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End of div_curl project
This commit is contained in:
Grant Sanderson
parent
14cbc64819
commit
748fd8db16
2 changed files with 422 additions and 91 deletions
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@ -11,79 +11,6 @@ class ComplexAnalysisOverlay(Scene):
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self.wait()
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class CompelxAnalyticFluidFlow(ComplexTransformationScene, MovingCameraScene):
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CONFIG = {
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"num_anchors_to_add_per_line": 200,
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"plane_config": {"y_radius": 8}
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}
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def setup(self):
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MovingCameraScene.setup(self)
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ComplexTransformationScene.setup(self)
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def construct(self):
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self.camera.frame.shift(2 * UP)
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self.camera.frame.scale(0.5, about_point=ORIGIN)
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plane = NumberPlane(
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x_radius=15,
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y_radius=25,
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y_unit_size=0.5,
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secondary_line_ratio=0,
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)
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plane.next_to(ORIGIN, UP, buff=0.001)
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horizontal_lines = VGroup(*filter(
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lambda l: np.abs(l.get_center()[0]) < 0.1,
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list(plane.main_lines) + [plane.axes[0]]
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))
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plane.set_stroke(MAROON_B, width=2)
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horizontal_lines.set_stroke(BLUE, width=2)
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for line in horizontal_lines:
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# To lag the paths of the droplets
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line.scale(1 + random.random())
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self.prepare_for_transformation(plane)
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self.add_transformable_mobjects(plane)
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self.background.set_stroke(width=2)
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for label in self.background.coordinate_labels:
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label.set_stroke(width=0)
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label.scale(0.75, about_edge=UR)
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words = TextMobject("Flow near \\\\", "a wall")
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words.scale(0.75)
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words.add_background_rectangle_to_submobjects()
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words.next_to(0.75 * UP, LEFT, MED_LARGE_BUFF)
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equation = TexMobject("z \\rightarrow z^{1/2}")
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equation.scale(0.75)
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equation.add_background_rectangle()
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equation.next_to(words, UP)
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self.apply_complex_function(
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lambda x: x**(1. / 2),
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added_anims=[Write(equation)]
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)
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self.play(Write(words, run_time=1))
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dots = VGroup()
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num_dots_per_line = 50
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for x in range(num_dots_per_line):
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for line in horizontal_lines:
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dot = Dot(radius=0.025)
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opacity = 1.0 - x / float(num_dots_per_line)
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dot.set_fill(opacity=opacity)
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dot.path = line
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dots.add(dot)
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dots.set_color_by_gradient(BLUE_B, BLUE_D)
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self.play(LaggedStart(
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MoveAlongPath, dots,
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lambda d: (d, d.path),
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run_time=3,
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lag_ratio=0.9
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))
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class AnalyzeZSquared(ComplexTransformationScene, ZoomedScene):
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CONFIG = {
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"num_anchors_to_add_per_line": 20,
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@ -630,13 +630,13 @@ class ShowWritingTrajectory(TeacherStudentsScene):
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)
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complex_words.generate_target()
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complex_words.target.move_to(bubble.get_bubble_center())
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self.play(
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FadeOut(screen),
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FadeOut(arrow),
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ShowCreation(bubble),
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self.teacher.change, "hooray",
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MoveToTarget(complex_words),
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)
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# self.play(
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# FadeOut(screen),
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# FadeOut(arrow),
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# ShowCreation(bubble),
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# self.teacher.change, "hooray",
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# MoveToTarget(complex_words),
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# )
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s0 = self.students[0]
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s0.target_center = s0.get_center()
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@ -930,6 +930,28 @@ class CylinderModel(Scene):
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)
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class OkayNotToUnderstand(Scene):
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def construct(self):
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words = TextMobject(
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"It's okay not to \\\\ understand this just yet."
