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import streamlit as st
import matplotlib.pyplot as plt
import numpy as np
# Define golden_ratio as a global constant
golden_ratio = (1 + np.sqrt(5)) / 2
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):
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)
ax.add_artist(circle)
return fig
def generate_symmetrical_circle_layout(num_layers):
fig, ax = plt.subplots(figsize=(6, 6))
ax.set_aspect('equal')
ax.axis('off')
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
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)
ax.add_artist(circle)
return fig
def generate_fibonacci_spiral_layout(num_points):
fig, ax = plt.subplots(figsize=(6, 6))
ax.axis('off')
radius = 0.05
for i in range(num_points):
angle = i * 2 * np.pi / golden_ratio
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)
ax.add_artist(circle)
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')
radius = 0.05
for i in range(1, num_points + 1):
if is_prime(i):
angle = i * 2 * np.pi / golden_ratio
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)
ax.add_artist(circle)
ax.set_aspect('equal')
return fig
# Streamlit UI
st.title("Circle Packings Visualization")
mode = st.radio(
"Choose a visualization mode:",
("Random Circle Packings", "Symmetrical Circle Layouts", "Fibonacci Spiral Layout", "Prime Number Spiral")
)
if mode == "Random Circle Packings":
num_circles = st.slider("Number of Circles", 5, 50, 10)
fig = generate_colored_circle_template(num_circles)
elif mode == "Symmetrical Circle Layouts":
num_layers = st.slider("Number of Symmetrical Layers", 1, 5, 3)
fig = generate_symmetrical_circle_layout(num_layers)
elif mode == "Fibonacci Spiral Layout":
num_points = st.slider("Number of Points", 10, 100, 30)
fig = generate_fibonacci_spiral_layout(num_points)
elif mode == "Prime Number Spiral":
num_points = st.slider("Number of Points", 10, 1000, 200)
fig = generate_prime_number_spiral(num_points)
st.pyplot(fig)
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