def snells_law_at_every_point(self, cycloid, chopped_cycloid):
square = Square(side_length = 0.2, color = WHITE)
words = TextMobject(["Snell's law ", "everywhere"])
snells, rest = words.split()
colon = TextMobject(":")
words.next_to(square)
words.shift(0.3*UP)
combo = Mobject(square, words)
combo.get_center = lambda : square.get_center()
new_snells = snells.copy().center().to_edge(UP, buff = 1.5)
colon.next_to(new_snells)
colon.shift(0.05*DOWN)
self.play(MoveAlongPath(
combo, cycloid,
run_time = 5
))
self.play(MoveAlongPath(
combo, chopped_cycloid,
run_time = 4
))
dot = Dot(combo.get_center())
self.play(Transform(square, dot))
self.play(
Transform(snells, new_snells),
Transform(rest, colon)
)
self.dither()
return colon
def solve_energy(self):
loss_in_potential = TextMobject("Loss in potential: ")
loss_in_potential.shift(2 * UP)
potential = TexMobject("m g y".split())
potential.next_to(loss_in_potential)
kinetic = TexMobject(["\\dfrac{1}{2}", "m", "v", "^2", "="])
kinetic.next_to(potential, LEFT)
nudge = 0.1 * UP
kinetic.shift(nudge)
loss_in_potential.shift(nudge)
ms = Mobject(kinetic.split()[1], potential.split()[0])
two = TexMobject("2")
two.shift(ms.split()[1].get_center())
half = kinetic.split()[0]
sqrt = TexMobject("\\sqrt{\\phantom{2mg}}")
sqrt.shift(potential.get_center())
nudge = 0.2 * LEFT
sqrt.shift(nudge)
squared = kinetic.split()[3]
equals = kinetic.split()[-1]
new_eq = equals.copy().next_to(kinetic.split()[2])
self.play(
Transform(Point(loss_in_potential.get_left()), loss_in_potential),
*map(GrowFromCenter, potential.split()))
self.dither(2)
self.play(FadeOut(loss_in_potential), GrowFromCenter(kinetic))
self.dither(2)
self.play(ApplyMethod(ms.shift, 5 * UP))
self.dither()
self.play(Transform(half, two, path_func=counterclockwise_path()))
self.dither()
self.play(Transform(squared, sqrt, path_func=clockwise_path()),
Transform(equals, new_eq))
self.dither(2)
def construct(self):
glass = Region(lambda x, y: y < 0, color=BLUE_E)
kwargs = {"density": self.zoom_factor * DEFAULT_POINT_DENSITY_1D}
top_line = Line(SPACE_HEIGHT * UP + 2 * LEFT, ORIGIN, **kwargs)
extension = Line(ORIGIN, SPACE_HEIGHT * DOWN + 2 * RIGHT, **kwargs)
bottom_line = Line(ORIGIN, SPACE_HEIGHT * DOWN + RIGHT, **kwargs)
path1 = Mobject(top_line, extension)
path2 = Mobject(top_line, bottom_line)
for mob in path1, path2:
mob.ingest_submobjects()
extension.highlight(RED)
theta1 = np.arctan(bottom_line.get_slope())
theta2 = np.arctan(extension.get_slope())
arc = Arc(theta2 - theta1, start_angle=theta1, radius=2)
question_mark = TextMobject("$\\theta$?")
question_mark.shift(arc.get_center() + 0.5 * DOWN + 0.25 * RIGHT)
wave = self.wavify(path2)
wave.highlight(YELLOW)
wave.scale(0.5)
self.add(glass)
self.play(ShowCreation(path1))
self.play(Transform(path1, path2))
self.wait()
# self.activate_zooming()
self.wait()
self.play(ShowPassingFlash(wave, run_time=3, rate_func=None))
self.wait()
self.play(ShowCreation(extension))
self.play(ShowCreation(arc), ShimmerIn(question_mark))
def construct(self):
logo = ImageMobject("LogoGeneration", invert = False)
name_mob = TextMobject("3Blue1Brown").center()
name_mob.highlight("grey")
name_mob.shift(2*DOWN)
self.add(name_mob, logo)
new_text = TextMobject(["with ", "Steven Strogatz"])
new_text.next_to(name_mob, DOWN)
self.play(*[
ShimmerIn(part)
for part in new_text.split()
])
self.dither()
with_word, steve = new_text.split()
steve_copy = steve.copy().center().to_edge(UP)
# logo.sort_points(lambda p : -np.linalg.norm(p))
sort_by_color(logo)
self.play(
Transform(steve, steve_copy),
DelayByOrder(Transform(logo, Point())),
FadeOut(with_word),
FadeOut(name_mob),
run_time = 3
)
def construct(self):
self.add_cycloid_end_points()
start = self.point_a.get_center()
end = self.point_b.get_center()
angle = 2 * np.pi / 3
path = Arc(angle, radius=3)
path.gradient_highlight(RED_D, WHITE)
radius = Line(ORIGIN, path.points[0])
randy = Randolph()
randy.scale(RANDY_SCALE_FACTOR)
randy.shift(-randy.get_bottom())
randy_copy = randy.copy()
words = TextMobject(
"Circular paths are good, \\\\ but still not the best")
words.shift(UP)
self.play(
ShowCreation(path),
ApplyMethod(radius.rotate, angle, path_func=path_along_arc(angle)))
self.play(FadeOut(radius))
self.play(ApplyMethod(path.position_endpoints_on,
start,
end,
path_func=path_along_arc(-angle)),
run_time=3)
self.adjust_mobject_to_index(randy_copy, 1, path.points)
self.play(FadeIn(randy_copy))
self.remove(randy_copy)
self.slide(randy, path)
self.play(ShimmerIn(words))
self.dither()
class LogoGeneration(Scene):
CONFIG = {
"radius" : 1.5,
"inner_radius_ratio" : 0.55,
"circle_density" : 100,
"circle_blue" : "skyblue",
"circle_brown" : DARK_BROWN,
"circle_repeats" : 5,
"sphere_density" : 50,
"sphere_blue" : DARK_BLUE,
"sphere_brown" : LIGHT_BROWN,
"interpolation_factor" : 0.3,
"frame_duration" : 0.03,
"run_time" : 3,
}
def construct(self):
digest_config(self, {})
