Central_Limit_Theorem_Visualization_in_the_Bizarrely_Universe.java

import java.util.Random;
import org.apache.commons.math3.stat.descriptive.moment.Mean;
import org.apache.commons.math3.distribution.NormalDistribution;

public class CentralLimitTheoremAnimation {
    public static double[][] generateBizarrelyUniverse(int numGalaxies, int numDimensions) {
        Random random = new Random();
        double[][] galaxies = new double[numGalaxies][numDimensions];
        for (int i = 0; i < numGalaxies; i++) {
            for (int j = 0; j < numDimensions; j++) {
                galaxies[i][j] = random.nextGaussian();
            }
        }
        return galaxies;
    }

    public static double[] centralLimitTheorem(int numGalaxies, int numDimensions, int numSamples, int sampleSize) {
        double[] sampleMeans = new double[numSamples];
        for (int s = 0; s < numSamples; s++) {
            double[][] galaxies = generateBizarrelyUniverse(numGalaxies, numDimensions);
            double[] sample = new double[sampleSize];
            for (int i = 0; i < sampleSize; i++) {
                sample[i] = galaxies[i][0]; // Take the first dimension for simplicity
            }
            Mean mean = new Mean();
            sampleMeans[s] = mean.evaluate(sample);
        }
        return sampleMeans;
    }

    public static void main(String[] args) {
        int numGalaxies = 1000;
        int numDimensions = 3;
        int numSamples = 100;
        int sampleSize = 10;

        // Step 5: Explanation
        System.out.println("Welcome to the CLT Bizarrely Universe!");
        System.out.println("In this universe, galaxies are randomly scattered in a 3D space.");
        System.out.println("Let's visualize the Bizarrely Universe:");

        double[][] galaxies = generateBizarrelyUniverse(numGalaxies, numDimensions);

        // Visualization of the Bizarrely Universe
        // Your Java plotting code goes here

        System.out.println("\nNow, let's apply the Central Limit Theorem.");
        System.out.println("We'll take " + numSamples + " samples of size " + sampleSize +
                " and observe how their means converge to a Gaussian distribution.");
        System.out.println("Creating the animation...");

        double[] sampleMeans = centralLimitTheorem(numGalaxies, numDimensions, numSamples, sampleSize);

        // Animation of the Central Limit Theorem
        // Your Java plotting code goes here
    }
}