manim 生成勾股树

以下是使用 Manim 生成勾股树的示例代码：

from manim import *

class PythagorasTree(Scene):
    def construct(self):
        # 绘制勾股树
        self.pythagoras_tree()

    def pythagoras_tree(self, depth=4, size=2, angle=0, position=ORIGIN):
        if depth == 0:
            return
        # 绘制直角三角形
        triangle = Polygon(
            ORIGIN, size * RIGHT, size * RIGHT + size * UP * np.sin(angle),
            stroke_width=1, stroke_color=WHITE, fill_opacity=0
        )
        # 绘制斜边
        hypotenuse = Line(size * RIGHT, size * RIGHT + size * UP * np.sin(angle), stroke_width=1, stroke_color=WHITE)

        # 计算左右子树的位置
        left_pos = hypotenuse.get_end()
        right_pos = triangle.get_vertices()[2]

        # 绘制左右子树
        left_tree = self.pythagoras_tree(depth - 1, size * np.sin(angle), angle + PI / 4, left_pos)
        right_tree = self.pythagoras_tree(depth - 1, size * np.cos(angle), angle - PI / 4, right_pos)

        # 添加到场景中
        self.play(Create(triangle), Create(hypotenuse))
        self.play(left_tree, right_tree)
        self.wait(0.5)

运行上述代码，即可生成勾股树的动画效果。可以根据需要修改 `depth`、`size`、`angle` 和 `position` 等参数来控制勾股树的形态。