## Usually shouldn't need this...
self.frame_duration = self.CONFIG["frame_duration"]
##
digest_config(self, {})
circle = Circle(
density = self.circle_density,
color = self.circle_blue
)
circle.repeat(self.circle_repeats)
circle.scale(self.radius)
sphere = Sphere(
density = self.sphere_density,
color = self.sphere_blue
)
sphere.scale(self.radius)
sphere.rotate(-np.pi / 7, [1, 0, 0])
sphere.rotate(-np.pi / 7)
iris = Mobject()
iris.interpolate(
circle, sphere,
self.interpolation_factor
)
for mob, color in [(iris, self.sphere_brown), (circle, self.circle_brown)]:
mob.highlight(color, lambda (x, y, z) : x < 0 and y > 0)
mob.highlight(
"black",
lambda point: np.linalg.norm(point) < \
self.inner_radius_ratio*self.radius
)
self.name_mob = TextMobject("3Blue1Brown").center()
self.name_mob.highlight("grey")
self.name_mob.shift(2*DOWN)
self.play(Transform(
circle, iris,
run_time = self.run_time
))
self.frames = drag_pixels(self.frames)
self.save_image(IMAGE_DIR)
self.logo = MobjectFromPixelArray(self.frames[-1])
self.add(self.name_mob)
self.wait()
def show_equation(self):
equation = TexMobject([
"\\left(\\dfrac{1}{\\phantom{v_air}}\\right)", "\\sin(\\theta_1)",
"=", "\\left(\\dfrac{1}{\\phantom{v_water}}\\right)",
"\\sin(\\theta_2)"
])
equation.to_corner(UP + RIGHT)
frac1, sin1, equals, frac2, sin2 = equation.split()
v_air, v_water = [
TexMobject("v_{\\text{%s}}" % s, size="\\Large")
for s in "air", "water"
]
v_air.next_to(Point(frac1.get_center()), DOWN)
v_water.next_to(Point(frac2.get_center()), DOWN)
frac1.add(v_air)
frac2.add(v_water)
f1, f2 = [TexMobject("F_%d" % d, size="\\Large") for d in 1, 2]
f1.next_to(sin1, LEFT)
f2.next_to(equals, RIGHT)
sin2_start = sin2.copy().next_to(f2, RIGHT)
bar1 = TexMobject("\\dfrac{\\qquad}{\\qquad}")
bar2 = bar1.copy()
bar1.next_to(sin1, DOWN)
bar2.next_to(sin2, DOWN)
v_air_copy = v_air.copy().next_to(bar1, DOWN)
v_water_copy = v_water.copy().next_to(bar2, DOWN)
bars = Mobject(bar1, bar2)
new_eq = equals.copy().center().shift(bars.get_center())
snells = TextMobject("Snell's Law")
snells.highlight(YELLOW)
snells.shift(new_eq.get_center()[0] * RIGHT)
snells.shift(UP)
anims = []
for mob in f1, sin1, equals, f2, sin2_start:
anims.append(ShimmerIn(mob))
self.play(*anims)
self.wait()
for f, frac in (f1, frac1), (f2, frac2):
target = frac.copy().ingest_submobjects()
also = []
if f is f2:
also.append(Transform(sin2_start, sin2))
sin2 = sin2_start
self.play(Transform(f, target), *also)
self.remove(f)
self.add(frac)
self.wait()
self.play(FadeOut(frac1), FadeOut(frac2), Transform(v_air, v_air_copy),
Transform(v_water, v_water_copy), ShowCreation(bars),
Transform(equals, new_eq))
self.wait()
frac1 = Mobject(sin1, bar1, v_air)
frac2 = Mobject(sin2, bar2, v_water)
for frac, vect in (frac1, LEFT), (frac2, RIGHT):
self.play(ApplyMethod(frac.next_to, equals, vect))
self.wait()
self.play(ShimmerIn(snells))
self.wait()
def construct(self):
dated_events = [
{
"date" : 1696,
"text": "Johann Bernoulli poses Brachistochrone problem",
"picture" : "Johann_Bernoulli2"
},
{
"date" : 1662,
"text" : "Fermat states his principle of least time",
"picture" : "Pierre_de_Fermat"
}
]
speical_dates = [2016] + [
obj["date"] for obj in dated_events
]
centuries = range(1600, 2100, 100)
timeline = NumberLine(
numerical_radius = 300,
number_at_center = 1800,
unit_length_to_spatial_width = SPACE_WIDTH/100,
tick_frequency = 10,
numbers_with_elongated_ticks = centuries
)
timeline.add_numbers(*centuries)
centers = [
Point(timeline.number_to_point(year))
for year in speical_dates
]
timeline.add(*centers)
timeline.shift(-centers[0].get_center())
self.add(timeline)
self.dither()
run_times = iter([3, 1])
for point, event in zip(centers[1:], dated_events):
self.play(ApplyMethod(
timeline.shift, -point.get_center(),
run_time = run_times.next()
))
picture = ImageMobject(event["picture"], invert = False)
picture.scale_to_fit_width(2)
picture.to_corner(UP+RIGHT)
event_mob = TextMobject(event["text"])
event_mob.shift(2*LEFT+2*UP)
date_mob = TexMobject(str(event["date"]))
date_mob.scale(0.5)
date_mob.shift(0.6*UP)
line = Line(event_mob.get_bottom(), 0.2*UP)
self.play(
ShimmerIn(event_mob),
ShowCreation(line),
ShimmerIn(date_mob)
)
self.play(FadeIn(picture))
self.dither(3)
self.play(*map(FadeOut, [event_mob, date_mob, line, picture]))
def construct(self, order):
if order == 2:
result_tex = "(0.125, 0.75)"
elif order == 3:
result_tex = "(0.0758, 0.6875)"
phc, arg, result = TexMobject([
"\\text{PHC}_%d"%order,
"(0.3)",
"= %s"%result_tex
]).to_edge(UP).split()
function = TextMobject("Function", size = "\\normal")
function.shift(phc.get_center()+DOWN+2*LEFT)
function_arrow = Arrow(function, phc)
line = Line(5*LEFT, 5*RIGHT)
curve = HilbertCurve(order = order)
line.match_colors(curve)
grid = Grid(2**order, 2**order)
grid.fade()
for mob in curve, grid:
mob.scale(0.7)
index = int(0.3*line.get_num_points())
dot1 = Dot(line.points[index])
arrow1 = Arrow(arg, dot1, buff = 0.1)
dot2 = Dot(curve.points[index])
arrow2 = Arrow(result.get_bottom(), dot2, buff = 0.1)
self.add(phc)
self.play(
ShimmerIn(function),
ShowCreation(function_arrow)
)
self.wait()
self.remove(function_arrow, function)
self.play(ShowCreation(line))
self.wait()
self.play(
ShimmerIn(arg),
ShowCreation(arrow1),
ShowCreation(dot1)
)
self.wait()
self.remove(arrow1)
self.play(
FadeIn(grid),
Transform(line, curve),
Transform(dot1, dot2),
run_time = 2
)
self.wait()
self.play(
ShimmerIn(result),
ShowCreation(arrow2)
)
self.wait()
def draw_circles(self):
input_value = 0.45
input_radius = 0.04
for dot in self.input_dot, self.output_dot:
dot.center()
kwargs = {
"rate_func" : lambda t : interpolate(1, input_value, smooth(t))
}
self.play(
Homotopy(self.input_homotopy, self.input_dot, **kwargs),
Homotopy(self.output_homotopy, self.output_dot, **kwargs)
)
A, B = map(Mobject.get_center, [self.input_dot, self.output_dot])
A_text = TextMobject("A")
A_text.shift(A+2*(LEFT+UP))
A_arrow = Arrow(
A_text, self.input_dot,
color = self.input_color
)
B_text = TextMobject("B")
B_text.shift(B+2*RIGHT+DOWN)
B_arrow = Arrow(
B_text, self.output_dot,
color = self.output_color
)
tup = self.get_circles_and_points(
input_value-input_radius,
input_value+input_radius
)
input_circle, input_points, output_circle, output_points = tup
for text, arrow in [(A_text, A_arrow), (B_text, B_arrow)]:
self.play(
ShimmerIn(text),
ShowCreation(arrow)
)
self.wait()
self.remove(A_text, A_arrow, B_text, B_arrow)
self.play(ShowCreation(input_circle))
self.wait()
self.play(ShowCreation(input_points))
self.wait()
input_points_copy = input_points.copy()
self.play(
Transform(input_points_copy, output_points),
run_time = 2
)
self.wait()
self.play(ShowCreation(output_circle))
self.wait()
self.wait()
self.remove(*[
input_circle, input_points,
output_circle, input_points_copy
])
def draw_circles(self):
input_value = 0.45
input_radius = 0.04
for dot in self.input_dot, self.output_dot:
dot.center()
kwargs = {
"rate_func" : lambda t : interpolate(1, input_value, smooth(t))
}
self.play(
Homotopy(self.input_homotopy, self.input_dot, **kwargs),
Homotopy(self.output_homotopy, self.output_dot, **kwargs)
)
A, B = map(Mobject.get_center, [self.input_dot, self.output_dot])
A_text = TextMobject("A")
A_text.shift(A+2*(LEFT+UP))
A_arrow = Arrow(
A_text, self.input_dot,
color = self.input_color
)
B_text = TextMobject("B")
B_text.shift(B+2*RIGHT+DOWN)
B_arrow = Arrow(
B_text, self.output_dot,
color = self.output_color
)
tup = self.get_circles_and_points(
input_value-input_radius,
input_value+input_radius
)
input_circle, input_points, output_circle, output_points = tup
for text, arrow in [(A_text, A_arrow), (B_text, B_arrow)]:
self.play(
ShimmerIn(text),
ShowCreation(arrow)
)
self.dither()
self.remove(A_text, A_arrow, B_text, B_arrow)
self.play(ShowCreation(input_circle))
self.dither()
self.play(ShowCreation(input_points))
self.dither()
input_points_copy = input_points.copy()
self.play(
Transform(input_points_copy, output_points),
run_time = 2
)
self.dither()
self.play(ShowCreation(output_circle))
self.dither()
self.dither()
self.remove(*[
input_circle, input_points,
output_circle, input_points_copy
])
def construct(self, order):
if order == 2:
result_tex = "(0.125, 0.75)"
elif order == 3:
result_tex = "(0.0758, 0.6875)"
phc, arg, result = TexMobject([
"\\text{PHC}_%d"%order,
"(0.3)",
"= %s"%result_tex
]).to_edge(UP).split()
function = TextMobject("Function", size = "\\normal")
function.shift(phc.get_center()+DOWN+2*LEFT)
function_arrow = Arrow(function, phc)
line = Line(5*LEFT, 5*RIGHT)
curve = HilbertCurve(order = order)
line.match_colors(curve)
grid = Grid(2**order, 2**order)
grid.fade()
for mob in curve, grid:
mob.scale(0.7)
index = int(0.3*line.get_num_points())
dot1 = Dot(line.points[index])
arrow1 = Arrow(arg, dot1, buff = 0.1)
dot2 = Dot(curve.points[index])
arrow2 = Arrow(result.get_bottom(), dot2, buff = 0.1)
self.add(phc)
self.play(
ShimmerIn(function),
ShowCreation(function_arrow)
)
self.dither()
self.remove(function_arrow, function)
self.play(ShowCreation(line))
self.dither()
self.play(
ShimmerIn(arg),
ShowCreation(arrow1),
ShowCreation(dot1)
)
self.dither()
self.remove(arrow1)
self.play(
FadeIn(grid),
Transform(line, curve),
Transform(dot1, dot2),
run_time = 2
)
self.dither()
self.play(
ShimmerIn(result),
ShowCreation(arrow2)
)
self.dither()
def show_change_side_by_side(self):
seed = TextMobject("Seed")
seed.shift(3 * LEFT + 2 * DOWN)
fractal = TextMobject("Fractal")
fractal.shift(3 * RIGHT + 2 * DOWN)
words = map(TextMobject, [
"A sharper angle results in a richer curve",
"A more obtuse angle gives a sparser curve",
"And as the angle approaches 0\\dots",
"We have a new space-filling curve."
