Branin Function Optimization Landscape

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.colors import LinearSegmentedColormap

# Branin function (optimization benchmark)
x = np.linspace(-5, 10, 200)
y = np.linspace(0, 15, 200)
X, Y = np.meshgrid(x, y)

a = 1
b = 5.1 / (4 * np.pi**2)
c = 5 / np.pi
r = 6
s = 10
t = 1 / (8 * np.pi)

Z = a * (Y - b * X**2 + c * X - r)**2 + s * (1 - t) * np.cos(X) + s

fig, ax = plt.subplots(figsize=(10, 8), facecolor='#ffffff')
ax.set_facecolor('#ffffff')

# Custom colormap - green to coral
colors = ['#dcfce7', '#22c55e', '#F5B027', '#F5276C']
cmap = LinearSegmentedColormap.from_list('green_coral', colors, N=256)

cs = ax.contourf(X, Y, Z, levels=35, cmap=cmap)
ax.contour(X, Y, Z, levels=20, colors='#374151', linewidths=0.4, alpha=0.5)

cbar = plt.colorbar(cs, ax=ax, pad=0.02)
cbar.set_label('f(x, y)', color='#374151', fontsize=11)
cbar.ax.tick_params(colors='#6b7280', labelsize=9)

# Mark global minima
minima = [(-np.pi, 12.275), (np.pi, 2.275), (9.42478, 2.475)]
for mx, my in minima:
    ax.scatter(mx, my, color='#5314E6', s=80, marker='*', zorder=5, edgecolor='white', linewidth=1)

ax.set_xlabel('x', fontsize=11, color='#374151')
ax.set_ylabel('y', fontsize=11, color='#374151')
ax.set_title('Branin Function Optimization Landscape', fontsize=14, color='#1f2937', fontweight='bold', pad=15)
ax.tick_params(colors='#6b7280', labelsize=9)
for spine in ax.spines.values():
    spine.set_color('#d1d5db')

plt.tight_layout()
plt.show()