Update app.py

app.py

@@ -5,6 +5,7 @@ import matplotlib.colors as mcolors
 
 # Global constant for golden ratio
 golden_ratio = (1 + np.sqrt(5)) / 2
+color_wheel = plt.get_cmap('hsv')  # Use the HSV color wheel for harmonious colors
 
 def is_prime(n):
     """Check if a number is prime."""
@@ -23,43 +24,51 @@ def fib_sequence(n):
     return fib_seq[2:]  # Exclude first two numbers for this use case
 
 def adjust_color_brightness(color, factor):
-    """Darken a color by a given factor."""
-    color = np.array(mcolors.to_rgb(color)) * factor
-    return tuple(color)
+    """Adjust the brightness of a color."""
+    return tuple(np.array(mcolors.to_rgb(color)) * factor)
 
 def generate_colored_circle_template(num_circles):
+    """Improved use of color and symmetry in circle generation."""
     fig, ax = plt.subplots(figsize=(6, 6))
     ax.set_xlim(0, 1)
     ax.set_ylim(0, 1)
     ax.axis('off')
 
     for i in range(num_circles):
-        radius = np.random.uniform(0.05, 0.15)
-        center = (np.random.uniform(radius, 1-radius), np.random.uniform(radius, 1-radius))
-        base_color = np.random.rand(3,)
-        darker_color = adjust_color_brightness(base_color, 0.5)
-        color_variation = base_color * (0.95 + 0.1 * np.random.rand())  # Slight color variation
-        circle = plt.Circle(center, radius, color=color_variation, ec=darker_color, lw=1, alpha=0.5)
+        radius = np.random.uniform(0.05, 0.1)
+        angle = 2 * np.pi * i / num_circles
+        distance = np.sqrt(np.random.uniform(0.1, 0.9))
+        x = 0.5 + distance * np.cos(angle)
+        y = 0.5 + distance * np.sin(angle)
+        color = color_wheel(i / num_circles)
+        alpha = 0.6 + 0.4 * (1 - distance)  # More transparent further out
+        circle = plt.Circle((x, y), radius, color=color, alpha=alpha)
         ax.add_artist(circle)
     return fig
 
 def generate_symmetrical_circle_layout(num_layers):
+    """Generate a more symmetrical circle layout."""
     fig, ax = plt.subplots(figsize=(6, 6))
     ax.set_aspect('equal')
     ax.axis('off')
-    
+
+    max_radius = 0.1 + 0.15 * (num_layers - 1)  # Adjust so outer circles don't overlap the figure boundary
     center = (0.5, 0.5)
-    for i in range(num_layers):
-        radius = (i + 1) * 0.1
-        for j in range(6):
-            angle = np.pi / 3 * j
+
+    for layer in range(num_layers):
+        radius = 0.05 + layer * 0.1
+        num_circles = layer * 6 if layer > 0 else 1  # Increase circles in outer layers
+        for i in range(num_circles):
+            angle = 2 * np.pi * i / num_circles
             x = center[0] + radius * np.cos(angle)
             y = center[1] + radius * np.sin(angle)
-            circle = plt.Circle((x, y), radius=0.05, color=np.random.rand(3,), fill=True)
+            color = color_wheel(i / num_circles)
+            circle = plt.Circle((x, y), max_radius / num_layers, color=color, alpha=0.5 + 0.5 * (1 - layer / num_layers))
             ax.add_artist(circle)
     return fig
 
 def generate_fibonacci_spiral_layout(num_points):
+    """Generate layout based on Fibonacci spiral."""
     fig, ax = plt.subplots(figsize=(6, 6))
     ax.axis('off')
     radius = 0.05
@@ -68,12 +77,14 @@ def generate_fibonacci_spiral_layout(num_points):
         distance = np.sqrt(i) * radius
         x = 0.5 + distance * np.cos(angle)
         y = 0.5 + distance * np.sin(angle)
-        circle = plt.Circle((x, y), radius, color=np.random.rand(3,), fill=True)
+        color = color_wheel(i / num_points)
+        circle = plt.Circle((x, y), radius, color=color, fill=True, alpha=0.8)
         ax.add_artist(circle)
     ax.set_aspect('equal')
     return fig
 
 def generate_prime_number_spiral(num_points):
+    """Generate spiral layout highlighting prime numbers."""
     fig, ax = plt.subplots(figsize=(6, 6))
     ax.axis('off')
     radius = 0.05
@@ -83,12 +94,14 @@ def generate_prime_number_spiral(num_points):
             distance = np.sqrt(i) * radius
             x = 0.5 + distance * np.cos(angle)
             y = 0.5 + distance * np.sin(angle)
-            circle = plt.Circle((x, y), radius, color=np.random.rand(3,), fill=True)
+            color = color_wheel(i / num_points)
+            circle = plt.Circle((x, y), radius, color=color, fill=True, alpha=0.8)
             ax.add_artist(circle)
     ax.set_aspect('equal')
     return fig
 
 def emoji_dynamics_and_number_theory_simulation(size):
+    """Simulate emoji dynamics based on number theory."""
     fib_seq = fib_sequence(size**2)
     grid = []