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7D_hypercube_(7D_tesseract)_Seventh_Dimension.java
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7D_hypercube_(7D_tesseract)_Seventh_Dimension.java
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import org.apache.commons.math3.linear.MatrixUtils;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.RealVector;
import org.apache.commons.math3.linear.ArrayRealVector;
import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
import org.jfree.chart.ChartFactory;
import org.jfree.chart.ChartPanel;
import org.jfree.chart.JFreeChart;
import org.jfree.chart.plot.PlotOrientation;
import org.jfree.data.xy.XYSeries;
import org.jfree.data.xy.XYSeriesCollection;
import javax.swing.*;
import java.awt.*;
import java.util.ArrayList;
import java.util.List;
public class TesseractPlot {
public static void main(String[] args) {
// Define tesseract vertices with the seventh dimension
RealMatrix vertices = MatrixUtils.createRealMatrix(new double[][]{
{-1, -1, -1, -1, -1, -1, -1},
{-1, -1, -1, -1, -1, -1, 1},
{-1, -1, -1, -1, -1, 1, -1},
{-1, -1, -1, -1, -1, 1, 1},
{-1, -1, -1, -1, 1, -1, -1},
{-1, -1, -1, -1, 1, -1, 1},
{-1, -1, -1, -1, 1, 1, -1},
{-1, -1, -1, -1, 1, 1, 1},
{-1, -1, -1, 1, -1, -1, -1},
{-1, -1, -1, 1, -1, -1, 1},
{-1, -1, -1, 1, -1, 1, -1},
{-1, -1, -1, 1, -1, 1, 1},
{-1, -1, 1, -1, -1, -1, -1},
{-1, -1, 1, -1, -1, -1, 1},
{-1, -1, 1, -1, -1, 1, -1},
{-1, -1, 1, -1, -1, 1, 1},
{-1, -1, 1, -1, 1, -1, -1},
{-1, -1, 1, -1, 1, -1, 1},
{-1, -1, 1, -1, 1, 1, -1},
{-1, -1, 1, -1, 1, 1, 1},
{-1, -1, 1, 1, -1, -1, -1},
{-1, -1, 1, 1, -1, -1, 1},
{-1, -1, 1, 1, -1, 1, -1},
{-1, -1, 1, 1, -1, 1, 1},
{-1, -1, 1, 1, 1, -1, -1},
{-1, -1, 1, 1, 1, -1, 1},
{-1, -1, 1, 1, 1, 1, -1},
{-1, -1, 1, 1, 1, 1, 1},
{-1, 1, -1, -1, -1, -1, -1},
{-1, 1, -1, -1, -1, -1, 1},
{-1, 1, -1, -1, -1, 1, -1},
{-1, 1, -1, -1, -1, 1, 1},
{-1, 1, -1, -1, 1, -1, -1},
{-1, 1, -1, -1, 1, -1, 1},
{-1, 1, -1, -1, 1, 1, -1},
{-1, 1, -1, -1, 1, 1, 1},
{-1, 1, -1, 1, -1, -1, -1},
{-1, 1, -1, 1, -1, -1, 1},
{-1, 1, -1, 1, -1, 1, -1},
{-1, 1, -1, 1, -1, 1, 1},
{-1, 1, -1, 1, 1, -1, -1},
{-1, 1, -1, 1, 1, -1, 1},
{-1, 1, -1, 1, 1, 1, -1},
{-1, 1, -1, 1, 1, 1, 1},
{-1, 1, 1, -1, -1, -1, -1},
{-1, 1, 1, -1, -1, -1, 1},
{-1, 1, 1, -1, -1, 1, -1},
{-1, 1, 1, -1, -1, 1, 1},
{-1, 1, 1, -1, 1, -1, -1},
{-1, 1, 1, -1, 1, -1, 1},
{-1, 1, 1, -1, 1, 1, -1},
{-1, 1, 1, -1, 1, 1, 1},
{-1, 1, 1, 1, -1, -1, -1},
{-1, 1, 1, 1, -1, -1, 1},
{-1, 1, 1, 1, -1, 1, -1},
{-1, 1, 1, 1, -1, 1, 1},
{-1, 1, 1, 1, 1, -1, -1},
{-1, 1, 1, 1, 1, -1, 1},
{-1, 1, 1, 1, 1, 1, -1},
{-1, 1, 1, 1, 1, 1, 1},
{1, -1, -1, -1, -1, -1, -1},
{1, -1, -1, -1, -1, -1, 1},
{1, -1, -1, -1, -1, 1, -1},
{1, -1, -1, -1, -1, 1, 1},
{1, -1, -1, -1, 1, -1, -1},
{1, -1, -1, -1, 1, -1, 1},
{1, -1, -1, -1, 1, 1, -1},
{1, -1, -1, -1, 1, 1, 1},
{1, -1, -1, 1, -1, -1, -1},
{1, -1, -1, 1, -1, -1, 1},
{1, -1, -1, 1, -1, 1, -1},
{1, -1, -1, 1, -1, 1, 1},
{1, -1, -1, 1, 1, -1, -1},
{1, -1, -1, 1, 1, -1, 1},
{1, -1, -1, 1, 1, 1, -1},
{1, -1, -1, 1, 1, 1, 1},
{1, -1, 1, -1, -1, -1, -1},
{1, -1, 1, -1, -1, -1, 1},
{1, -1, 1, -1, -1, 1, -1},
{1, -1, 1, -1, -1, 1, 1},
{1, -1, 1, -1, 1, -1, -1},
{1, -1, 1, -1, 1, -1, 1},
{1, -1, 1, -1, 1, 1, -1},
{1, -1, 1, -1, 1, 1, 1},
{1, -1, 1, 1, -1, -1, -1},
{1, -1, 1, 1, -1, -1, 1},
{1, -1, 1, 1, -1, 1, -1},
{1, -1, 1, 1, -1, 1, 1},
{1, -1, 1, 1, 1, -1, -1},
{1, -1, 1, 1, 1, -1, 1},
{1, -1, 1, 1, 1, 1, -1},
{1, -1, 1, 1, 1, 1, 1},
{1, 1, -1, -1, -1, -1, -1},
{1, 1, -1, -1, -1, -1, 1},
{1, 1, -1, -1, -1, 1, -1},
{1, 1, -1, -1, -1, 1, 1},
{1, 1, -1, -1, 1, -1, -1},
{1, 1, -1, -1, 1, -1, 1},
{1, 1, -1, -1, 1, 1, -1},
{1, 1, -1, -1, 1, 1, 1},
{1, 1, -1, 1, -1, -1, -1},
{1, 1, -1, 1, -1, -1, 1},
{1, 1, -1, 1, -1, 1, -1},
{1, 1, -1, 1, -1, 1, 1},
{1, 1, -1, 1, 1, -1, -1},
{1, 1, -1, 1, 1, -1, 1},
{1, 1, -1, 1, 1, 1, -1},
{1, 1, -1, 1, 1, 1, 1},
{1, 1, 1, -1, -1, -1, -1},
{1, 1, 1, -1, -1, -1, 1},
{1, 1, 1, -1, -1, 1, -1},
{1, 1, 1, -1, -1, 1, 1},
{1, 1, 1, -1, 1, -1, -1},
{1, 1, 1, -1, 1, -1, 1},
{1, 1, 1, -1, 1, 1, -1},
{1, 1, 1, -1, 1, 1, 1},
{1, 1, 1, 1, -1, -1, -1},
{1, 1, 1, 1, -1, -1, 1},
{1, 1, 1, 1, -1, 1, -1},
{1, 1, 1, 1, -1, 1, 1},
{1, 1, 1, 1, 1, -1, -1},
{1, 1, 1, 1, 1, -1, 1},
{1, 1, 1, 1, 1, 1, -1},
{1, 1, 1, 1, 1, 1, 1}
});
// Define edges of the tesseract
List<int[]> edges = new ArrayList<>();
edges.add(new int[]{0, 1});
edges.add(new int[]{0, 2});
edges.add(new int[]{0, 4});
edges.add(new int[]{1, 3});
edges.add(new int[]{1, 5});
edges.add(new int[]{2, 3});
edges.add(new int[]{2, 6});
edges.add(new int[]{3, 7});
edges.add(new int[]{4, 5});
edges.add(new int[]{4, 6});
edges.add(new int[]{5, 7});
edges.add(new int[]{6, 7});
edges.add(new int[]{8, 9});
edges.add(new int[]{8, 10});
edges.add(new int[]{8, 12});
edges.add(new int[]{9, 11});
edges.add(new int[]{9, 13});
edges.add(new int[]{10, 11});
edges.add(new int[]{10, 14});
edges.add(new int[]{11, 15});
edges.add(new int[]{12, 13});
edges.add(new int[]{12, 14});
edges.add(new int[]{13, 15});
edges.add(new int[]{14, 15});
edges.add(new int[]{0, 8});
edges.add(new int[]{1, 9});
edges.add(new int[]{2, 10});
edges.add(new int[]{3, 11});
edges.add(new int[]{4, 12});
edges.add(new int[]{5, 13});
edges.add(new int[]{6, 14});
edges.add(new int[]{7, 15});
edges.add(new int[]{16, 17});
edges.add(new int[]{16, 18});
edges.add(new int[]{16, 20});
edges.add(new int[]{17, 19});
edges.add(new int[]{17, 21});
edges.add(new int[]{18, 19});
edges.add(new int[]{18, 22});
edges.add(new int[]{19, 23});
edges.add(new int[]{20, 21});
edges.add(new int[]{20, 22});
edges.add(new int[]{21, 23});
edges.add(new int[]{22, 23});
edges.add(new int[]{0, 16});
edges.add(new int[]{1, 17});
edges.add(new int[]{2, 18});
edges.add(new int[]{3, 19});
edges.add(new int[]{4, 20});
edges.add(new int[]{5, 21});
edges.add(new int[]{6, 22});
edges.add(new int[]{7, 23});
XYSeriesCollection dataset = new XYSeriesCollection();
RealMatrix rotationMatrix3D = MatrixUtils.createRealMatrix(new double[][]{
// Define rotation matrix for the first three dimensions
{Math.cos(Math.PI / 4), 0, -Math.sin(Math.PI / 4)},
{0, Math.cos(Math.PI / 4), 0},
{Math.sin(Math.PI / 4), 0, Math.cos(Math.PI / 4)}
});
RealMatrix projectedVertices3D = vertices.getSubMatrix(0, vertices.getRowDimension() - 1, 0, 2)
.multiply(rotationMatrix3D);
// Define rotation matrix for the fourth, fifth, sixth, and seventh dimensions
RealMatrix rotationMatrix4567 = MatrixUtils.createRealMatrix(new double[][]{
{1, 0, 0},
{0, Math.cos(Math.PI / 4), -Math.sin(Math.PI / 4)},
{0, Math.sin(Math.PI / 4), Math.cos(Math.PI / 4)}
});
RealMatrix projectedVertices4567 = projectedVertices3D.multiply(rotationMatrix4567);
// Create a series for the scatter plot
XYSeries series = new XYSeries("Tesseract");
// Add projected vertices to the series
for (int i = 0; i < projectedVertices3D.getRowDimension(); i++) {
RealVector vertex = projectedVertices3D.getRowVector(i);
double x = vertex.getEntry(0);
double y = vertex.getEntry(1);
double z = vertex.getEntry(2);
series.add(x, y);
}
// Add the series to the dataset
dataset.addSeries(series);
// Create the scatter plot
JFreeChart chart = ChartFactory.createScatterPlot("Tesseract Projection", "X", "Y",
dataset, PlotOrientation.VERTICAL, true, true, false);
// Create a chart panel to display the plot
ChartPanel chartPanel = new ChartPanel(chart);
chartPanel.setPreferredSize(new Dimension(500, 500));
// Create a frame to hold the chart panel
JFrame frame = new JFrame("Tesseract Projection");
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
frame.setContentPane(chartPanel);
frame.pack();
frame.setVisible(true);
}
}