Python Spirals

python_spirals.py

from __future__ import division

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
from scipy.special import fresnel

theta = np.linspace(0, 10 * np.pi, 1000)

# Archimedean Spiral
a, b = 0, 1
r_archimedean = a + b * theta
x_archimedean = r_archimedean * np.cos(theta)
y_archimedean = r_archimedean * np.sin(theta)

# Logarithmic Spiral
a, b = 1, 0.1
r_logarithmic = a * np.exp(b * theta)
x_logarithmic = r_logarithmic * np.cos(theta)
y_logarithmic = r_logarithmic * np.sin(theta)

# Fermat's Spiral
r_fermat = np.sqrt(theta)
x_fermat = r_fermat * np.cos(theta)
y_fermat = r_fermat * np.sin(theta)

# Hyperbolic Spiral
a = 1
r_hyperbolic = a / theta
x_hyperbolic = r_hyperbolic * np.cos(theta)
y_hyperbolic = r_hyperbolic * np.sin(theta)

# Lituus Spiral
a = 1
r_lituus = np.sqrt(a**2 / theta)
x_lituus = r_lituus * np.cos(theta)
y_lituus = r_lituus * np.sin(theta)

# Golden Spiral
phi = (1 + np.sqrt(5)) / 2 # Golden Ratio
a = 1
b = 0.306349 # Related to the golden ratio, b = (2 * pi) / log(phi)
r_golden = a * np.exp(b * theta)
x_golden = r_golden * np.cos(theta)
y_golden = r_golden * np.sin(theta)

# Cornu Spiral
t_cornu = np.linspace(-np.sqrt(np.pi), np.sqrt(np.pi), 1000)
x_cornu, y_cornu = fresnel(t_cornu)

# Spherical Spiral
# Define the parameters
phi_spherical = np.linspace(0, 20 * np.pi, 1000)  # Angle with respect to the z-axis
theta_spherical = phi_spherical * np.tan(np.radians(45))  # Constant angle with respect to a fixed diameter
r_spherical = 1  # Radius of the sphere

# Convert to Cartesian coordinates
x_spherical = r_spherical * np.sin(phi_spherical) * np.cos(theta_spherical)
y_spherical = r_spherical * np.sin(phi_spherical) * np.sin(theta_spherical)
z_spherical = r_spherical * np.cos(phi_spherical)


# Sinusoidal Spiral
a_sinusoidal = 1
k_sinusoidal = 2
r_sinusoidal = a_sinusoidal * np.cos(k_sinusoidal * theta)
x_sinusoidal = r_sinusoidal * np.cos(theta)
y_sinusoidal = r_sinusoidal * np.sin(theta)

# Catenary Spiral
t_catenary = np.linspace(-5, 5, 1000)
a_catenary = 1
b_catenary = 1
x_catenary = a_catenary * np.cosh(t_catenary / a_catenary)
y_catenary = b_catenary * t_catenary

# Display
fig, axes = plt.subplots(5, 2, figsize=(10, 10))

axes[0, 0].plot(x_archimedean, y_archimedean)
axes[0, 0].set_title("Archimedean Spiral")
axes[0, 0].axis("equal")

axes[0, 1].plot(x_logarithmic, y_logarithmic)
axes[0, 1].set_title("Logarithmic Spiral")
axes[0, 1].axis("equal")

axes[1, 0].plot(x_fermat, y_fermat)
axes[1, 0].set_title("Fermat's Spiral")
axes[1, 0].axis("equal")

axes[1, 1].plot(x_hyperbolic, y_hyperbolic)
axes[1, 1].set_title("Hyperbolic Spiral")
axes[1, 1].axis("equal")

axes[2, 0].plot(x_lituus, y_lituus)
axes[2, 0].set_title("Lituus Spiral")
axes[2, 0].axis("equal")

axes[2, 1].plot(x_golden, y_golden)
axes[2, 1].set_title("Golden Spiral")
axes[2, 1].axis("equal")

axes[3, 0].plot(x_cornu, y_cornu)
axes[3, 0].set_title("Cornu Spiral")
axes[3, 0].axis("equal")

axes[3, 1].cla()
ax_spherical = fig.add_subplot(5, 2, 8, projection='3d')
ax_spherical.plot(x_spherical, y_spherical, z_spherical)
ax_spherical.set_title("Spherical Spiral")


axes[4, 0].plot(x_sinusoidal, y_sinusoidal)
axes[4, 0].set_title("Sinusoidal Spiral")
axes[4, 0].axis("equal")

axes[4, 1].plot(x_catenary, y_catenary)
axes[4, 1].set_title("Catenary Spiral")
axes[4, 1].axis("equal")

plt.tight_layout()
plt.show()