Update app.py

app.py

@@ -1,21 +1,45 @@
 import streamlit as st
 import matplotlib.pyplot as plt
 import numpy as np
+import matplotlib.colors as mcolors
 
-# Define golden_ratio as a global constant
+# Global constant for golden ratio
 golden_ratio = (1 + np.sqrt(5)) / 2
 
+def is_prime(n):
+    """Check if a number is prime."""
+    if n <= 1:
+        return False
+    for i in range(2, int(n**0.5) + 1):
+        if n % i == 0:
+            return False
+    return True
+
+def fib_sequence(n):
+    """Generate Fibonacci sequence up to n."""
+    fib_seq = [0, 1]
+    while fib_seq[-1] + fib_seq[-2] <= n:
+        fib_seq.append(fib_seq[-1] + fib_seq[-2])
+    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)
+
 def generate_colored_circle_template(num_circles):
     fig, ax = plt.subplots(figsize=(6, 6))
     ax.set_xlim(0, 1)
     ax.set_ylim(0, 1)
     ax.axis('off')
 
-    for _ in range(num_circles):
+    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))
-        color = np.random.rand(3,)
-        circle = plt.Circle(center, radius, color=color, alpha=0.8)
+        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)
         ax.add_artist(circle)
     return fig
 
@@ -49,14 +73,6 @@ def generate_fibonacci_spiral_layout(num_points):
     ax.set_aspect('equal')
     return fig
 
-def is_prime(n):
-    if n <= 1:
-        return False
-    for i in range(2, int(n**0.5) + 1):
-        if n % i == 0:
-            return False
-    return True
-
 def generate_prime_number_spiral(num_points):
     fig, ax = plt.subplots(figsize=(6, 6))
     ax.axis('off')
@@ -72,12 +88,29 @@ def generate_prime_number_spiral(num_points):
     ax.set_aspect('equal')
     return fig
 
-# Streamlit UI
-st.title("Circle Packings Visualization")
+def emoji_dynamics_and_number_theory_simulation(size):
+    fib_seq = fib_sequence(size**2)
+    grid = []
+
+    for i in range(1, size**2 + 1):
+        if i in fib_seq:
+            grid.append("🌀")  # Fibonacci positions
+        elif is_prime(i):
+            grid.append("🌟")  # Prime positions
+        else:
+            grid.append("⚪")  # Other positions
+
+        if i % size == 0:
+            grid.append("\n")  # Newline at the end of each row
+
+    return "".join(grid)
+
+# Streamlit UI setup
+st.title("Circle Packings and Number Theory Visualizations")
 
 mode = st.radio(
     "Choose a visualization mode:",
-    ("Random Circle Packings", "Symmetrical Circle Layouts", "Fibonacci Spiral Layout", "Prime Number Spiral")
+    ("Random Circle Packings", "Symmetrical Circle Layouts", "Fibonacci Spiral Layout", "Prime Number Spiral", "Emoji Dynamics and Number Theory Simulation")
 )
 
 if mode == "Random Circle Packings":
@@ -92,5 +125,12 @@ elif mode == "Fibonacci Spiral Layout":
 elif mode == "Prime Number Spiral":
     num_points = st.slider("Number of Points", 10, 1000, 200)
     fig = generate_prime_number_spiral(num_points)
+elif mode == "Emoji Dynamics and Number Theory Simulation":
+    size = st.slider("Grid Size", 5, 20, 10)
+    simulation = emoji_dynamics_and_number_theory_simulation(size)
+    st.text(simulation)
+else:
+    st.text("Select a visualization mode to display.")
 
-st.pyplot(fig)
+if 'fig' in locals():
+    st.pyplot(fig)