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Finished turbulence project
This commit is contained in:
Grant Sanderson
parent
29afc50756
commit
3fb98ba2e8
1 changed files with 525 additions and 4 deletions
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@ -3,6 +3,7 @@ from old_projects.div_curl import PureAirfoilFlow
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from old_projects.div_curl import VectorFieldSubmobjectFlow
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from old_projects.div_curl import VectorFieldPointFlow
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from old_projects.div_curl import four_swirls_function
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from old_projects.lost_lecture import ShowWord
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class CreationDestructionMobject(VMobject):
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@ -433,12 +434,10 @@ class SomeTurbulenceEquations(PiCreatureScene):
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navier_stokes.scale(1.2)
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distribution = TexMobject(
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"E(k)=\\alpha \\epsilon^{2/3}_d k^{-5/3}",
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"E(k) \\propto k^{-5/3}",
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tex_to_color_map={
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"k": GREEN,
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"-5/3": YELLOW,
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"\\epsilon": BLUE,
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"_d": BLUE,
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}
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)
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distribution.next_to(morty, UL)
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@ -642,7 +641,7 @@ class SetAsideTurbulence(PiCreatureScene):
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class WavingRodLabel(Scene):
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def construct(self):
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words = TextMobject(
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"(Waving a glass rod \\\\ through the air)"
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"(Waving a small flag \\\\ through the air)"
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)
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self.play(Write(words))
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self.wait()
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@ -1263,3 +1262,525 @@ class FiguresOfFluidDynamics(Scene):
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image_groups[-1].center,
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)
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self.wait()
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class KineticEnergyBreakdown(Scene):
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def construct(self):
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title = TextMobject("Kinetic energy breakdown")
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title.to_edge(UP)
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h_line = Line(LEFT, RIGHT).set_width(FRAME_WIDTH)
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h_line.next_to(title, DOWN)
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v_line = Line(h_line.get_center(), FRAME_HEIGHT * DOWN / 2)
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lc_title = TextMobject("Simpler physics")
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lc_title.set_color(YELLOW)
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rc_title = TextMobject("Turbulence physics")
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rc_title.set_color(GREEN)
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for word, vect in (lc_title, LEFT), (rc_title, RIGHT):
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word.next_to(h_line, DOWN)
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word.shift(FRAME_WIDTH * vect / 4)
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left_items = VGroup(
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TextMobject("- Big moving things"),
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TextMobject("- Heat"),
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)
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left_items.arrange_submobjects(DOWN, aligned_edge=LEFT)
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left_items.next_to(lc_title, DOWN, MED_LARGE_BUFF)
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left_items.to_edge(LEFT)
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self.play(
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Write(VGroup(*it.chain(
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title, h_line, v_line, lc_title, rc_title
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)))
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)
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self.wait()
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for item in left_items:
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self.play(FadeInFrom(item))
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self.wait()
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class MovingCar(Scene):
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def construct(self):
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car = Car()
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x = 3
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car.move_to(x * LEFT)
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self.play(MoveCar(car, x * RIGHT, run_time=4))
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class Heat(Scene):
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def construct(self):
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box = Square(
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side_length=2,
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stroke_color=WHITE,
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)
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balls = VGroup(*[
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self.get_ball(box)
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for x in range(20)
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])
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self.add(box, balls)
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self.wait(20)
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def get_ball(self, box):
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speed_factor = random.random()
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ball = Dot(
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radius=0.05,
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color=interpolate_color(BLUE, RED, speed_factor)
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)
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speed = 2 + 3 * speed_factor
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direction = rotate_vector(RIGHT, TAU * random.random())
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ball.velocity = speed * direction
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x0, y0, z0 = box.get_corner(DL)
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x1, y1, z1 = box.get_corner(UR)
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ball.move_to(np.array([
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interpolate(x0, x1, random.random()),
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interpolate(y0, y1, random.random()),
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0
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]))
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def update(ball, dt):
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ball.shift(ball.velocity * dt)
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if ball.get_left()[0] < box.get_left()[0]:
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ball.velocity[0] = abs(ball.velocity[0])
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if ball.get_right()[0] > box.get_right()[0]:
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ball.velocity[0] = -abs(ball.velocity[0])
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if ball.get_bottom()[1] < box.get_bottom()[1]:
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ball.velocity[1] = abs(ball.velocity[1])
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if ball.get_top()[1] > box.get_top()[1]:
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ball.velocity[1] = -abs(ball.velocity[1])
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return ball
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ball.add_updater(update)
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return ball
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class GrowArrowScene(Scene):
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def construct(self):
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arrow = Arrow(UP, DOWN, color=WHITE)