])
for text in words:
text.to_edge(UP)
sharper, duller, space_filling = [
CurveClass(order=1).shift(3 * LEFT)
for CurveClass in SharperKoch, DullerKoch, SpaceFillingKoch
]
shaper_f, duller_f, space_filling_f = [
CurveClass(order=self.max_order).shift(3 * RIGHT)
for CurveClass in SharperKoch, DullerKoch, SpaceFillingKoch
]
self.add(words[0])
left_curve = SharperKoch(order=1)
right_curve = SharperKoch(order=1)
self.play(
Transform(left_curve, sharper),
ApplyMethod(right_curve.shift, 3 * RIGHT),
)
self.play(
Transform(right_curve,
SharperKoch(order=2).shift(3 * RIGHT)), ShimmerIn(seed),
ShimmerIn(fractal))
for order in range(3, self.max_order):
self.play(
Transform(right_curve,
SharperKoch(order=order).shift(3 * RIGHT)))
self.remove(words[0])
self.add(words[1])
kwargs = {
"run_time": 4,
}
self.play(Transform(left_curve, duller, **kwargs),
Transform(right_curve, duller_f, **kwargs))
self.wait()
kwargs["run_time"] = 7
kwargs["rate_func"] = None
self.remove(words[1])
self.add(words[2])
self.play(Transform(left_curve, space_filling, **kwargs),
Transform(right_curve, space_filling_f, **kwargs))
self.remove(words[2])
self.add(words[3])
self.wait()
def construct(self):
all_points = TextMobject("$f$ is continuous at every input point")
continuous = TextMobject("$f$ is continuous")
all_points.shift(UP)
continuous.shift(DOWN)
arrow = Arrow(all_points, continuous)
self.play(ShimmerIn(all_points))
self.play(ShowCreation(arrow))
self.play(ShimmerIn(continuous))
self.dither()
def construct(self):
all_points = TextMobject("$f$ is continuous at every input point")
continuous = TextMobject("$f$ is continuous")
all_points.shift(UP)
continuous.shift(DOWN)
arrow = Arrow(all_points, continuous)
self.play(ShimmerIn(all_points))
self.play(ShowCreation(arrow))
self.play(ShimmerIn(continuous))
self.wait()
def construct(self):
freq_line = get_freq_line()
self.add(freq_line)
self.dither()
for tex, vect in zip(["20 Hz", "20{,}000 Hz"], [LEFT, RIGHT]):
tex_mob = TextMobject(tex)
tex_mob.to_edge(vect)
tex_mob.shift(UP)
arrow = Arrow(tex_mob, freq_line.get_edge_center(vect))
self.play(ShimmerIn(tex_mob), ShowCreation(arrow))
self.dither()
def construct(self):
top_words = TextMobject("Different pixel-frequency association")
bottom_words = TextMobject("Need to relearn sight-via-sound")
top_words.shift(UP)
bottom_words.shift(DOWN)
arrow = Arrow(top_words, bottom_words)
self.play(ShimmerIn(top_words))
self.dither()
self.play(ShowCreation(arrow))
self.play(ShimmerIn(bottom_words))
self.dither()
def solve_energy(self):
loss_in_potential = TextMobject("Loss in potential: ")
loss_in_potential.shift(2*UP)
potential = TexMobject("m g y".split())
potential.next_to(loss_in_potential)
kinetic = TexMobject([
"\\dfrac{1}{2}","m","v","^2","="
])
kinetic.next_to(potential, LEFT)
nudge = 0.1*UP
kinetic.shift(nudge)
loss_in_potential.shift(nudge)
ms = Mobject(kinetic.split()[1], potential.split()[0])
two = TexMobject("2")
two.shift(ms.split()[1].get_center())
half = kinetic.split()[0]
sqrt = TexMobject("\\sqrt{\\phantom{2mg}}")
sqrt.shift(potential.get_center())
nudge = 0.2*LEFT
sqrt.shift(nudge)
squared = kinetic.split()[3]
equals = kinetic.split()[-1]
new_eq = equals.copy().next_to(kinetic.split()[2])
self.play(
Transform(
Point(loss_in_potential.get_left()),
loss_in_potential
),
*map(GrowFromCenter, potential.split())
)
self.dither(2)
self.play(
FadeOut(loss_in_potential),
GrowFromCenter(kinetic)
)
self.dither(2)
self.play(ApplyMethod(ms.shift, 5*UP))
self.dither()
self.play(Transform(
half, two,
path_func = counterclockwise_path()
))
self.dither()
self.play(
Transform(
squared, sqrt,
path_func = clockwise_path()
),
Transform(equals, new_eq)
)
self.dither(2)
def construct(self):
snells = TextMobject("Snell's")
snells.shift(-snells.get_left())
snells.to_edge(UP)
for vect in [RIGHT, RIGHT, LEFT, DOWN, DOWN, DOWN]:
snells.add(snells.copy().next_to(snells, vect))
snells.ingest_submobjects()
snells.show()
condensed = TextMobject("condensed")
self.add(snells)
self.dither()
self.play(DelayByOrder(Transform(snells, condensed, run_time=2)))
self.dither()
def construct(self):
horiz_radius = 5
vert_radius = 3
vert_axis = NumberLine(numerical_radius=vert_radius)
vert_axis.rotate(np.pi / 2)
vert_axis.shift(horiz_radius * LEFT)
horiz_axis = NumberLine(numerical_radius=5,
numbers_with_elongated_ticks=[])
axes = Mobject(horiz_axis, vert_axis)
graph = FunctionGraph(lambda x: 0.4 * (x - 2) * (x + 2) + 3,
x_min=-2,
x_max=2,
density=3 * DEFAULT_POINT_DENSITY_1D)
graph.stretch_to_fit_width(2 * horiz_radius)
graph.highlight(YELLOW)
min_point = Dot(graph.get_bottom())
nature_finds = TextMobject("Nature finds this point")
nature_finds.scale(0.5)
nature_finds.highlight(GREEN)
nature_finds.shift(2 * RIGHT + 3 * UP)
arrow = Arrow(nature_finds.get_bottom(), min_point, color=GREEN)
side_words_start = TextMobject("Parameter describing")
top_words, last_side_words = [
map(TextMobject, pair)
for pair in [("Light's travel time",
"Potential energy"), ("path", "mechanical state")]
]
for word in top_words + last_side_words + [side_words_start]:
word.scale(0.7)
side_words_start.next_to(horiz_axis, DOWN)
side_words_start.to_edge(RIGHT)
for words in top_words:
words.next_to(vert_axis, UP)
words.to_edge(LEFT)
for words in last_side_words:
words.next_to(side_words_start, DOWN)
for words in top_words[1], last_side_words[1]:
words.highlight(RED)
self.add(axes, top_words[0], side_words_start, last_side_words[0])
self.play(ShowCreation(graph))
self.play(ShimmerIn(nature_finds), ShowCreation(arrow),
ShowCreation(min_point))
self.dither()
self.play(FadeOut(top_words[0]), FadeOut(last_side_words[0]),
GrowFromCenter(top_words[1]),
GrowFromCenter(last_side_words[1]))
self.dither(3)
def label_spaces(self):
input_space = TextMobject("Input Space")
input_space.to_edge(UP)
input_space.shift(LEFT * SPACE_WIDTH / 2)
output_space = TextMobject("Output Space")
output_space.to_edge(UP)
