walk_in_well.py

import numpy as np
import matplotlib.pyplot as plt

x = np.arange(-10, 10, 0.01)
f = lambda x : x*x/4
y = f(x)

x0 = np.abs(np.random.randn() * 5) # initial point
x_vals = []
y_vals = []
DELTA = 0.1
mul_sign = 1
y0 = f(x0)
while abs(y0) > 1e-14:
    x_vals.append(x0)
    y_vals.append(y0)
    new_x0 = x0 - mul_sign * DELTA
    new_y0 = f(new_x0)
    if new_y0 < y0:
        x0 = new_x0
        y0 = new_y0
    else:
        DELTA = DELTA / 2
        mul_sign *= -1
    print((x0, y0))
#plt.plot(x, y)
#plt.scatter(x_vals, y_vals, c='k')
#plt.show()