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)
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morty = Mortimer()
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morty.change("confused")
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words.next_to(morty, UP)
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self.add(morty, words)
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class ThatsKindOfInteresting(TeacherStudentsScene):
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def construct(self):
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self.student_says(
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"Cool!", target_mode="hooray",
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student_index=2,
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added_anims=[self.teacher.change, "happy"]
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)
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self.change_student_modes("happy", "happy")
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self.wait(2)
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class ElectricField(CylinderModel, MovingCameraScene):
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def construct(self):
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self.add_plane()
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@ -1067,18 +1089,53 @@ class ElectricField(CylinderModel, MovingCameraScene):
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if y != 0
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])
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h_lines.apply_complex_function(inverse_joukowsky_map)
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for h_line in h_lines:
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h_line.save_state()
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voltage = DecimalNumber(
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10, num_decimal_places=1,
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unit="\\, V",
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color=YELLOW,
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include_background_rectangle=True,
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)
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vp_prop = 0.1
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voltage_point = VectorizedPoint(
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h_lines[4].point_from_proportion(vp_prop)
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)
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def get_voltage(dummy_arg):
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y = voltage_point.get_center()[1]
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return 10 - y
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voltage_update = ContinualChangingDecimal(
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voltage, get_voltage,
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position_update_func=lambda v: v.next_to(
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voltage_point, UP, SMALL_BUFF
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)
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)
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self.play(ShowCreation(
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h_lines,
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run_time=2,
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submobject_mode="all_at_once"
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))
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for x in range(4):
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self.play(LaggedStart(
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ApplyMethod, h_lines,
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lambda m: (m.set_stroke, TEAL, 4),
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rate_func=there_and_back,
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))
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self.add(voltage_update)
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self.add_foreground_mobjects(voltage)
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self.play(
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UpdateFromAlphaFunc(
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voltage, lambda m, a: m.set_fill(opacity=a)
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),
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h_lines[4].set_stroke, YELLOW, 4,
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)
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for hl1, hl2 in zip(h_lines[4:], h_lines[5:]):
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self.play(
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voltage_point.move_to,
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hl2.point_from_proportion(vp_prop),
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hl1.restore,
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hl2.set_stroke, YELLOW, 3,
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run_time=0.5
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)
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self.wait(0.5)
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class AskQuestions(TeacherStudentsScene):
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@ -1567,6 +1624,17 @@ class ThreeDVectorField(ExternallyAnimatedScene):
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pass
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class ThreeDVectorFieldEquation(Scene):
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def construct(self):
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vector = Matrix([
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"yz",
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"xz",
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"xy",
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])
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vector.scale_to_fit_height(FRAME_HEIGHT - 1)
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self.add(vector)
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class GravityFluidFlow(IntroduceVectorField):
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def construct(self):
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self.vector_field = VectorField(
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@ -1808,6 +1876,58 @@ class DefineDivergenceJustFlow(DefineDivergence):
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self.show_flow()
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class DefineDivergenceSymbols(Scene):
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def construct(self):
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tex_mob = TexMobject(
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"\\text{div}",
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"\\textbf{F}",
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"(x, y)",
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"=",
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)
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div, F, xy, eq = tex_mob
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output = DecimalNumber(0, include_sign=True)
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output.next_to(tex_mob, RIGHT)
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time_tracker = ValueTracker()
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self.add(ContinualMovement(time_tracker, rate=1))
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output_animation = ContinualChangingDecimal(
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output, lambda a: 3 * np.cos(int(time_tracker.get_value())),
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)
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F.set_color(BLUE)
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xy.set_color(YELLOW)
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F_brace = Brace(F, UP, buff=SMALL_BUFF)
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F_label = F_brace.get_text(
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"Vector field function",
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)
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F_label.match_color(F)
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xy_brace = Brace(xy, DOWN, buff=SMALL_BUFF)
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xy_label = xy_brace.get_text("Some point")
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xy_label.match_color(xy)
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output_brace = Brace(output, UP, buff=SMALL_BUFF)
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output_label = output_brace.get_text(
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"Measure of how much \\\\ "
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"$(x, y)$ ``generates'' fluid"
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)
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brace_label_pairs = [
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(F_brace, F_label),
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(xy_brace, xy_label),
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(output_brace, output_label),
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]
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self.add(tex_mob, output_animation)
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fade_anims = []
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for brace, label in brace_label_pairs:
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self.play(
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GrowFromCenter(brace),
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FadeInFromDown(label),
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*fade_anims
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)
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self.wait(2)
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fade_anims = map(FadeOut, [brace, label])
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self.wait()
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class DivergenceAtSlowFastPoint(Scene):
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CONFIG = {
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"vector_field_config": {
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@ -2623,8 +2743,8 @@ class MaxwellsEquations(Scene):
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field_definitions = VGroup(*[
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TexMobject(text, tex_to_color_map=tex_to_color_map)
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for text in [
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"\\text{Electric fild: } \\textbf{E}",
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"\\text{Magnetic fild: } \\textbf{B}",
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"\\text{Electric field: } \\textbf{E}",
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"\\text{Magnetic field: } \\textbf{B}",
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]
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])
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field_definitions.arrange_submobjects(
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@ -2720,6 +2840,12 @@ class MaxwellsEquations(Scene):
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self.wait()
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class ThatWeKnowOf(Scene):
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def construct(self):
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words = TextMobject("*That we know of!")