output_space.shift(RIGHT * SPACE_WIDTH / 2)
line = Line(UP * SPACE_HEIGHT, DOWN * SPACE_HEIGHT, color=WHITE)
self.play(
ShimmerIn(input_space),
ShimmerIn(output_space),
ShowCreation(line),
ShowCreation(self.interval),
)
self.dither()
def construct(self):
freq_line = get_freq_line()
self.add(freq_line)
self.dither()
for tex, vect in zip(["20 Hz", "20{,}000 Hz"], [LEFT, RIGHT]):
tex_mob = TextMobject(tex)
tex_mob.to_edge(vect)
tex_mob.shift(UP)
arrow = Arrow(tex_mob, freq_line.get_edge_center(vect))
self.play(
ShimmerIn(tex_mob),
ShowCreation(arrow)
)
self.dither()
def construct(self):
r_range = np.arange(0.5, 2, 0.25)
cycloids = Mobject(*[
Cycloid(radius = r, end_theta=2*np.pi)
for r in r_range
])
lower_left = 2*DOWN+6*LEFT
lines = Mobject(*[
Line(
lower_left,
lower_left+5*r*np.cos(np.arctan(r))*RIGHT+2*r*np.sin(np.arctan(r))*UP
)
for r in r_range
])
nl = NumberLine(numbers_with_elongated_ticks = [])
x_axis = nl.copy().shift(3*UP)
y_axis = nl.copy().rotate(np.pi/2).shift(6*LEFT)
t_axis = nl.copy().shift(2*DOWN)
x_label = TexMobject("x")
x_label.next_to(x_axis, DOWN)
x_label.to_edge(RIGHT)
y_label = TexMobject("y")
y_label.next_to(y_axis, RIGHT)
y_label.shift(2*DOWN)
t_label = TexMobject("t")
t_label.next_to(t_axis, UP)
t_label.to_edge(RIGHT)
theta_label = TexMobject("\\theta")
theta_label.next_to(y_axis, RIGHT)
theta_label.to_edge(UP)
words = TextMobject("Boundary conditions?")
words.next_to(lines, RIGHT)
words.shift(2*UP)
self.play(ShowCreation(x_axis), ShimmerIn(x_label))
self.play(ShowCreation(y_axis), ShimmerIn(y_label))
self.play(ShowCreation(cycloids))
self.dither()
self.play(
Transform(cycloids, lines),
Transform(x_axis, t_axis),
Transform(x_label, t_label),
Transform(y_label, theta_label),
run_time = 2
)
self.dither()
self.play(ShimmerIn(words))
self.dither()
def construct(self):
snells = TextMobject("Snell's")
snells.shift(-snells.get_left())
snells.to_edge(UP)
for vect in [RIGHT, RIGHT, LEFT, DOWN, DOWN, DOWN]:
snells.add(snells.copy().next_to(snells, vect))
snells.ingest_submobjects()
snells.show()
condensed = TextMobject("condensed")
self.add(snells)
self.dither()
self.play(DelayByOrder(
Transform(snells, condensed, run_time = 2)
))
self.dither()
def construct(self):
start_words = TextMobject([
"``", "Space Filling", "Curve ''",
]).to_edge(TOP, buff = 0.25)
quote, space_filling, curve_quote = start_words.copy().split()
curve_quote.shift(
space_filling.get_left()-\
curve_quote.get_left()
)
space_filling = Point(space_filling.get_center())
end_words = Mobject(*[
quote, space_filling, curve_quote
]).center().to_edge(TOP, buff = 0.25)
space_filling_fractal = TextMobject("""
``Space Filling Fractal''
""").to_edge(UP)
curve = HilbertCurve(order = 2).shift(DOWN)
fine_curve = HilbertCurve(order = 8)
fine_curve.replace(curve)
dots = Mobject(*[
Dot(
curve.points[n*curve.get_num_points()/15],
color = YELLOW_C
)
for n in range(1, 15)
if n not in [4, 11]
])
start_words.shift(2*(UP+LEFT))
self.play(
ApplyMethod(start_words.shift, 2*(DOWN+RIGHT))
)
self.dither()
self.play(Transform(start_words, end_words))
self.dither()
self.play(ShowCreation(curve))
self.dither()
self.play(ShowCreation(
dots,
run_time = 3,
))
self.dither()
self.clear()
self.play(ShowCreation(fine_curve, run_time = 5))
self.dither()
self.play(ShimmerIn(space_filling_fractal))
self.dither()
def construct(self):
start_words = TextMobject([
"``", "Space Filling", "Curve ''",
]).to_edge(TOP, buff = 0.25)
quote, space_filling, curve_quote = start_words.copy().split()
curve_quote.shift(
space_filling.get_left()-\
curve_quote.get_left()
)
space_filling = Point(space_filling.get_center())
end_words = Mobject(*[
quote, space_filling, curve_quote
]).center().to_edge(TOP, buff = 0.25)
space_filling_fractal = TextMobject("""
``Space Filling Fractal''
""").to_edge(UP)
curve = HilbertCurve(order = 2).shift(DOWN)
fine_curve = HilbertCurve(order = 8)
fine_curve.replace(curve)
dots = Mobject(*[
Dot(
curve.points[n*curve.get_num_points()/15],
color = YELLOW_C
)
for n in range(1, 15)
if n not in [4, 11]
])
start_words.shift(2*(UP+LEFT))
self.play(
ApplyMethod(start_words.shift, 2*(DOWN+RIGHT))
)
self.wait()
self.play(Transform(start_words, end_words))
self.wait()
self.play(ShowCreation(curve))
self.wait()
self.play(ShowCreation(
dots,
run_time = 3,
))
self.wait()
self.clear()
self.play(ShowCreation(fine_curve, run_time = 5))
self.wait()
self.play(ShimmerIn(space_filling_fractal))
self.wait()
def vary_circle_sizes(self):
input_value = 0.45
radius = 0.04
vary_circles = VaryCircles(
self,
input_value,
radius,
run_time=5,
)
self.play(vary_circles)
self.dither()
text = TextMobject("Function is ``Continuous at A''")
text.shift(2 * UP).to_edge(LEFT)
arrow = Arrow(text, self.input_dot)
self.play(ShimmerIn(text), ShowCreation(arrow))
self.dither()
self.remove(vary_circles.mobject, text, arrow)
def construct(self):
digest_config(self, {})
## Usually shouldn't need this...
self.frame_duration = self.DEFAULT_CONFIG["frame_duration"]
##
digest_config(self, {})
circle = Circle(
density = self.circle_density,
color = self.circle_blue
)
circle.repeat(self.circle_repeats)
circle.scale(self.radius)
sphere = Sphere(
density = self.sphere_density,
color = self.sphere_blue
)
sphere.scale(self.radius)
sphere.rotate(-np.pi / 7, [1, 0, 0])
sphere.rotate(-np.pi / 7)
iris = Mobject()
iris.interpolate(
circle, sphere,
self.interpolation_factor
)
for mob, color in [(iris, self.sphere_brown), (circle, self.circle_brown)]:
mob.highlight(color, lambda (x, y, z) : x < 0 and y > 0)
mob.highlight(
"black",
lambda point: np.linalg.norm(point) < \
self.inner_radius_ratio*self.radius
)
name = TextMobject("3Blue1Brown").center()
name.highlight("grey")
name.shift(2*DOWN)
self.play(Transform(
circle, iris,
run_time = self.run_time
))
self.frames = drag_pixels(self.frames)
self.save_image(IMAGE_DIR)
self.show_frame()
self.add(name)
self.dither()
print "Dragging pixels..."
