demo9.py

from manimx import *


class OpeningManimExample(Scene):
    def construct(self):
        intro_words = Text("""
            The original motivation for manim was to
            better illustrate mathematical functions
            as transformations.
        """)
        intro_words.to_edge(UP)

        self.play(Write(intro_words))
        self.wait(2)

        # Linear transform
        grid = NumberPlane((-10, 10), (-5, 5))
        matrix = [[1, 1], [0, 1]]
        linear_transform_words = VGroup(
            Text("This is what the matrix"),
            IntegerMatrix(matrix),
            Text("looks like")
        )
        linear_transform_words.arrange(RIGHT)
        linear_transform_words.to_edge(UP)
        linear_transform_words.set_stroke(BLACK, 10, background=True)

        self.play(
            ShowCreation(grid),
            FadeTransform(intro_words, linear_transform_words)
        )
        self.wait()
        self.play(grid.animate.apply_matrix(matrix), run_time=3)
        self.wait()

        # Complex map
        c_grid = ComplexPlane()
        moving_c_grid = c_grid.copy()
        moving_c_grid.prepare_for_nonlinear_transform()
        c_grid.set_stroke(BLUE_E, 1)
        c_grid.add_coordinate_labels(font_size=24)
        complex_map_words = TexText("""
            Or thinking of the plane as $\\mathds{C}$,\\\\
            this is the map $z \\rightarrow z^2$
        """)
        complex_map_words.to_corner(UR)
        complex_map_words.set_stroke(BLACK, 5, background=True)

        self.play(
            FadeOut(grid),
            Write(c_grid, run_time=3),
            FadeIn(moving_c_grid),
            FadeTransform(linear_transform_words, complex_map_words),
        )
        self.wait()
        self.play(
            moving_c_grid.animate.apply_complex_function(lambda z: z**2),
            run_time=6,
        )
        self.wait(2)