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self.play(GrowArrow(arrow))
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self.wait()
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class Poem(Scene):
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def construct(self):
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picture = ImageMobject("Lewis_Richardson")
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picture.set_height(4)
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picture.center().to_edge(LEFT, buff=LARGE_BUFF)
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title = TextMobject("Poem by Lewis F. Richardson")
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title.to_edge(UP)
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poem_text = """
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Big{\\,\\,}whirls have little{\\,\\,}whirls\\\\
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which feed on their velocity,\\\\
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And little{\\,\\,}whirls have lesser{\\,\\,}whirls\\\\
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And so on to viscosity.\\\\
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"""
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poem_words = [s for s in poem_text.split(" ") if s]
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poem = TextMobject(*poem_words, alignment="")
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poem.next_to(picture, RIGHT, LARGE_BUFF)
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self.add(picture)
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self.play(FadeInFrom(title, DOWN))
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self.wait()
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for word in poem:
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if "whirl" in word.get_tex_string():
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word.set_color(BLUE)
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self.play(ShowWord(word))
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self.wait(0.005 * len(word)**1.5)
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class SwirlDiameterD(Scene):
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def construct(self):
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kwargs = {
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"path_arc": PI,
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"buff": SMALL_BUFF,
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"use_rectangular_stem": False,
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"color": WHITE
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}
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swirl = VGroup(
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Arrow(RIGHT, LEFT, **kwargs),
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Arrow(LEFT, RIGHT, **kwargs),
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)
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swirl.set_stroke(width=5)
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f = 1.5
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swirl.scale(f)
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h_line = DashedLine(
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f * LEFT, f * RIGHT,
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color=YELLOW,
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)
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D_label = TexMobject("D")
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D_label.scale(2)
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D_label.next_to(h_line, UP, SMALL_BUFF)
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D_label.match_color(h_line)
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# diam = VGroup(h_line, D_label)
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self.play(*map(ShowCreation, swirl))
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self.play(
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GrowFromCenter(h_line),
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FadeInFrom(D_label, UP),
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)
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self.wait()
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class KolmogorovGraph(Scene):
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def construct(self):
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axes = Axes(
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x_min=-1,
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y_min=-1,
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x_max=7,
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y_max=9,
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y_axis_config={
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"unit_size": 0.7,
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}
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)
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axes.center().shift(1.5 * RIGHT)
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x_label = TexMobject("\\log(D)")
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x_label.next_to(axes.x_axis.get_right(), UP)
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y_label = TexMobject("\\log(\\text{K.E. at length scale D})")
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y_label.scale(0.8)
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y_label.next_to(axes.y_axis.get_top(), LEFT)
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y_label.shift_onto_screen()
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axes.add(x_label, y_label)
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v_lines = VGroup(*[
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DashedLine(
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axes.coords_to_point(x, 0),
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axes.coords_to_point(x, 9),
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color=YELLOW,
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stroke_width=1
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)
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for x in [0.5, 5]
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])
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inertial_subrange = TextMobject("``Inertial subrange''")
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inertial_subrange.scale(0.7)
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inertial_subrange.next_to(v_lines.get_bottom(), UP)
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def func(x):
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if 0.5 < x < 5:
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return (5 / 3) * x
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elif x < 0.5:
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return 5 * (x - 0.5) + 0.5 * (5 / 3)
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elif x > 5:
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return np.log(x) + (5 / 3) * 5 - np.log(5)
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graph = axes.get_graph(func, x_min=0.3, x_max=7)
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prop_label = TexMobject("\\text{K.E.} \\propto D^{5/3}")
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prop_label.next_to(
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graph.point_from_proportion(0.5), UL,
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buff=0
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)
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self.add(axes)
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self.play(ShowCreation(graph))
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self.play(FadeInFromDown(prop_label))
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self.wait()
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self.add(v_lines)
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self.play(Write(inertial_subrange))
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self.wait()
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class TechnicalNote(Scene):
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def construct(self):
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title = TextMobject("Technical note:")
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title.to_edge(UP)
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title.set_color(RED)
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self.add(title)
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words = TextMobject("""
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This idea of quantifying the energy held at different
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length scales is typically defined
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in terms of an ``energy spectrum'' involving the Fourier
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transform of a function measuring the correlations
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between the fluid's velocities at different points in space.
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I know, yikes!
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\\quad\\\\
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\\quad\\\\
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Building up the relevant background for that is a bit cumbersome,
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so we'll be thinking about the energy at different scales in
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terms of all eddy's with a given diameter. This is admittedly
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a less well-defined notion, but it does capture the spirit
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of Kolmogorov's result.
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\\quad\\\\
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\\quad\\\\
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See the links in the description for more details,
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if you're curious.
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""", alignment="")
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words.scale(0.75)
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words.next_to(title, DOWN, LARGE_BUFF)
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self.add(title, words)
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class FiveThirds(TeacherStudentsScene):
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def construct(self):
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words = TextMobject(
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"5/3", "is a sort of fundamental\\\\ constant of turbulence"
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)
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self.teacher_says(words)
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self.change_student_modes("pondering", "maybe", "erm")
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self.play(
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FadeOut(self.teacher.bubble),
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FadeOut(words[1]),
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self.teacher.change, "raise_right_hand",
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words[0].scale, 1.5,
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words[0].move_to, self.hold_up_spot
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)
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self.change_student_modes("thinking", "pondering", "hooray")
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self.wait(3)
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class TurbulenceGifLabel(Scene):
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def construct(self):
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title = TextMobject("Turbulence in 2d")
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title.to_edge(UP)
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attribution = TextMobject(
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"Animation by Gabe Weymouth (@gabrielweymouth)"
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)
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attribution.scale(0.5)
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attribution.to_edge(DOWN)
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self.play(Write(title))
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self.play(FadeInFrom(attribution, UP))
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self.wait()
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class VortexStretchingLabel(Scene):
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def construct(self):
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title = TextMobject("Vortex stretching")
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self.play(Write(title))
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self.wait()
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class VortedStretching(ThreeDScene):
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CONFIG = {
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"n_circles": 200,
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}
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def construct(self):
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axes = ThreeDAxes()
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axes.set_stroke(width=1)
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self.add(axes)
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self.move_camera(
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phi=70 * DEGREES,
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theta=-145 * DEGREES,
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run_time=0,
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)
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self.begin_ambient_camera_rotation()
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short_circles = self.get_cylinder_circles(2, 0.5, 0.5)
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tall_circles = short_circles.copy().scale(0.125)
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tall_circles.stretch(16 * 4, 2)
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torus_circles = tall_circles.copy()
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for circle in torus_circles:
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circle.shift(RIGHT)
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z = circle.get_center()[2]
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circle.shift(z * IN)
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angle = PI * z / 2
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circle.rotate(angle, axis=DOWN, about_point=ORIGIN)
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circles = short_circles.copy()
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flow_lines = self.get_flow_lines(circles)
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self.add(circles, flow_lines)
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self.play(LaggedStart(ShowCreation, circles))
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self.wait(5)
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self.play(Transform(circles, tall_circles, run_time=3))
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self.wait(10)
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self.play(Transform(
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circles, torus_circles,
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run_time=3
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))
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self.wait(10)
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def get_cylinder_circles(self, radius, radius_var, max_z):
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return VGroup(*[
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ParametricFunction(
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lambda t: np.array([
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np.cos(TAU * t) * r,
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np.sin(TAU * t) * r,
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z
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]),
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**self.get_circle_kwargs()
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)
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for z in sorted(max_z * np.random.random(self.n_circles))
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for r in [radius + radius_var * random.random()]
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]).center()
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def get_torus_circles(self, out_r, in_r, in_r_var):
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result = VGroup()
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for u in sorted(np.random.random(self.n_circles)):
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r = in_r + in_r_var * random.random()
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circle = ParametricFunction(
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lambda t: r * np.array([
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np.cos(TAU * t),
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np.sin(TAU * t),