def vary_circle_sizes(self):
input_value = 0.45
radius = 0.04
vary_circles = VaryCircles(
self, input_value, radius,
run_time = 5,
)
self.play(vary_circles)
self.dither()
text = TextMobject("Function is ``Continuous at A''")
text.shift(2*UP).to_edge(LEFT)
arrow = Arrow(text, self.input_dot)
self.play(
ShimmerIn(text),
ShowCreation(arrow)
)
self.dither()
self.remove(vary_circles.mobject, text, arrow)
def label_spaces(self):
input_space = TextMobject("Input Space")
input_space.to_edge(UP)
input_space.shift(LEFT*SPACE_WIDTH/2)
output_space = TextMobject("Output Space")
output_space.to_edge(UP)
output_space.shift(RIGHT*SPACE_WIDTH/2)
line = Line(
UP*SPACE_HEIGHT, DOWN*SPACE_HEIGHT,
color = WHITE
)
self.play(
ShimmerIn(input_space),
ShimmerIn(output_space),
ShowCreation(line),
ShowCreation(self.interval),
)
self.dither()
def snells_law_at_every_point(self, cycloid, chopped_cycloid):
square = Square(side_length=0.2, color=WHITE)
words = TextMobject(["Snell's law ", "everywhere"])
snells, rest = words.split()
colon = TextMobject(":")
words.next_to(square)
words.shift(0.3 * UP)
combo = Mobject(square, words)
combo.get_center = lambda: square.get_center()
new_snells = snells.copy().center().to_edge(UP, buff=1.5)
colon.next_to(new_snells)
colon.shift(0.05 * DOWN)
self.play(MoveAlongPath(combo, cycloid, run_time=5))
self.play(MoveAlongPath(combo, chopped_cycloid, run_time=4))
dot = Dot(combo.get_center())
self.play(Transform(square, dot))
self.play(Transform(snells, new_snells), Transform(rest, colon))
self.dither()
return colon
def construct(self):
logo = ImageMobject("LogoGeneration", invert=False)
name_mob = TextMobject("3Blue1Brown").center()
name_mob.highlight("grey")
name_mob.shift(2 * DOWN)
self.add(name_mob, logo)
new_text = TextMobject(["with ", "Steven Strogatz"])
new_text.next_to(name_mob, DOWN)
self.play(*[ShimmerIn(part) for part in new_text.split()])
self.dither()
with_word, steve = new_text.split()
steve_copy = steve.copy().center().to_edge(UP)
# logo.sort_points(lambda p : -np.linalg.norm(p))
sort_by_color(logo)
self.play(Transform(steve, steve_copy),
DelayByOrder(Transform(logo, Point())),
FadeOut(with_word),
FadeOut(name_mob),
run_time=3)
def equivalence(self, left_mob, arrow, right_mob):
self.clear()
self.add(left_mob, arrow, right_mob)
words = TextMobject("is equivalent to")
words.shift(0.25 * LEFT)
words.highlight(BLUE)
new_left = left_mob.copy().shift(RIGHT)
new_right = right_mob.copy()
new_right.shift(
(words.get_right()[0]-\
right_mob.get_left()[0]+\
0.5
)*RIGHT
)
for mob in arrow, words:
mob.sort_points(np.linalg.norm)
self.play(ApplyMethod(left_mob.shift, RIGHT), Transform(arrow, words),
ApplyMethod(right_mob.to_edge, RIGHT))
self.wait()
def construct(self):
glass = Region(lambda x, y : y < 0, color = BLUE_E)
self.generate_start_and_end_points()
straight = Line(self.start_point, self.end_point)
slow = TextMobject("Slow")
slow.rotate(np.arctan(straight.get_slope()))
slow.shift(straight.points[int(0.7*straight.get_num_points())])
slow.shift(0.5*DOWN)
too_long = TextMobject("Too long")
too_long.shift(UP)
air = TextMobject("Air").shift(2*UP)
water = TextMobject("Water").shift(2*DOWN)
self.add(glass)
self.play(GrowFromCenter(air))
self.play(GrowFromCenter(water))
self.dither()
self.remove(air, water)
ShowMultiplePathsScene.construct(self)
self.play(
Transform(self.path, straight)
)
self.dither()
self.play(GrowFromCenter(slow))
self.dither()
self.remove(slow)
self.leftmost.ingest_submobjects()
self.play(Transform(self.path, self.leftmost, run_time = 3))
self.dither()
self.play(ShimmerIn(too_long))
self.dither()
def construct(self):
glass = Region(lambda x, y : y < 0, color = BLUE_E)
self.generate_start_and_end_points()
straight = Line(self.start_point, self.end_point)
slow = TextMobject("Slow")
slow.rotate(np.arctan(straight.get_slope()))
slow.shift(straight.points[int(0.7*straight.get_num_points())])
slow.shift(0.5*DOWN)
too_long = TextMobject("Too long")
too_long.shift(UP)
air = TextMobject("Air").shift(2*UP)
water = TextMobject("Water").shift(2*DOWN)
self.add(glass)
self.play(GrowFromCenter(air))
self.play(GrowFromCenter(water))
self.wait()
self.remove(air, water)
ShowMultiplePathsScene.construct(self)
self.play(
Transform(self.path, straight)
)
self.wait()
self.play(GrowFromCenter(slow))
self.wait()
self.remove(slow)
self.leftmost.ingest_submobjects()
self.play(Transform(self.path, self.leftmost, run_time = 3))
self.wait()
self.play(ShimmerIn(too_long))
self.wait()
def discontinuous_point(self):
point_description = TextMobject("Point where the function jumps")
point_description.shift(3 * RIGHT)
discontinuous_at_A = TextMobject("``Discontinuous at A''",
size="\\Large")
discontinuous_at_A.shift(2 * UP).to_edge(LEFT)
text = TextMobject("""
Circle around ouput \\\\
points can never \\\\
be smaller than \\\\
the jump
""")
text.scale(0.75)
text.shift(3.5 * RIGHT)
input_value = 0.5
input_radius = 0.04
vary_circles = VaryCircles(
self,
input_value,
input_radius,
run_time=5,
)
for dot in self.input_dot, self.output_dot:
dot.center()
kwargs = {
"rate_func": lambda t: interpolate(0.45, input_value, smooth(t))
}
self.play(Homotopy(self.input_homotopy, self.input_dot, **kwargs),
Homotopy(self.output_homotopy, self.output_dot, **kwargs))
discontinuous_arrow = Arrow(discontinuous_at_A, self.input_dot)
arrow = Arrow(point_description,
self.output_dot,
buff=0.05,
color=self.output_color)
self.play(ShimmerIn(point_description), ShowCreation(arrow))
self.dither()
self.remove(point_description, arrow)
tup = self.get_circles_and_points(input_value - input_radius,
input_value + input_radius)
input_circle, input_points, output_circle, output_points = tup
input_points_copy = input_points.copy()
self.play(ShowCreation(input_circle))
self.play(ShowCreation(input_points))
self.play(Transform(input_points_copy, output_points), run_time=2)
self.play(ShowCreation(output_circle))
self.dither()
self.play(ShimmerIn(text))
self.remove(input_circle, input_points, output_circle,
input_points_copy)
self.play(vary_circles)
self.dither()
self.play(ShimmerIn(discontinuous_at_A),
ShowCreation(discontinuous_arrow))
self.dither(3)
self.remove(vary_circles.mobject, discontinuous_at_A,
discontinuous_arrow)
def equivalence(self, left_mob, arrow, right_mob):
self.clear()
self.add(left_mob, arrow, right_mob)
words = TextMobject("is equivalent to")
words.shift(0.25*LEFT)
words.highlight(BLUE)
new_left = left_mob.copy().shift(RIGHT)
new_right = right_mob.copy()
new_right.shift(
(words.get_right()[0]-\
right_mob.get_left()[0]+\
0.5
)*RIGHT
)
for mob in arrow, words:
mob.sort_points(np.linalg.norm)
self.play(
ApplyMethod(left_mob.shift, RIGHT),
Transform(arrow, words),
ApplyMethod(right_mob.to_edge, RIGHT)
)
self.dither()
def construct(self):
self.add_cycloid_end_points()
start = self.point_a.get_center()
end = self.point_b.get_center()
angle = 2*np.pi/3
path = Arc(angle, radius = 3)
path.gradient_highlight(RED_D, WHITE)
radius = Line(ORIGIN, path.points[0])
randy = Randolph()
randy.scale(RANDY_SCALE_VAL)
randy.shift(-randy.get_bottom())
randy_copy = randy.copy()
words = TextMobject("Circular paths are good, \\\\ but still not the best")
words.shift(UP)
self.play(
ShowCreation(path),
ApplyMethod(
radius.rotate,
angle,
path_func = path_along_arc(angle)
)
)
self.play(FadeOut(radius))
self.play(
ApplyMethod(
path.position_endpoints_on, start, end,
path_func = path_along_arc(-angle)
),
run_time = 3
)
self.adjust_mobject_to_index(randy_copy, 1, path.points)
self.play(FadeIn(randy_copy))
self.remove(randy_copy)
self.slide(randy, path)
self.play(ShimmerIn(words))
self.dither()
def construct(self):
glass = Region(lambda x, y : y < 0, color = BLUE_E)
kwargs = {
"density" : self.zoom_factor*DEFAULT_POINT_DENSITY_1D
}
top_line = Line(SPACE_HEIGHT*UP+2*LEFT, ORIGIN, **kwargs)
extension = Line(ORIGIN, SPACE_HEIGHT*DOWN+2*RIGHT, **kwargs)
bottom_line = Line(ORIGIN, SPACE_HEIGHT*DOWN+RIGHT, **kwargs)
path1 = Mobject(top_line, extension)
path2 = Mobject(top_line, bottom_line)
for mob in path1, path2:
mob.ingest_submobjects()
extension.highlight(RED)
theta1 = np.arctan(bottom_line.get_slope())
theta2 = np.arctan(extension.get_slope())
arc = Arc(theta2-theta1, start_angle = theta1, radius = 2)
question_mark = TextMobject("$\\theta$?")
question_mark.shift(arc.get_center()+0.5*DOWN+0.25*RIGHT)
wave = self.wavify(path2)
wave.highlight(YELLOW)
wave.scale(0.5)
self.add(glass)
self.play(ShowCreation(path1))
self.play(Transform(path1, path2))
self.dither()
# self.activate_zooming()
self.dither()
self.play(ShowPassingFlash(
wave, run_time = 3, rate_func = None
))
self.dither()
self.play(ShowCreation(extension))
self.play(
ShowCreation(arc),
ShimmerIn(question_mark)
)
def construct(self):
clock = Circle(radius = 2, color = WHITE)
clock.add(Dot(ORIGIN))
ticks = Mobject(*[
Line(1.8*vect, 2*vect, color = GREY)
for vect in compass_directions(12)
])
clock.add(ticks)
hour_hand = Line(ORIGIN, UP)
minute_hand = Line(ORIGIN, 1.5*UP)
clock.add(hour_hand, minute_hand)
clock.to_corner(UP+RIGHT)
hour_hand.get_center = lambda : clock.get_center()
minute_hand.get_center = lambda : clock.get_center()
solution = ImageMobject(
"Newton_brachistochrone_solution2",
use_cache = False
)
solution.stroke_width = 3
solution.highlight(GREY)
solution.scale_to_fit_width(5)
solution.to_corner(UP+RIGHT)
newton = ImageMobject("Old_Newton", invert = False)
newton.scale(0.8)
phil_trans = TextMobject("Philosophical Transactions")
rect = Rectangle(height = 6, width = 4.5, color = WHITE)
rect.to_corner(UP+RIGHT)
rect.shift(DOWN)
phil_trans.scale_to_fit_width(0.8*rect.get_width())
phil_trans.next_to(Point(rect.get_top()), DOWN)
new_solution = solution.copy()
new_solution.scale_to_fit_width(phil_trans.get_width())
new_solution.next_to(phil_trans, DOWN, buff = 1)
not_newton = TextMobject("-Totally not by Newton")
not_newton.scale_to_fit_width(2.5)
not_newton.next_to(new_solution, DOWN, aligned_edge = RIGHT)
phil_trans.add(rect)
newton_complaint = TextMobject([
"``I do not love to be",
" \\emph{dunned} ",
"and teased by foreigners''"
], size = "\\small")
newton_complaint.to_edge(UP, buff = 0.2)
dunned = newton_complaint.split()[1]
dunned.highlight()
dunned_def = TextMobject("(old timey term for making \\\\ demands on someone)")
dunned_def.scale(0.7)
dunned_def.next_to(phil_trans, LEFT)
dunned_def.shift(2*UP)
dunned_arrow = Arrow(dunned_def, dunned)
johann = ImageMobject("Johann_Bernoulli2", invert = False)
johann.scale(0.4)
johann.to_edge(LEFT)
johann.shift(DOWN)
johann_quote = TextMobject("``I recognize the lion by his claw''")
johann_quote.next_to(johann, UP, aligned_edge = LEFT)
self.play(ApplyMethod(newton.to_edge, LEFT))
self.play(ShowCreation(clock))
kwargs = {
"axis" : OUT,
"rate_func" : smooth
}
self.play(
Rotating(hour_hand, radians = -2*np.pi, **kwargs),
Rotating(minute_hand, radians = -12*2*np.pi, **kwargs),
run_time = 5
)
self.dither()
self.clear()
self.add(newton)
clock.ingest_submobjects()
self.play(Transform(clock, solution))
self.remove(clock)
self.add(solution)
self.dither()
self.play(
FadeIn(phil_trans),
Transform(solution, new_solution)
)
self.dither()
self.play(ShimmerIn(not_newton))
phil_trans.add(solution, not_newton)
self.dither()
self.play(*map(ShimmerIn, newton_complaint.split()))
self.dither()
self.play(
ShimmerIn(dunned_def),
ShowCreation(dunned_arrow)
)
self.dither()
self.remove(dunned_def, dunned_arrow)
self.play(FadeOut(newton_complaint))
self.remove(newton_complaint)
self.play(
FadeOut(newton),
GrowFromCenter(johann)
)
self.remove(newton)
self.dither()
self.play(ShimmerIn(johann_quote))
self.dither()
def construct(self):
horiz_radius = 5
vert_radius = 3
vert_axis = NumberLine(numerical_radius = vert_radius)
vert_axis.rotate(np.pi/2)
vert_axis.shift(horiz_radius*LEFT)
horiz_axis = NumberLine(
numerical_radius = 5,
numbers_with_elongated_ticks = []
)
axes = Mobject(horiz_axis, vert_axis)
graph = FunctionGraph(
lambda x : 0.4*(x-2)*(x+2)+3,
x_min = -2,
x_max = 2,
density = 3*DEFAULT_POINT_DENSITY_1D
)
graph.stretch_to_fit_width(2*horiz_radius)
graph.highlight(YELLOW)
min_point = Dot(graph.get_bottom())
nature_finds = TextMobject("Nature finds this point")
nature_finds.scale(0.5)
nature_finds.highlight(GREEN)
nature_finds.shift(2*RIGHT+3*UP)
arrow = Arrow(
nature_finds.get_bottom(), min_point,
color = GREEN
)
side_words_start = TextMobject("Parameter describing")
top_words, last_side_words = [
map(TextMobject, pair)
for pair in [
("Light's travel time", "Potential energy"),
("path", "mechanical state")
]
]
for word in top_words + last_side_words + [side_words_start]:
word.scale(0.7)
side_words_start.next_to(horiz_axis, DOWN)
side_words_start.to_edge(RIGHT)
for words in top_words:
words.next_to(vert_axis, UP)
words.to_edge(LEFT)
for words in last_side_words:
words.next_to(side_words_start, DOWN)
for words in top_words[1], last_side_words[1]:
words.highlight(RED)
self.add(
axes, top_words[0], side_words_start,
last_side_words[0]
)
self.play(ShowCreation(graph))
self.play(
ShimmerIn(nature_finds),
ShowCreation(arrow),
ShowCreation(min_point)
)
self.dither()
self.play(
FadeOut(top_words[0]),
FadeOut(last_side_words[0]),
GrowFromCenter(top_words[1]),
GrowFromCenter(last_side_words[1])
)
self.dither(3)
def construct(self):
clock = Circle(radius=2, color=WHITE)
clock.add(Dot(ORIGIN))
ticks = Mobject(*[
Line(1.8 * vect, 2 * vect, color=GREY)
for vect in compass_directions(12)
])
clock.add(ticks)
hour_hand = Line(ORIGIN, UP)
minute_hand = Line(ORIGIN, 1.5 * UP)
clock.add(hour_hand, minute_hand)
clock.to_corner(UP + RIGHT)
hour_hand.get_center = lambda: clock.get_center()
minute_hand.get_center = lambda: clock.get_center()
solution = ImageMobject("Newton_brachistochrone_solution2",
use_cache=False)
solution.stroke_width = 3
solution.highlight(GREY)
solution.scale_to_fit_width(5)
solution.to_corner(UP + RIGHT)
newton = ImageMobject("Old_Newton", invert=False)
newton.scale(0.8)
phil_trans = TextMobject("Philosophical Transactions")
rect = Rectangle(height=6, width=4.5, color=WHITE)
rect.to_corner(UP + RIGHT)
rect.shift(DOWN)
phil_trans.scale_to_fit_width(0.8 * rect.get_width())
phil_trans.next_to(Point(rect.get_top()), DOWN)
new_solution = solution.copy()
new_solution.scale_to_fit_width(phil_trans.get_width())
new_solution.next_to(phil_trans, DOWN, buff=1)
not_newton = TextMobject("-Totally not by Newton")
not_newton.scale_to_fit_width(2.5)
not_newton.next_to(new_solution, DOWN, aligned_edge=RIGHT)
phil_trans.add(rect)
newton_complaint = TextMobject([
"``I do not love to be", " \\emph{dunned} ",
"and teased by foreigners''"
],
size="\\small")
newton_complaint.to_edge(UP, buff=0.2)
dunned = newton_complaint.split()[1]
dunned.highlight()
dunned_def = TextMobject(
"(old timey term for making \\\\ demands on someone)")
dunned_def.scale(0.7)
dunned_def.next_to(phil_trans, LEFT)
dunned_def.shift(2 * UP)
dunned_arrow = Arrow(dunned_def, dunned)
johann = ImageMobject("Johann_Bernoulli2", invert=False)
johann.scale(0.4)
johann.to_edge(LEFT)
johann.shift(DOWN)
johann_quote = TextMobject("``I recognize the lion by his claw''")
johann_quote.next_to(johann, UP, aligned_edge=LEFT)
self.play(ApplyMethod(newton.to_edge, LEFT))
self.play(ShowCreation(clock))
kwargs = {"axis": OUT, "rate_func": smooth}
self.play(Rotating(hour_hand, radians=-2 * np.pi, **kwargs),
Rotating(minute_hand, radians=-12 * 2 * np.pi, **kwargs),
run_time=5)
self.wait()
self.clear()
self.add(newton)
clock.ingest_submobjects()
self.play(Transform(clock, solution))
self.remove(clock)
self.add(solution)
self.wait()
self.play(FadeIn(phil_trans), Transform(solution, new_solution))
self.wait()
self.play(ShimmerIn(not_newton))
phil_trans.add(solution, not_newton)
self.wait()
self.play(*map(ShimmerIn, newton_complaint.split()))
self.wait()
self.play(ShimmerIn(dunned_def), ShowCreation(dunned_arrow))
self.wait()
self.remove(dunned_def, dunned_arrow)
self.play(FadeOut(newton_complaint))
self.remove(newton_complaint)
self.play(FadeOut(newton), GrowFromCenter(johann))
self.remove(newton)
self.wait()
self.play(ShimmerIn(johann_quote))
self.wait()
def construct(self):
word = TextMobject(["Bra", "chis", "to", "chrone"])
original_word = word.copy()
dots = []
for part in word.split():
if dots:
part.next_to(dots[-1], buff=0.06)
dot = TexMobject("\\cdot")
dot.next_to(part, buff=0.06)
dots.append(dot)
dots = Mobject(*dots[:-1])
dots.shift(0.1 * DOWN)
Mobject(word, dots).center()
overbrace1 = Brace(Mobject(*word.split()[:-1]), UP)
overbrace2 = Brace(word.split()[-1], UP)
shortest = TextMobject("Shortest")
shortest.next_to(overbrace1, UP)
shortest.highlight(YELLOW)
time = TextMobject("Time")
time.next_to(overbrace2, UP)
time.highlight(YELLOW)
chrono_example = TextMobject("""
As in ``Chronological'' \\\\
or ``Synchronize''
""")
chrono_example.scale(0.5)
chrono_example.to_edge(RIGHT)
chrono_example.shift(2 * UP)
chrono_example.highlight(BLUE_D)
chrono_arrow = Arrow(word.get_right(),
chrono_example.get_bottom(),
color=BLUE_D)
brachy_example = TextMobject("As in . . . brachydactyly?")
brachy_example.scale(0.5)
brachy_example.to_edge(LEFT)
brachy_example.shift(2 * DOWN)
brachy_example.highlight(GREEN)
brachy_arrow = Arrow(word.get_left(),
brachy_example.get_top(),
color=GREEN)
pronunciation = TextMobject(
["/br", "e", "kist", "e", "kr$\\bar{o}$n/"])
pronunciation.split()[1].rotate_in_place(np.pi)
pronunciation.split()[3].rotate_in_place(np.pi)
pronunciation.scale(0.7)
pronunciation.shift(DOWN)
latin = TextMobject(list("Latin"))
greek = TextMobject(list("Greek"))
for mob in latin, greek:
mob.to_edge(LEFT)
question_mark = TextMobject("?").next_to(greek, buff=0.1)
stars = Stars().highlight(BLACK)
stars.scale(0.5).shift(question_mark.get_center())
self.play(Transform(original_word, word), ShowCreation(dots))
self.play(ShimmerIn(pronunciation))
self.dither()
self.play(GrowFromCenter(overbrace1), GrowFromCenter(overbrace2))
self.dither()
self.play(ShimmerIn(latin))
self.play(FadeIn(question_mark))
self.play(Transform(latin, greek, path_func=counterclockwise_path()))
self.dither()
self.play(Transform(question_mark, stars))
self.remove(stars)
self.dither()
self.play(ShimmerIn(shortest))
self.play(ShimmerIn(time))
for ex, ar in [(chrono_example, chrono_arrow),
(brachy_example, brachy_arrow)]:
self.play(ShowCreation(ar), ShimmerIn(ex))
self.dither()
def show_change_side_by_side(self):
seed = TextMobject("Seed")
seed.shift(3*LEFT+2*DOWN)
fractal = TextMobject("Fractal")
fractal.shift(3*RIGHT+2*DOWN)
words = map(TextMobject, [
"A sharper angle results in a richer curve",
"A more obtuse angle gives a sparser curve",
"And as the angle approaches 0\\dots",
"We have a new space-filling curve."
