Yes, all computer languages can simulate Lissajous figures because these figures are generated using mathematical equations that are universally understood and implementable in any programming language. A Lissajous figure is defined by the parametric equations:

x(t)=Asin(at+δ) y(t)=Bsin(bt)

Where:

• A and B are amplitudes,
• a and b are frequencies,
• δ is the phase difference,
• t is time.

Here are examples in a few popular languages:

1. Python: Using matplotlib for plotting.

   python
   Copia codice
   import numpy as np
   import matplotlib.pyplot as plt
   
   t = np.linspace(0, 2 * np.pi, 1000)
   x = np.sin(3 * t + np.pi/2)
   y = np.sin(4 * t)
   
   plt.plot(x, y)
   plt.show()
   

2. JavaScript: Using HTML5 Canvas.

   html
   Copia codice
   <canvas id="lissajous" width="500" height="500"></canvas>
   <script>
       var canvas = document.getElementById("lissajous");
       var ctx = canvas.getContext("2d");
       ctx.translate(250, 250);
       ctx.beginPath();
       for (var t = 0; t < 2 * Math.PI; t += 0.01) {
           var x = 100 * Math.sin(3 * t + Math.PI / 2);
           var y = 100 * Math.sin(4 * t);
           ctx.lineTo(x, y);
       }
       ctx.stroke();
   </script>
   

3. Java: Using JavaFX.

   java
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   import javafx.application.Application;
   import javafx.scene.Scene;
   import javafx.scene.canvas.Canvas;
   import javafx.scene.canvas.GraphicsContext;
   import javafx.scene.layout.Pane;
   import javafx.scene.paint.Color;
   import javafx.stage.Stage;
   
   public class LissajousFigure extends Application {
       @Override
       public void start(Stage primaryStage) {
           Canvas canvas = new Canvas(500, 500);
           GraphicsContext gc = canvas.getGraphicsContext2D();
           gc.translate(250, 250);
           gc.setStroke(Color.BLACK);
           gc.beginPath();
           for (double t = 0; t < 2 * Math.PI; t += 0.01) {
               double x = 100 * Math.sin(3 * t + Math.PI / 2);
               double y = 100 * Math.sin(4 * t);
               gc.lineTo(x, y);
           }
           gc.stroke();
           Pane root = new Pane(canvas);
           Scene scene = new Scene(root, 500, 500);
           primaryStage.setTitle("Lissajous Figure");
           primaryStage.setScene(scene);
           primaryStage.show();
       }
   
       public static void main(String[] args) {
           launch(args);
       }
   }
   

4. C++: Using SFML.

   cpp
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   #include <SFML/Graphics.hpp>
   #include <cmath>
   
   int main() {
       sf::RenderWindow window(sf::VideoMode(500, 500), "Lissajous Figure");
       sf::VertexArray lines(sf::LinesStrip, 1000);
       for (int i = 0; i < 1000; ++i) {
           float t = i * 2 * M_PI / 999;
           float x = 250 + 100 * std::sin(3 * t + M_PI / 2);
           float y = 250 + 100 * std::sin(4 * t);
           lines[i].position = sf::Vector2f(x, y);
       }
       while (window.isOpen()) {
           sf::Event event;
           while (window.pollEvent(event)) {
               if (event.type == sf::Event::Closed)
                   window.close();
           }
           window.clear();
           window.draw(lines);
           window.display();
       }
       return 0;
   }
   

These examples show that the concept of simulating Lissajous figures can be implemented in any programming language with graphics capabilities. The fundamental requirement is to calculate the coordinates using the sine functions and plot them accordingly.