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import streamlit as st
import matplotlib.pyplot as plt
import numpy as np
import matplotlib.colors as mcolors
# 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 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)
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 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
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", "Emoji Dynamics and Number Theory Simulation")
)
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)
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.")
if 'fig' in locals():
st.pyplot(fig)
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