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Minor changes and renaming
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Grant Sanderson
183
active_projects/holomorphic.py
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183
active_projects/holomorphic.py
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@ -0,0 +1,183 @@
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from big_ol_pile_of_manim_imports import *
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class ComplexAnalysisOverlay(Scene):
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def construct(self):
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words = TextMobject("Complex analysis")
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words.scale(1.25)
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words.to_edge(UP)
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words.add_background_rectangle()
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self.add(words)
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self.wait()
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class AnalyzeZSquared(ComplexTransformationScene, ZoomedScene):
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CONFIG = {
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"plane_config": {
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"line_frequency": 0.1,
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},
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"num_anchors_to_add_per_line": 20,
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"complex_homotopy": lambda z, t: z**(1.0 + t),
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"zoom_factor": 0.05,
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}
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def setup(self):
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ComplexTransformationScene.setup(self)
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ZoomedScene.setup(self)
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def construct(self):
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self.edit_background_plane()
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self.add_title()
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# self.add_transforming_planes()
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# self.preview_some_numbers()
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self.zoom_in_to_one_plus_half_i()
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self.write_derivative()
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def add_title(self):
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title = TexMobject("z \\rightarrow z^2")
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title.add_background_rectangle()
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title.scale(1.5)
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title.to_corner(UL, buff=MED_SMALL_BUFF)
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self.add_foreground_mobject(title)
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def edit_background_plane(self):
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self.background.main_lines.set_stroke(GREY, 2)
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self.background.secondary_lines.set_stroke(DARK_GREY, 1)
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self.add_foreground_mobject(self.background.coordinate_labels)
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def add_transforming_planes(self):
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self.plane = self.get_plane()
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self.add_transformable_mobjects(self.plane)
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def preview_some_numbers(self):
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dots = VGroup(*[
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Dot().move_to(self.background.number_to_point(z))
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for z in [
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1, 2, complex(0, 1),
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-1, complex(2, 0.5), complex(-1, -1), complex(3, 0.5),
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]
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])
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dots.set_color_by_gradient(RED, YELLOW)
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d_angle = 30 * DEGREES
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dot_groups = VGroup()
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for dot in dots:
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point = dot.get_center()
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z = self.background.point_to_number(point)
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z_out = self.complex_homotopy(z, 1)
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out_point = self.background.number_to_point(z_out)
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path_arc = angle_of_vector(point)
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if abs(z - 1) < 0.01:
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# One is special
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arrow = Arc(
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start_angle=(-90 * DEGREES + d_angle),
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angle=(360 * DEGREES - 2 * d_angle),
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radius=0.25
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)
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arrow.add_tip(tip_length=0.15)
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arrow.pointwise_become_partial(arrow, 0, 0.9)
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arrow.next_to(dot, UP, buff=0)
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else:
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arrow = Arrow(
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point, out_point,
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use_rectangular_stem=False,
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path_arc=path_arc,
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buff=SMALL_BUFF,
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)
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arrow.match_color(dot)
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out_dot = dot.copy()
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# out_dot.set_fill(opacity=0.5)
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out_dot.set_stroke(BLUE, 1)
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out_dot.move_to(out_point)
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dot.path_arc = path_arc
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dot.out_dot = out_dot
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dot_group = VGroup(dot, arrow, out_dot)
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dot_groups.add(dot_group)
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dot_copy = dot.copy()
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dot.save_state()
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dot.scale(3)
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dot.fade(1)
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dot_group.anim = Succession(
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ApplyMethod(dot.restore),
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AnimationGroup(
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ShowCreation(arrow),
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ReplacementTransform(
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dot_copy, out_dot,
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path_arc=path_arc
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)
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)
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)
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for dot_group in dot_groups[:3]:
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self.play(dot_group.anim)
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self.wait()
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self.play(*[dg.anim for dg in dot_groups[3:]])
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self.apply_complex_homotopy(
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self.complex_homotopy,
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added_anims=[Animation(dot_groups)]
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)
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self.wait()
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self.play(FadeOut(dot_groups))
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self.wait()
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self.play(FadeOut(self.plane))
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self.transformable_mobjects.remove(self.plane)
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def zoom_in_to_one_plus_half_i(self):
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z = complex(1, 0.5)
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point = self.background.number_to_point(z)
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point_mob = VectorizedPoint(point)
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frame = self.zoomed_camera.frame
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frame.move_to(point)
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tiny_plane = NumberPlane(
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x_radius=2, y_radius=2,
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color=GREEN,
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secondary_color=GREEN_E
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)
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tiny_plane.replace(frame)
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plane = self.get_plane()
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words = TextMobject("What does this look like")
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words.add_background_rectangle()
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words.next_to(self.zoomed_display, LEFT, aligned_edge=UP)
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arrow = Arrow(words.get_bottom(), self.zoomed_display.get_left())
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VGroup(words, arrow).set_color(YELLOW)
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self.play(FadeIn(plane))
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self.activate_zooming(animate=True)
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self.play(ShowCreation(tiny_plane))
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self.wait()
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self.add_transformable_mobjects(plane, tiny_plane, point_mob)
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self.add_foreground_mobjects(words, arrow)
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self.apply_complex_homotopy(
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self.complex_homotopy,
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added_anims=[
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Write(words),
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GrowArrow(arrow),
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MaintainPositionRelativeTo(frame, point_mob)
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]
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)
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self.wait(2)
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def write_derivative(self):
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pass
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# Helpers
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def get_plane(self):
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top_plane = NumberPlane(
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y_radius=FRAME_HEIGHT / 2,
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x_line_frequency=0.1,
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y_line_frequency=0.1,
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)
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self.prepare_for_transformation(top_plane)
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bottom_plane = top_plane.copy()
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tiny_tiny_buff = 0.001
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top_plane.next_to(ORIGIN, UP, buff=tiny_tiny_buff)
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bottom_plane.next_to(ORIGIN, DOWN, buff=tiny_tiny_buff)
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return VGroup(top_plane, bottom_plane)
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