])
for text in words:
text.to_edge(UP)
sharper, duller, space_filling = [
CurveClass(order = 1).shift(3*LEFT)
for CurveClass in SharperKoch, DullerKoch, SpaceFillingKoch
]
shaper_f, duller_f, space_filling_f = [
CurveClass(order = self.max_order).shift(3*RIGHT)
for CurveClass in SharperKoch, DullerKoch, SpaceFillingKoch
]
self.add(words[0])
left_curve = SharperKoch(order = 1)
right_curve = SharperKoch(order = 1)
self.play(
Transform(left_curve, sharper),
ApplyMethod(right_curve.shift, 3*RIGHT),
)
self.play(
Transform(
right_curve,
SharperKoch(order = 2).shift(3*RIGHT)
),
ShimmerIn(seed),
ShimmerIn(fractal)
)
for order in range(3, self.max_order):
self.play(Transform(
right_curve,
SharperKoch(order = order).shift(3*RIGHT)
))
self.remove(words[0])
self.add(words[1])
kwargs = {
"run_time" : 4,
}
self.play(
Transform(left_curve, duller, **kwargs),
Transform(right_curve, duller_f, **kwargs)
)
self.dither()
kwargs["run_time"] = 7
kwargs["rate_func"] = None
self.remove(words[1])
self.add(words[2])
self.play(
Transform(left_curve, space_filling, **kwargs),
Transform(right_curve, space_filling_f, **kwargs)
)
self.remove(words[2])
self.add(words[3])
self.dither()
def discontinuous_point(self):
point_description = TextMobject(
"Point where the function jumps"
)
point_description.shift(3*RIGHT)
discontinuous_at_A = TextMobject(
"``Discontinuous at A''",
size = "\\Large"
)
discontinuous_at_A.shift(2*UP).to_edge(LEFT)
text = TextMobject("""
Circle around ouput \\\\
points can never \\\\
be smaller than \\\\
the jump
""")
text.scale(0.75)
text.shift(3.5*RIGHT)
input_value = 0.5
input_radius = 0.04
vary_circles = VaryCircles(
self, input_value, input_radius,
run_time = 5,
)
for dot in self.input_dot, self.output_dot:
dot.center()
kwargs = {
"rate_func" : lambda t : interpolate(0.45, input_value, smooth(t))
}
self.play(
Homotopy(self.input_homotopy, self.input_dot, **kwargs),
Homotopy(self.output_homotopy, self.output_dot, **kwargs)
)
discontinuous_arrow = Arrow(discontinuous_at_A, self.input_dot)
arrow = Arrow(
point_description, self.output_dot,
buff = 0.05,
color = self.output_color
)
self.play(
ShimmerIn(point_description),
ShowCreation(arrow)
)
self.dither()
self.remove(point_description, arrow)
tup = self.get_circles_and_points(
input_value-input_radius,
input_value+input_radius
)
input_circle, input_points, output_circle, output_points = tup
input_points_copy = input_points.copy()
self.play(ShowCreation(input_circle))
self.play(ShowCreation(input_points))
self.play(
Transform(input_points_copy, output_points),
run_time = 2
)
self.play(ShowCreation(output_circle))
self.dither()
self.play(ShimmerIn(text))
self.remove(input_circle, input_points, output_circle, input_points_copy)
self.play(vary_circles)
self.dither()
self.play(
ShimmerIn(discontinuous_at_A),
ShowCreation(discontinuous_arrow)
)
self.dither(3)
self.remove(vary_circles.mobject, discontinuous_at_A, discontinuous_arrow)
def construct(self):
word = TextMobject(["Bra", "chis", "to", "chrone"])
original_word = word.copy()
dots = []
for part in word.split():
if dots:
part.next_to(dots[-1], buff = 0.06)
dot = TexMobject("\\cdot")
dot.next_to(part, buff = 0.06)
dots.append(dot)
dots = Mobject(*dots[:-1])
dots.shift(0.1*DOWN)
Mobject(word, dots).center()
overbrace1 = Brace(Mobject(*word.split()[:-1]), UP)
overbrace2 = Brace(word.split()[-1], UP)
shortest = TextMobject("Shortest")
shortest.next_to(overbrace1, UP)
shortest.highlight(YELLOW)
time = TextMobject("Time")
time.next_to(overbrace2, UP)
time.highlight(YELLOW)
chrono_example = TextMobject("""
As in ``Chronological'' \\\\
or ``Synchronize''
""")
chrono_example.scale(0.5)
chrono_example.to_edge(RIGHT)
chrono_example.shift(2*UP)
chrono_example.highlight(BLUE_D)
chrono_arrow = Arrow(
word.get_right(),
chrono_example.get_bottom(),
color = BLUE_D
)
brachy_example = TextMobject("As in . . . brachydactyly?")
brachy_example.scale(0.5)
brachy_example.to_edge(LEFT)
brachy_example.shift(2*DOWN)
brachy_example.highlight(GREEN)
brachy_arrow = Arrow(
word.get_left(),
brachy_example.get_top(),
color = GREEN
)
pronunciation = TextMobject(["/br", "e", "kist","e","kr$\\bar{o}$n/"])
pronunciation.split()[1].rotate_in_place(np.pi)
pronunciation.split()[3].rotate_in_place(np.pi)
pronunciation.scale(0.7)
pronunciation.shift(DOWN)
latin = TextMobject(list("Latin"))
greek = TextMobject(list("Greek"))
for mob in latin, greek:
mob.to_edge(LEFT)
question_mark = TextMobject("?").next_to(greek, buff = 0.1)
stars = Stars().highlight(BLACK)
stars.scale(0.5).shift(question_mark.get_center())
self.play(Transform(original_word, word), ShowCreation(dots))
self.play(ShimmerIn(pronunciation))
self.dither()
self.play(
GrowFromCenter(overbrace1),
GrowFromCenter(overbrace2)
)
self.dither()
self.play(ShimmerIn(latin))
self.play(FadeIn(question_mark))
self.play(Transform(
latin, greek,
path_func = counterclockwise_path()
))
self.dither()
self.play(Transform(question_mark, stars))
self.remove(stars)
self.dither()
self.play(ShimmerIn(shortest))
self.play(ShimmerIn(time))
for ex, ar in [(chrono_example, chrono_arrow), (brachy_example, brachy_arrow)]:
self.play(
ShowCreation(ar),
ShimmerIn(ex)
)
self.dither()
def show_equation(self):
equation = TexMobject([
"\\left(\\dfrac{1}{\\phantom{v_air}}\\right)",
"\\sin(\\theta_1)",
"=",
"\\left(\\dfrac{1}{\\phantom{v_water}}\\right)",
"\\sin(\\theta_2)"
])
equation.to_corner(UP+RIGHT)
frac1, sin1, equals, frac2, sin2 = equation.split()
v_air, v_water = [
TexMobject("v_{\\text{%s}}"%s, size = "\\Large")
for s in "air", "water"
]
v_air.next_to(Point(frac1.get_center()), DOWN)
v_water.next_to(Point(frac2.get_center()), DOWN)
frac1.add(v_air)
frac2.add(v_water)
f1, f2 = [
TexMobject("F_%d"%d, size = "\\Large")
for d in 1, 2
]
f1.next_to(sin1, LEFT)
f2.next_to(equals, RIGHT)
sin2_start = sin2.copy().next_to(f2, RIGHT)
bar1 = TexMobject("\\dfrac{\\qquad}{\\qquad}")
bar2 = bar1.copy()
bar1.next_to(sin1, DOWN)
bar2.next_to(sin2, DOWN)
v_air_copy = v_air.copy().next_to(bar1, DOWN)
v_water_copy = v_water.copy().next_to(bar2, DOWN)
bars = Mobject(bar1, bar2)
new_eq = equals.copy().center().shift(bars.get_center())
snells = TextMobject("Snell's Law")
snells.highlight(YELLOW)
snells.shift(new_eq.get_center()[0]*RIGHT)
snells.shift(UP)
anims = []
for mob in f1, sin1, equals, f2, sin2_start:
anims.append(ShimmerIn(mob))
self.play(*anims)
self.dither()
for f, frac in (f1, frac1), (f2, frac2):
target = frac.copy().ingest_submobjects()
also = []
if f is f2:
also.append(Transform(sin2_start, sin2))
sin2 = sin2_start
self.play(Transform(f, target), *also)
self.remove(f)
self.add(frac)
self.dither()
self.play(
FadeOut(frac1),
FadeOut(frac2),
Transform(v_air, v_air_copy),
Transform(v_water, v_water_copy),
ShowCreation(bars),
Transform(equals, new_eq)
)
self.dither()
frac1 = Mobject(sin1, bar1, v_air)
frac2 = Mobject(sin2, bar2, v_water)
for frac, vect in (frac1, LEFT), (frac2, RIGHT):
self.play(ApplyMethod(
frac.next_to, equals, vect
))
self.dither()
self.play(ShimmerIn(snells))
self.dither()