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self.add(words)
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class IllustrateGaussLaw(DefineDivergence, MovingCameraScene):
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CONFIG = {
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"flow_time": 10,
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@ -3329,6 +3455,80 @@ class PhaseSpaceOfPopulationModel(ShowTwoPopulations, PiCreatureScene, MovingCam
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self.wait(self.flow_time)
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class PhaseFlowWords(Scene):
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def construct(self):
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words = TextMobject("``Phase flow''")
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words.scale(2)
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self.play(Write(words))
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self.wait()
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class PhaseFlowQuestions(Scene):
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def construct(self):
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questions = VGroup(
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TextMobject(
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"Which points does the flow \\\\" +
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"converge to? Diverge away from?",
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),
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TextMobject("Where are there cycles?"),
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)
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questions.arrange_submobjects(DOWN, buff=LARGE_BUFF)
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questions.to_corner(UR)
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for question in questions:
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self.play(FadeInFromDown(question))
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self.wait(2)
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class ToolsBeyondDivAndCurlForODEs(PiCreatureScene):
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CONFIG = {
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"default_pi_creature_kwargs": {
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"color": GREY_BROWN,
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},
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"default_pi_creature_start_corner": DOWN,
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}
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def construct(self):
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morty = self.pi_creature
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div_curl = TextMobject("div \\\\", "curl")
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div_curl.set_color_by_tex("div", BLUE)
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div_curl.set_color_by_tex("curl", YELLOW)
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div_curl.next_to(morty.get_corner(UL), UP, MED_LARGE_BUFF)
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jacobian = TextMobject("Analyze the \\\\ Jacobian")
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jacobian.set_color(GREEN)
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jacobian.next_to(morty.get_corner(UR), UP, MED_LARGE_BUFF)
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flow_intuitions = TextMobject("Flow-based intuitions")
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flow_intuitions.next_to(
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VGroup(div_curl, jacobian),
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UP, buff=1.5
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)
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arrow1 = Arrow(div_curl.get_top(), flow_intuitions.get_bottom())
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arrow2 = Arrow(flow_intuitions.get_bottom(), jacobian.get_top())
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self.play(
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FadeInFromDown(div_curl),
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morty.change, "raise_left_hand",
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)
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self.wait()
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self.play(
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FadeInFromDown(jacobian),
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morty.change, "raise_right_hand"
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)
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self.wait()
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self.play(
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ReplacementTransform(
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flow_intuitions.copy().fade(1).move_to(div_curl),
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flow_intuitions,
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),
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GrowArrow(arrow1),
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morty.change, "pondering"
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)
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self.wait(0.5)
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self.play(GrowArrow(arrow2))
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self.wait()
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class AskAboutComputation(TeacherStudentsScene):
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def construct(self):
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self.student_says(
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@ -3355,6 +3555,14 @@ class AskAboutComputation(TeacherStudentsScene):
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self.wait(5)
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class QuickWordsOnNotation(Scene):
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def construct(self):
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words = TextMobject("Quick words on notation:")
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words.scale(1.5)
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self.play(FadeInFromDown(words))
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self.wait()
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class NablaNotation(PiCreatureScene, MovingCameraScene):
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CONFIG = {
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"default_pi_creature_kwargs": {
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@ -4060,6 +4268,80 @@ class DivergenceTinyNudgesView(MovingCameraScene):
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))
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class ZToHalfFlowNearWall(ComplexTransformationScene, MovingCameraScene):
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CONFIG = {
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"num_anchors_to_add_per_line": 200,
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"plane_config": {"y_radius": 8}
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}
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def setup(self):
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MovingCameraScene.setup(self)
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ComplexTransformationScene.setup(self)
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def construct(self):
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# self.camera.frame.shift(2 * UP)
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self.camera.frame.scale(0.5, about_point=ORIGIN)
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plane = NumberPlane(
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x_radius=15,
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y_radius=25,
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y_unit_size=0.5,
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secondary_line_ratio=0,
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)
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plane.next_to(ORIGIN, UP, buff=0.001)
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horizontal_lines = VGroup(*filter(
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lambda l: np.abs(l.get_center()[0]) < 0.1,
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list(plane.main_lines) + [plane.axes[0]]
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))
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plane.set_stroke(MAROON_B, width=2)
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horizontal_lines.set_stroke(BLUE, width=2)
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self.prepare_for_transformation(plane)
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self.add_transformable_mobjects(plane)
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self.background.set_stroke(width=2)
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for label in self.background.coordinate_labels:
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label.set_stroke(width=0)
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label.scale(0.75, about_edge=UR)
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words = TextMobject("(Idealized) Flow \\\\", "near a wall")
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words.scale(0.75)
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words.add_background_rectangle_to_submobjects()
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words.next_to(0.75 * UP, LEFT, MED_LARGE_BUFF)
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equation = TexMobject("z \\rightarrow z^{1/2}")
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equation.scale(0.75)
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equation.add_background_rectangle()
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equation.next_to(words, UP)
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self.apply_complex_function(
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lambda x: x**(1. / 2),
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added_anims=[Write(equation)]
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)
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self.play(Write(words, run_time=1))
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def func(point):
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z = R3_to_complex(point)
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d_half = derivative(lambda z: z**2)
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return complex_to_R3(d_half(z).conjugate())
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stream_lines = StreamLines(
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func,
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start_points_generator_config={
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"x_min": 0.01,
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"y_min": 0.01,
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"delta_x": 0.125,
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"delta_y": 0.125,
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},
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virtual_time=3,
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stroke_width=2,
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max_magnitude=10,
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)
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stream_line_animation = StreamLineAnimation(stream_lines)
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self.add(stream_line_animation)
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self.wait(7)
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class IncmpressibleAndIrrotational(Scene):
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def construct(self):
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div_0 = TextMobject("div$\\textbf{F} = 0$")
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@ -4068,7 +4350,7 @@ class IncmpressibleAndIrrotational(Scene):
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irrotational = TextMobject("Irrotational")
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for text in [div_0, curl_0, incompressible, irrotational]:
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text.add_background_rectangle(buff=SMALL_BUFF)
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self.stylize_word_for_background(text)
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div_0.to_edge(UP)
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curl_0.next_to(div_0, DOWN, MED_LARGE_BUFF)
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@ -4076,7 +4358,7 @@ class IncmpressibleAndIrrotational(Scene):
|
|||
for op, word in (div_0, incompressible), (curl_0, irrotational):
|
||||
op.generate_target()
|
||||
group = VGroup(op.target, word)
|
||||
group.arrange_submobjects(RIGHT, buff=LARGE_BUFF)
|
||||
group.arrange_submobjects(RIGHT, buff=MED_LARGE_BUFF)
|
||||
group.move_to(op)
|
||||
|
||||
self.play(FadeInFromDown(div_0))
|
||||
|
|
@ -4097,12 +4379,30 @@ class IncmpressibleAndIrrotational(Scene):
|
|||
question = TextMobject("Does this actually happen?")
|
||||
question.next_to(rect, DOWN)
|
||||
question.match_color(rect)
|
||||
question.add_background_rectangle()
|
||||
self.stylize_word_for_background(question)
|
||||
|
||||
self.play(ShowCreation(rect))
|
||||
self.play(Write(question))
|
||||
self.wait()
|
||||
|
||||
def stylize_word_for_background(self, word):
|
||||
word.add_background_rectangle()
|
||||
|
||||
|
||||
class NoChargesOverlay(Scene):
|
||||
def construct(self):
|
||||
rect = FullScreenFadeRectangle()
|
||||
rect.set_fill(BLUE_D, 0.75)
|
||||
circle = Circle(radius=1.5, num_anchors=5000)
|
||||
circle.rotate(135 * DEGREES)
|
||||
rect.add_subpath(circle.points)
|
||||
|
||||
words = TextMobject("No charges outside wire")
|
||||
words.scale(1.5)
|
||||
words.to_edge(UP)
|
||||
|
||||
self.add(rect, words)
|
||||
|
||||
|
||||
# End message
|
||||
class BroughtToYouBy(PiCreatureScene):
|
||||
|
|
@ -4483,3 +4783,107 @@ class PeopleValueGraph(GraphScene):
|
|||
run_time=4,
|
||||
)
|
||||
self.wait()
|
||||
|
||||
|
||||
class DivCurlEndScreen(PatreonEndScreen):
|
||||
CONFIG = {
|
||||
"specific_patrons": [
|
||||
"Juan Benet",
|
||||
"Keith Smith",
|
||||
"Chloe Zhou",
|
||||
"Desmos ",
|
||||
"Burt Humburg",
|
||||
"CrypticSwarm",
|
||||
"Andrew Sachs",
|
||||
"Devin Scott",
|
||||
"Akash Kumar",
|
||||
"Felix Tripier",
|
||||
"Arthur Zey",
|
||||
"David Kedmey",
|
||||
"Ali Yahya",
|
||||
"Mayank M. Mehrotra",
|
||||
"Lukas Biewald",
|
||||
"Yana Chernobilsky",
|
||||
"Kaustuv DeBiswas",
|
||||
"Yu Jun",
|
||||
"Dave Nicponski",
|
||||
"Damion Kistler",
|
||||
"Jordan Scales",
|
||||
"Markus Persson",
|
||||
"Fela ",
|
||||
"Fred Ehrsam",
|
||||
"Randy C. Will",
|
||||
"Britt Selvitelle",
|
||||
"Jonathan Wilson",
|
||||
"Ryan Atallah",
|
||||
"Joseph John Cox",
|
||||
"Luc Ritchie",
|
||||
"Omar Zrien",
|
||||
"Sindre Reino Trosterud",
|
||||
"Jeff Straathof",
|
||||
"Matt Langford",
|
||||
"Matt Roveto",
|
||||
"Marek Cirkos",
|
||||
"Magister Mugit",
|
||||
"Stevie Metke",
|
||||
"Cooper Jones",
|
||||
"James Hughes",
|
||||
"John V Wertheim",
|
||||
"Chris Giddings",
|
||||
"Song Gao",
|
||||
"Alexander Feldman",
|
||||
"Richard Burgmann",
|
||||
"John Griffith",
|
||||
"Chris Connett",
|
||||
"Steven Tomlinson",
|
||||
"Jameel Syed",
|
||||
"Bong Choung",
|
||||
"Ignacio Freiberg",
|
||||
"Zhilong Yang",
|
||||
"Giovanni Filippi",
|
||||
"Eric Younge",
|
||||
"Prasant Jagannath",
|
||||
"James H. Park",
|
||||
"Norton Wang",
|
||||
"Kevin Le",
|
||||
"Tianyu Ge",
|
||||
"David MacCumber",
|
||||
"Oliver Steele",
|
||||
"Yaw Etse",
|
||||
"Dave B",
|
||||
"Waleed Hamied",
|
||||
"George Chiesa",
|
||||
"supershabam ",
|
||||
"Delton Ding",
|
||||
"Thomas Tarler",
|
||||
"1stViewMaths",
|
||||
"Jacob Magnuson",
|
||||
"Mark Govea",
|
||||
"Clark Gaebel",
|
||||
"Mathias Jansson",
|
||||
"David Clark",
|
||||
"Michael Gardner",
|
||||
"Mads Elvheim",
|
||||
"Awoo ",
|
||||
"Dr . David G. Stork",
|
||||
"Ted Suzman",
|
||||
"Linh Tran",
|
||||
"Andrew Busey",
|
||||
"John Haley",
|
||||
"Ankalagon ",
|
||||
"Eric Lavault",
|
||||
"Boris Veselinovich",
|
||||
"Julian Pulgarin",
|
||||
"Jeff Linse",
|
||||
"Robert Teed",
|
||||
"Jason Hise",
|
||||
"Bernd Sing",
|
||||
"Mustafa Mahdi",
|
||||
"Mathew Bramson",
|
||||
"Jerry Ling",
|
||||
"Sh\\`im\\'in Ku\\=ang",
|
||||
"Rish Kundalia",
|
||||
"Achille Brighton",
|
||||
"Ripta Pasay",
|
||||
],
|
||||
}
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue