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https://github.com/3b1b/manim.git
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Added FailureOfComposition Scene
This commit is contained in:
Grant Sanderson
parent
4a47d2bca6
commit
c5f1531727
1 changed files with 410 additions and 15 deletions
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@ -48,24 +48,129 @@ class IntroSceneWrapper(PiCreatureScene):
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"height" : 2,
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},
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"default_pi_creature_start_corner" : DOWN+LEFT,
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# "default_pi_creature_height" : 1,
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}
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def construct(self):
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self.introduce_two_words()
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self.describe_main_topic()
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self.describe_meta_topic()
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def introduce_two_words(self):
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morty = self.pi_creature
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rect = ScreenRectangle(height = 5)
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rect.to_corner(UP+RIGHT)
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self.add(rect)
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main_topic, meta_topic = toipcs = VGroup(
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h_line = Line(LEFT, RIGHT).scale(2)
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h_line.to_corner(UP+LEFT)
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h_line.shift(0.5*DOWN)
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main_topic, meta_topic = topics = VGroup(
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TextMobject("Main topic"),
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TextMobject("Meta topic"),
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)
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topics.arrange_submobjects(DOWN, aligned_edge = LEFT)
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topics.next_to(morty, UP)
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topics.shift_onto_screen()
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self.play(
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morty.change, "raise_left_hand",
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FadeInFromDown(main_topic)
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)
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self.wait()
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self.play(
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morty.change, "raise_right_hand",
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main_topic.next_to, meta_topic.get_top(), UP, MED_SMALL_BUFF,
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FadeInFromDown(meta_topic)
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)
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self.wait()
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self.play(
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morty.change, "happy",
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main_topic.next_to, h_line, UP,
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meta_topic.set_fill, {"opacity" : 0.2},
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)
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self.play(ShowCreation(h_line))
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self.wait()
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self.set_variables_as_attrs(h_line, main_topic, meta_topic)
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def describe_main_topic(self):
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h_line = self.h_line
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morty = self.pi_creature
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main_topic = self.main_topic
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meta_topic = self.meta_topic
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solver = TextMobject("2d equation solver")
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solver.match_width(h_line)
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solver.next_to(h_line, DOWN)
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rainbow_solver1 = solver.copy()
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rainbow_solver2 = solver.copy()
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colors = ["RED", "ORANGE", "YELLOW", "GREEN", BLUE, "PURPLE", PINK]
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rainbow_solver1.gradient_highlight(*colors)
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rainbow_solver2.gradient_highlight(*reversed(colors))
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xy_equation = TexMobject(
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"y", "e", "^x", "=\\sin(|", "x", "y", "|)"
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)
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xy_equation.highlight_by_tex_to_color_map({
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"x" : BLUE,
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"y" : YELLOW
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})
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xy_equation.next_to(solver, DOWN, MED_LARGE_BUFF)
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z_equation = TexMobject("z", "^5", "+", "z", "+", "1", "=", "0")
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z_equation.highlight_by_tex("z", GREEN)
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z_equation.move_to(xy_equation, UP)
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zeta = TexMobject("\\zeta(s) = 0")
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zeta[2].highlight(GREEN)
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zeta.next_to(z_equation, DOWN, MED_LARGE_BUFF)
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self.play(Write(solver))
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self.play(
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LaggedStart(FadeIn, xy_equation, run_time = 1),
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morty.change, "pondering"
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)
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self.wait(2)
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self.play(
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FadeOut(xy_equation),
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FadeIn(z_equation)
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)
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self.wait()
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self.play(Write(zeta))
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self.wait()
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solver.save_state()
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for rainbow_solver in rainbow_solver1, rainbow_solver2:
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self.play(Transform(
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solver, rainbow_solver,
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run_time = 2,
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submobject_mode = "lagged_start"
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))
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self.play(solver.restore)
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self.wait()
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self.play(LaggedStart(
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FadeOut, VGroup(solver, z_equation, zeta)
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))
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self.play(
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main_topic.move_to, meta_topic,
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main_topic.set_fill, {"opacity" : 0.2},
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meta_topic.move_to, main_topic,
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meta_topic.set_fill, {"opacity" : 1},
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morty.change, "hesitant",
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path_arc = TAU/8,
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)
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def describe_meta_topic(self):
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h_line = self.h_line
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morty = self.pi_creature
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words = TextMobject("Seek constructs which \\\\ compose nicely")
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words.scale(0.7)
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words.next_to(h_line, DOWN)
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self.play(Write(words))
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self.play(morty.change, "happy")
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self.wait(3)
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class PiCreaturesAreIntrigued(AltTeacherStudentsScene):
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def construct(self):
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@ -155,6 +260,93 @@ class RewriteEquationWithTeacher(AltTeacherStudentsScene):
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self.play(dot.move_to, plane.coords_to_point(*coords))
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self.wait()
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class TwoDScreenInOurThreeDWorld(AltTeacherStudentsScene, ThreeDScene):
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def construct(self):
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self.ask_about_2d_functions()
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self.show_3d()
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def ask_about_2d_functions(self):
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in_plane = NumberPlane(x_radius = 2.5, y_radius = 2.5)
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in_plane.add_coordinates()
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in_plane.scale_to_fit_height(3)
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out_plane = in_plane.copy()
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in_text = TextMobject("Input space")
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out_text = TextMobject("Output space")
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VGroup(in_text, out_text).scale(0.75)
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in_text.next_to(in_plane, UP, SMALL_BUFF)
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out_text.next_to(out_plane, UP, SMALL_BUFF)
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in_plane.add(in_text)
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out_plane.add(out_text)
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arrow = CurvedArrow(RIGHT, LEFT, angle = TAU/4)
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arrow.pointwise_become_partial(arrow, 0.05, 1.0)
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group = VGroup(in_plane, arrow, out_plane)
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group.arrange_submobjects(RIGHT)
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arrow.shift(UP)
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group.move_to(self.students)
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group.to_edge(UP)
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dots = VGroup()
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dots_target = VGroup()
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for x in np.arange(-2.5, 3.0, 0.5):
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for y in np.arange(-2.5, 3.0, 0.5):
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dot = Dot(radius = 0.05)
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dot.move_to(in_plane.coords_to_point(x, y))
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dot.generate_target()
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dot.target.move_to(out_plane.coords_to_point(
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x + 0.25*np.cos(5*y), y + 0.25*np.sin(3*x)
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))
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dots.add(dot)
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dots_target.add(dot.target)
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dots.gradient_highlight(YELLOW, RED)
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dots_target.gradient_highlight(YELLOW, RED)
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self.play(
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self.teacher.change, "raise_right_hand",
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Write(in_plane, run_time = 1)
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)
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self.play(
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ShowCreation(arrow),
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ReplacementTransform(
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in_plane.copy(), out_plane,
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path_arc = -TAU/4,
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)
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)
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self.play(
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LaggedStart(GrowFromCenter, dots, run_time = 1),
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self.get_student_changes(*3*["erm"]),
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)
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self.play(LaggedStart(MoveToTarget, dots, path_arc = -TAU/4))
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self.wait(3)
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def show_3d(self):
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laptop = Laptop().scale(2)
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laptop.rotate(-TAU/12, DOWN)
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laptop.rotate(-5*TAU/24, LEFT)
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laptop.rotate(TAU/8, LEFT)
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laptop.scale(2.3*SPACE_WIDTH/laptop.screen_plate.get_width())
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laptop.shift(-laptop.screen_plate.get_center() + 0.1*IN)
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should_shade_in_3d(laptop)
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everything = VGroup(laptop, *self.mobjects)
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everything.generate_target()
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# for mob in everything.target.submobject_family():
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# if isinstance(mob, PiCreature):
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# mob.change_mode("confused")
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everything.target.rotate(TAU/12, LEFT)
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everything.target.rotate(TAU/16, UP)
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everything.target.shift(4*UP)
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self.move_camera(
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distance = 12,
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run_time = 4,
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added_anims = [MoveToTarget(everything, run_time = 4)],
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)
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self.add(AmbientRotation(everything, axis = UP, rate = 3*DEGREES))
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self.wait(10)
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class DotsHoppingToColor(Scene):
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CONFIG = {
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"dot_radius" : 0.05,
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@ -247,13 +439,8 @@ class DotsHoppingToColor(Scene):
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inspector.scale(0.15)
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inspector_image = inspector.copy()
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def point_function(point):
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in_coords = input_plane.point_to_coords(point)
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out_coords = self.func(in_coords)
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return output_plane.coords_to_point(*out_coords)
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def update_inspector_image(inspector_image):
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inspector_image.move_to(point_function(inspector.get_center()))
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inspector_image.move_to(self.point_function(inspector.get_center()))
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inspector_image_update_anim = UpdateFromFunc(
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inspector_image, update_inspector_image
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@ -361,19 +548,23 @@ class DotsHoppingToColor(Scene):
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self.wait()
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###
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def func(self, coord_pair):
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out_coords = np.array(self.non_renormalized_func(coord_pair))
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out_norm = np.linalg.norm(out_coords)
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if out_norm > 0.5:
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if out_norm > 0.01:
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angle = angle_of_vector(out_coords)
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factor = 0.5-0.1*np.cos(4*angle)
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target_norm = factor*np.log(out_norm)
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out_coords *= target_norm / out_norm
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return tuple(out_coords)
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def point_function(self, point):
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in_coords = self.input_plane.point_to_coords(point)
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out_coords = self.func(in_coords)
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return self.output_plane.coords_to_point(*out_coords)
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def get_colorings(self):
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in_cmos = ColorMappedObjectsScene(
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func = lambda p : self.non_renormalized_func(
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@ -404,11 +595,11 @@ class DotsHoppingToColor(Scene):
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return colorings
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def get_planes(self):
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input_plane = NumberPlane(
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input_plane = self.input_plane = NumberPlane(
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x_radius = self.plane_width/2.0,
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y_radius = self.plane_height/2.0,
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)
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output_plane = input_plane.copy()
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output_plane = self.output_plane = input_plane.copy()
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planes = [input_plane, output_plane]
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vects = [LEFT, RIGHT]
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label_texts = ["Input", "Output"]
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@ -430,7 +621,6 @@ class DotsHoppingToColor(Scene):
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if isinstance(submob, TexMobject) and hasattr(submob, "background_rectangle"):
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submob.remove(submob.background_rectangle)
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return planes
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def get_dots(self, input_plane, output_plane):
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@ -491,7 +681,212 @@ class PiCreatureAsksWhatWentWrong(PiCreatureScene):
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)
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self.wait(5)
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class ForeverNarrowingLoop(DotsHoppingToColor):
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CONFIG = {
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"non_renormalized_func" : plane_func_by_wind_spec(
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(-2, -1, 2),
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(1, 1, 1),
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(2, -2, -1),
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),
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}
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def construct(self):
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input_coloring, output_coloring = colorings = VGroup(*self.get_colorings())
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input_plane, output_plane = planes = VGroup(*self.get_planes())
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for plane in planes:
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plane.white_parts.highlight(BLACK)
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plane.lines_to_fade.set_stroke(width = 0)
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v_line = Line(UP, DOWN).scale(SPACE_HEIGHT)
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v_line.set_stroke(WHITE, 5)
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self.add(colorings, v_line, planes)
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self.play(*it.chain(
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[
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ApplyMethod(coloring.set_fill, {"opacity" : 0.2})
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for coloring in colorings
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],
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[
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ApplyMethod(plane.white_parts.highlight, WHITE)
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for plane in planes
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]
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), run_time = 2)
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# circle
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circle = Circle(color = WHITE, radius = 2.25)
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circle.flip(axis = RIGHT)
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circle.insert_n_anchor_points(50)
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circle.next_to(input_coloring.get_corner(UP+RIGHT), DOWN+LEFT, SMALL_BUFF)
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circle.set_stroke(width = 5)
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circle_image = circle.copy()
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circle.match_background_image_file(input_coloring)
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circle_image.match_background_image_file(output_coloring)
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def update_circle_image(circle_image):
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circle_image.points = circle.points
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circle_image.apply_function(self.point_function)
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circle_image.make_smooth()
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circle_image_update_anim = UpdateFromFunc(
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circle_image, update_circle_image
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)
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self.play(
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ShowCreation(circle),
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ShowCreation(circle_image),
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run_time = 3,
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rate_func = bezier([0, 0, 1, 1])
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)
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# self.play(
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# ReplacementTransform(
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# circle.copy(),
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# circle_image.copy().match_background_image_file(
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# input_coloring
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# ).set_stroke(width = 0)
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# ),
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# ReplacementTransform(
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# circle.copy().match_background_image_file(
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# output_coloring
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# ).set_stroke(width = 0),
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# circle_image
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# ),
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# run_time = 2
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# )
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self.play(
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circle.scale, 0.015,
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circle.move_to, input_plane.coords_to_point(1, 1),
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circle_image_update_anim,
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run_time = 20,
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rate_func = bezier([0, 0, 1, 1])
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)
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class FailureOfComposition(ColorMappedObjectsScene):
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CONFIG = {
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"func" : lambda p : (
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np.cos(TAU*p[1]/3.5),
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np.sin(TAU*p[1]/3.5)
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)
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}
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def construct(self):
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ColorMappedObjectsScene.construct(self)
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big_square = Square(side_length = 4)
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big_square.move_to(ORIGIN, RIGHT)
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small_squares = VGroup(*[
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Square(side_length = 2) for x in range(2)
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])
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small_squares.match_width(big_square, stretch = True)
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small_squares.arrange_submobjects(DOWN, buff = 0)
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small_squares.move_to(big_square)
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small_squares.space_out_submobjects(1.1)
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all_squares = VGroup(big_square, *small_squares)
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all_squares.set_stroke(width = 6)
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for square in all_squares:
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square.highlight(WHITE)
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square.color_using_background_image(self.background_image_file)
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question = TextMobject("Does my border go through every color?")
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question.to_edge(UP)
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no_answers = VGroup()
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yes_answers = VGroup()
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for square in all_squares:
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if square is big_square:
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square.answer = TextMobject("Yes")
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square.answer.highlight(GREEN)
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yes_answers.add(square.answer)
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else:
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square.answer = TextMobject("No")
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square.answer.highlight(RED)
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no_answers.add(square.answer)
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square.answer.move_to(square)
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no_answers_in_equation = no_answers.copy()
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yes_answers_in_equation = yes_answers.copy()
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plus, equals = plus_equals = TexMobject("+=")
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equation = VGroup(
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no_answers_in_equation[0], plus,
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no_answers_in_equation[1], equals,
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yes_answers_in_equation
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)
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equation.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
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equation.next_to(big_square, RIGHT, MED_LARGE_BUFF)
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q_marks = TexMobject("???")
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q_marks.next_to(equals, UP)
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self.add(question)
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self.play(LaggedStart(ShowCreation, small_squares, lag_ratio = 0.8))
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self.play(LaggedStart(Write, no_answers))
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self.wait()
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self.play(
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small_squares.arrange_submobjects, DOWN, {"buff" : 0},
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small_squares.move_to, big_square,
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no_answers.space_out_submobjects, 0.9,
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)
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self.add(big_square)
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no_answers_copy = no_answers.copy()
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small_squares.save_state()
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self.play(
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Transform(no_answers, no_answers_in_equation),
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Write(plus_equals),
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small_squares.set_stroke, {"width" : 0},
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)
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self.play(
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Write(yes_answers),
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Write(yes_answers_in_equation),
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)
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self.play(LaggedStart(FadeIn, q_marks, run_time = 1))
|
||||
self.wait(2)
|
||||
self.play(
|
||||
small_squares.restore,
|
||||
FadeOut(yes_answers),
|
||||
FadeIn(no_answers_copy),
|
||||
)
|
||||
self.wait()
|
||||
self.play(
|
||||
small_squares.set_stroke, {"width" : 0},
|
||||
FadeOut(no_answers_copy),
|
||||
FadeIn(yes_answers),
|
||||
)
|
||||
self.wait()
|
||||
|
||||
# We can find a better notion of what we want
|
||||
|
||||
cross = Cross(question)
|
||||
|
||||
self.play(
|
||||
ShowCreation(cross, run_time = 2),
|
||||
FadeOut(equation),
|
||||
FadeOut(no_answers),
|
||||
FadeOut(q_marks),
|
||||
FadeOut(yes_answers),
|
||||
)
|
||||
|
||||
x, plus, y = x_plus_y = TexMobject("x+y")
|
||||
x_plus_y.move_to(big_square)
|
||||
x_plus_y.save_state()
|
||||
x.move_to(no_answers_copy[0])
|
||||
y.move_to(no_answers_copy[1])
|
||||
plus.fade(1)
|
||||
|
||||
for square, char in zip(small_squares, [x, y]):
|
||||
ghost = square.copy()
|
||||
ghost.set_stroke(width = 5)
|
||||
ghost.background_image_file = None
|
||||
self.play(
|
||||
small_squares.restore,
|
||||
ShowPassingFlash(ghost),
|
||||
Write(char)
|
||||
)
|
||||
self.wait()
|
||||
ghost = big_square.copy()
|
||||
ghost.background_image_file = None
|
||||
self.play(
|
||||
small_squares.set_stroke, {"width" : 0},
|
||||
x_plus_y.restore,
|
||||
)
|
||||
self.play(ShowPassingFlash(ghost))
|
||||
self.wait()
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue