<s>[INST] write a python script that visualizes bezier curves [/INST] Here is a sample Python script that visualizes Bezier curves using the matplotlib library:

import numpy as np
import matplotlib.pyplot as plt

def bezier_curve(control_points, num_points=100):
    t = np.linspace(0, 1, num_points)
    curve = np.zeros((num_points, 2))
    n = len(control_points) - 1
    for i in range(num_points):
        t_i = t[i]
        curve[i, :] = (1 - t_i)**(n) * control_points[0] + \
                      np.sum([binom(n, j) * (1 - t_i)**(n-j) * t_i**j * control_points[j] for j in range(1, n+1)], axis=0)
    return curve

def binom(n, k):
    return np.math.factorial(n) // (np.math.factorial(k) * np.math.factorial(n - k))

if __name__ == "__main__":
    control_points = np.array([[0, 0], [0.5, 0.5], [1, 1]])
    curve = bezier_curve(control_points)
    plt.plot(control_points[:, 0], control_points[:, 1], 'ro-', markersize=8)
    plt.plot(curve[:, 0], curve[:, 1], 'b-')
    plt.show()

This script creates a Bezier curve from a set of control points using the de Casteljau algorithm, which is a recursive method for evaluating Bezier curves. The curve is plotted along with the control points using matplotlib. You can modify the control points to create different shapes of Bezier curves.</s>\ <s>[INST] Can you explain the de Casteljau algorithm in layman terms? [/INST] 