Add Fourier Series Visualizer project to Math Lab

Author: Kunwartejpal Sidhu

math/Fourier-Series-Visualizer/Fourier-Series-Visualizer.py

@@ -0,0 +1,140 @@
+import math
+import sys
+import time
+
+try:
+    import numpy as np
+    import matplotlib.pyplot as plt
+    from matplotlib.animation import FuncAnimation
+except ImportError:
+    print("❌ This project requires numpy and matplotlib.")
+    print("Install them using: pip install numpy matplotlib")
+    sys.exit(1)
+
+
+def main():
+    print("=" * 58)
+    print("📈 WELCOME TO FOURIER SERIES VISUALIZER 📈")
+    print("=" * 58)
+    print("Explore how complex waveforms can be approximated using harmonics.\n")
+
+    while True:
+        print("=" * 58)
+        print("Choose a waveform type:")
+        print("1️⃣  Square Wave")
+        print("2️⃣  Sawtooth Wave")
+        print("3️⃣  Triangle Wave")
+        print("4️⃣  Exit")
+
+        choice = input("🎯 Enter choice (1-4): ").strip()
+
+        if choice == "4":
+            print("\n👋 Exiting... Keep exploring math!\n")
+            break
+
+        if choice not in ["1", "2", "3"]:
+            print("❌ Invalid choice. Please pick 1, 2, 3, or 4.\n")
+            continue
+
+        waveform_type = {"1": "square", "2": "sawtooth", "3": "triangle"}[choice]
+
+        # Get number of harmonics
+        while True:
+            harmonics_in = input("📝 Enter number of harmonics (N) (1-50): ").strip()
+            try:
+                n_harmonics = int(harmonics_in)
+                if n_harmonics < 1:
+                    print("⚠️ Enter a value greater than or equal to 1.")
+                    continue
+                if n_harmonics > 50:
+                    print("⚠️ For performance, keep harmonics up to 50.")
+                    continue
+                break
+            except ValueError:
+                print("⚠️ Invalid number. Try again.")
+
+        print(f"\n⏳ Simulating {waveform_type} wave with {n_harmonics} harmonics...")
+        time.sleep(0.6)
+
+        print("\n🖥️  Opening animation window... Close it to return to menu.")
+
+        # Setup figure
+        fig, ax = plt.subplots(figsize=(10, 5))
+        ax.set_title(f"Fourier Series Approximation: {waveform_type.capitalize()} Wave (N={n_harmonics})")
+        
+        # We'll draw circles on the left and the wave on the right
+        ax.set_xlim(-3, 10)
+        ax.set_ylim(-3, 3)
+        ax.set_aspect('equal', adjustable='box')
+        ax.grid(True, linestyle='--', alpha=0.5)
+
+        # Plot elements
+        wave_line, = ax.plot([], [], color="#10b981", linewidth=2, label="Approximated Wave")
+        connect_line, = ax.plot([], [], color="gray", linestyle="--", alpha=0.5)
+        drawing_point, = ax.plot([], [], 'ro', markersize=4)
+        
+        circles = []
+        radii_lines = []
+        for _ in range(n_harmonics):
+            circle, = ax.plot([], [], color="blue", alpha=0.2)
+            circles.append(circle)
+            radius_line, = ax.plot([], [], color="blue", alpha=0.5)
+            radii_lines.append(radius_line)
+
+        time_val = 0
+        wave_data = []
+
+        def update(frame):
+            nonlocal time_val, wave_data
+            
+            x = 0
+            y = 0
+            
+            for i in range(n_harmonics):
+                prev_x = x
+                prev_y = y
+                
+                n = 0
+                radius = 0
+                
+                if waveform_type == 'square':
+                    n = i * 2 + 1
+                    radius = (4 / (n * math.pi))
+                elif waveform_type == 'sawtooth':
+                    n = i + 1
+                    radius = (2 * (-1)**(n + 1) / (n * math.pi))
+                elif waveform_type == 'triangle':
+                    n = i * 2 + 1
+                    radius = (8 * (-1)**((n - 1) / 2) / ((n**2) * (math.pi**2)))
+                
+                x += radius * math.cos(n * time_val)
+                y += radius * math.sin(n * time_val)
+                
+                # Draw circle
+                circle_theta = np.linspace(0, 2*np.pi, 50)
+                circles[i].set_data(prev_x + abs(radius)*np.cos(circle_theta), 
+                                  prev_y + abs(radius)*np.sin(circle_theta))
+                
+                # Draw radius line
+                radii_lines[i].set_data([prev_x, x], [prev_y, y])
+
+            wave_data.insert(0, y)
+            if len(wave_data) > 300:
+                wave_data.pop()
+                
+            wave_x = np.linspace(3, 3 + len(wave_data) * 0.03, len(wave_data))
+            wave_line.set_data(wave_x, wave_data)
+            
+            connect_line.set_data([x, 3], [y, wave_data[0]])
+            drawing_point.set_data([x], [y])
+            
+            time_val += 0.03
+            
+            # Matplotlib requires returning an iterable of updated artists
+            return [wave_line, connect_line, drawing_point] + circles + radii_lines
+
+        ani = FuncAnimation(fig, update, frames=400, interval=20, blit=True)
+        plt.show()
+
+if __name__ == "__main__":
+    main()

projects_registry.json

@@ -602,5 +602,21 @@
       "accuracy"
     ],
     "path": "utilities/Typing-Speed-Tester/Typing-Speed-Tester.py"
+  },
+  {
+    "name": "Fourier Series Visualizer",
+    "emoji": "📈",
+    "category": "math",
+    "difficulty": "intermediate",
+    "description": "Explore how complex waveforms can be approximated using harmonics.",
+    "keywords": [
+      "fourier",
+      "series",
+      "visualizer",
+      "math",
+      "wave",
+      "harmonics"
+    ],
+    "path": "math/Fourier-Series-Visualizer/Fourier-Series-Visualizer.py"
   }
 ]