在同一张图上绘制两条洛伦兹曲线,可以通过以下步骤实现:
以下是一个示例代码(使用Python和Matplotlib库):
import matplotlib.pyplot as plt
import numpy as np
# 准备数据
a1, b1, c1 = 10, 28, 8/3
a2, b2, c2 = 10, 40, 8/3
# 定义洛伦兹曲线的微分方程
def lorenz(x, y, z, a, b, c):
dx_dt = a * (y - x)
dy_dt = x * (b - z) - y
dz_dt = x * y - c * z
return dx_dt, dy_dt, dz_dt
# 设置时间步长和总步数
dt = 0.01
num_steps = 10000
# 初始化数组
x1 = np.zeros(num_steps + 1)
y1 = np.zeros(num_steps + 1)
z1 = np.zeros(num_steps + 1)
x2 = np.zeros(num_steps + 1)
y2 = np.zeros(num_steps + 1)
z2 = np.zeros(num_steps + 1)
# 设置初始条件
x1[0], y1[0], z1[0] = (1.0, 1.0, 1.0)
x2[0], y2[0], z2[0] = (2.0, 2.0, 2.0)
# 迭代计算洛伦兹曲线的坐标
for i in range(num_steps):
dx1, dy1, dz1 = lorenz(x1[i], y1[i], z1[i], a1, b1, c1)
dx2, dy2, dz2 = lorenz(x2[i], y2[i], z2[i], a2, b2, c2)
x1[i+1] = x1[i] + dx1 * dt
y1[i+1] = y1[i] + dy1 * dt
z1[i+1] = z1[i] + dz1 * dt
x2[i+1] = x2[i] + dx2 * dt
y2[i+1] = y2[i] + dy2 * dt
z2[i+1] = z2[i] + dz2 * dt
# 创建图形对象
fig = plt.figure()
# 绘制曲线
ax = fig.add_subplot(111, projection='3d')
ax.plot(x1, y1, z1, color='blue', label='Lorenz Curve 1')
ax.plot(x2, y2, z2, color='red', label='Lorenz Curve 2')
# 添加图例
ax.legend()
# 添加标题和标签
ax.set_title('Lorenz Curves')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
# 显示图形
plt.show()
这段代码使用了Matplotlib库来绘制三维图形,并通过迭代计算洛伦兹曲线的坐标。其中,洛伦兹曲线的微分方程通过函数lorenz()
实现,然后使用循环计算曲线的坐标,并使用ax.plot()
函数绘制曲线。最后,通过添加图例、标题和标签,以及调用plt.show()
函数显示图形。
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