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0,
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]),
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**self.get_circle_kwargs()
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)
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circle.shift(out_r * RIGHT)
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circle.rotate(
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TAU * u - PI,
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about_point=ORIGIN,
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axis=DOWN,
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)
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result.add(circle)
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return result
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def get_flow_lines(self, circle_group):
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window = 0.3
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def update_circle(circle, dt):
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circle.total_time += dt
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diameter = get_norm(
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circle.template.point_from_proportion(0) -
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circle.template.point_from_proportion(0.5)
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)
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modulus = np.sqrt(diameter) + 0.1
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alpha = (circle.total_time % modulus) / modulus
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circle.pointwise_become_partial(
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circle.template,
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max(interpolate(-window, 1, alpha), 0),
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min(interpolate(0, 1 + window, alpha), 1),
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)
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result = VGroup()
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for template in circle_group:
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circle = template.deepcopy()
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circle.set_stroke(
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color=interpolate_color(BLUE_A, BLUE_E, random.random()),
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# width=3 * random.random()
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width=1,
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)
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circle.template = template
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circle.total_time = 4 * random.random()
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circle.add_updater(update_circle)
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result.add(circle)
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return result
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def get_circle_kwargs(self):
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return {
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"stroke_color": BLACK,
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"stroke_width": 0,
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}
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class TurbulenceEndScreen(PatreonEndScreen):
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CONFIG = {
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"specific_patrons": [
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"1stViewMaths",
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"Adrian Robinson",
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"Alexis Olson",
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"Andrew Busey",
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"Ankalagon",
|
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"Art Ianuzzi",
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"Awoo",
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"Ayan Doss",
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"Bernd Sing",
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"Boris Veselinovich",
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"Brian Staroselsky",
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"Britt Selvitelle",
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"Carla Kirby",
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"Charles Southerland",
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"Chris Connett",
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"Christian Kaiser",
|
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"Clark Gaebel",
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"Cooper Jones",
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"Danger Dai",
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"Dave B",
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"Dave Kester",
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"David Clark",
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"Delton Ding",
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"Devarsh Desai",
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"eaglle",
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"Eric Younge",
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"Eryq Ouithaqueue",
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"Federico Lebron",
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"Florian Chudigiewitsch",
|
||||
"Giovanni Filippi",
|
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"Hal Hildebrand",
|
||||
"Igor Napolskikh",
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"Jacob Magnuson",
|
||||
"Jameel Syed",
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"James Hughes",
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||||
"Jan Pijpers",
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"Jason Hise",
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"Jeff Linse",
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"Jeff Straathof",
|
||||
"Jerry Ling",
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||||
"John Griffith",
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||||
"John Haley",
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"John V Wertheim",
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"Jonathan Eppele",
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||||
"Jonathan Wilson",
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||||
"Jordan Scales",
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||||
"Joseph John Cox",
|
||||
"Julian Pulgarin",
|
||||
"Kai-Siang Ang",
|
||||
"Kanan Gill",
|
||||
"L0j1k",
|
||||
"Linh Tran",
|
||||
"Luc Ritchie",
|
||||
"Ludwig Schubert",
|
||||
"Lukas -krtek.net- Novy",
|
||||
"Magister Mugit",
|
||||
"Magnus Dahlström",
|
||||
"Mark B Bahu",
|
||||
"Markus Persson",
|
||||
"Mathew Bramson",
|
||||
"Mathias Jansson",
|
||||
"Matt Langford",
|
||||
"Matt Roveto",
|
||||
"Matthew Cocke",
|
||||
"Mehdi Razavi",
|
||||
"Michael Faust",
|
||||
"Michael Hardel",
|
||||
"Mustafa Mahdi",
|
||||
"Márton Vaitkus",
|
||||
"Nero Li",
|
||||
"Oliver Steele",
|
||||
"Omar Zrien",
|
||||
"Peter Ehrnstrom",
|
||||
"Prasant Jagannath",
|
||||
"Randy C. Will",
|
||||
"Richard Burgmann",
|
||||
"Ripta Pasay",
|
||||
"Rish Kundalia",
|
||||
"Robert Teed",
|
||||
"Roobie",
|
||||
"Ryan Atallah",
|
||||
"Ryan Williams",
|
||||
"Sindre Reino Trosterud",
|
||||
"Solara570",
|
||||
"Song Gao",
|
||||
"Steven Soloway",
|
||||
"Steven Tomlinson",
|
||||
"Stevie Metke",
|
||||
"Ted Suzman",
|
||||
"Valeriy Skobelev",
|
||||
"Xavier Bernard",
|
||||
"Yaw Etse",
|
||||
"YinYangBalance.Asia",
|
||||
"Zach Cardwell",
|
||||
],
|
||||
}
|
||||
|
||||
|
||||
class LaserWord(Scene):
|
||||
def construct(self):
|
||||
self.add(TextMobject("Laser").scale(2))
|
||||
|
||||
|
||||
class TurbulenceWord(Scene):
|
||||
def construct(self):
|
||||
self.add(TextMobject("Turbulence").scale(2))
|
||||
|
||||
|
||||
class ArrowScene(Scene):
|
||||
def construct(self):
|
||||
arrow = Arrow(LEFT, RIGHT, color=WHITE)
|
||||
arrow.add_to_back(arrow.copy().set_stroke(BLACK, 5))
|
||||
self.add(arrow)
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue