plot_brownian_paths.py

"""
Figure 6 & 7 from the thesis:
- Independent Brownian motion paths (Figure 6)
- Fine and coarse approximation of a Brownian path (Figure 7)
"""

import numpy as np
import matplotlib.pyplot as plt
from core import sim_brownian_motion

np.random.seed(42)

# --- Figure 6: Independent Brownian motions ---
T = 1.0
l = 10
M = 4

bm = sim_brownian_motion(T, l, M)
t = np.linspace(0, T, 2**l + 1)

fig1, ax1 = plt.subplots(figsize=(8, 5))
for m in range(M):
    ax1.plot(t, bm[:, m])
ax1.set_xlabel('t')
ax1.set_ylabel(r'$W(t)$')
ax1.set_title('Independent Brownian motions')
fig1.tight_layout()
fig1.savefig('plot_independent_bm.png', dpi=150)
print("Saved: plot_independent_bm.png")

# --- Figure 7: Fine and coarse approximation ---
bm_single = sim_brownian_motion(T, l, 1)
t_fine = np.linspace(0, T, 2**l + 1)

fig2, ax2 = plt.subplots(figsize=(8, 5))

# Fine path (l=10)
ax2.plot(t_fine, bm_single[:, 0], label=f'l = {l}', linewidth=0.5)

# Coarse paths
for lc, color in [(4, 'tab:orange'), (3, 'tab:olive')]:
    step = 2**(l - lc)
    t_coarse = t_fine[::step]
    bm_coarse = bm_single[::step, 0]
    ax2.plot(t_coarse, bm_coarse, label=f'l = {lc}', linewidth=1.5)

ax2.set_xlabel('t')
ax2.set_ylabel(r'$\hat{W}^{(2^l)}(t)$')
ax2.legend()
ax2.set_title('Fine and coarse approximation of a Brownian path')
fig2.tight_layout()
fig2.savefig('plot_fine_coarse_bm.png', dpi=150)
print("Saved: plot_fine_coarse_bm.png")

plt.show()