def construct(self):
words = TextMobject([
"One does not simply define the limit \\\\ \
of a sequence of", "curves", "\\dots"
])
top_words = TextMobject(["curves", "are functions"]).to_edge(UP)
curves1 = words.split()[1]
curves2 = top_words.split()[0]
words.ingest_submobjects()
number = TexMobject("0.27")
pair = TexMobject("(0.53, 0.02)")
pair.next_to(number, buff=2)
arrow = Arrow(number, pair)
Mobject(number, arrow, pair).center().shift(UP)
number_line = UnitInterval()
number_line.stretch_to_fit_width(5)
number_line.to_edge(LEFT).shift(DOWN)
grid = Grid(4, 4).scale(0.4)
grid.next_to(number_line, buff=2)
low_arrow = Arrow(number_line, grid)
self.play(ShimmerIn(words))
self.dither()
self.play(FadeOut(words), ApplyMethod(curves1.replace, curves2),
ShimmerIn(top_words.split()[1]))
self.dither()
self.play(FadeIn(number))
self.play(ShowCreation(arrow))
self.play(FadeIn(pair))
self.dither()
self.play(ShowCreation(number_line))
self.play(ShowCreation(low_arrow))
self.play(ShowCreation(grid))
self.dither()
def setup_axes(self, animate=False):
##TODO, once eoc is done, refactor this to be less redundant.
x_num_range = float(self.x_max - self.x_min)
self.space_unit_to_x = self.x_axis_width / x_num_range
self.x_labeled_nums = self.x_labeled_nums or []
if self.x_leftmost_tick is None:
self.x_leftmost_tick = self.x_min
x_axis = NumberLine(x_min=self.x_min,
x_max=self.x_max,
unit_size=self.space_unit_to_x,
tick_frequency=self.x_tick_frequency,
leftmost_tick=self.x_leftmost_tick,
numbers_with_elongated_ticks=self.x_labeled_nums,
color=self.axes_color)
x_axis.shift(self.graph_origin - x_axis.number_to_point(0))
if len(self.x_labeled_nums) > 0:
if self.exclude_zero_label:
self.x_labeled_nums = filter(lambda x: x != 0,
self.x_labeled_nums)
x_axis.add_numbers(*self.x_labeled_nums)
x_label = TextMobject(self.x_axis_label)
x_label.next_to(x_axis.get_tick_marks(), UP + RIGHT, buff=SMALL_BUFF)
x_label.shift_onto_screen()
x_axis.add(x_label)
self.x_axis_label_mob = x_label
y_num_range = float(self.y_max - self.y_min)
self.space_unit_to_y = self.y_axis_height / y_num_range
self.y_labeled_nums = self.y_labeled_nums or []
if self.y_bottom_tick is None:
self.y_bottom_tick = self.y_min
y_axis = NumberLine(x_min=self.y_min,
x_max=self.y_max,
unit_size=self.space_unit_to_y,
tick_frequency=self.y_tick_frequency,
leftmost_tick=self.y_bottom_tick,
numbers_with_elongated_ticks=self.y_labeled_nums,
color=self.axes_color)
y_axis.shift(self.graph_origin - y_axis.number_to_point(0))
y_axis.rotate(np.pi / 2, about_point=y_axis.number_to_point(0))
if len(self.y_labeled_nums) > 0:
if self.exclude_zero_label:
self.y_labeled_nums = filter(lambda y: y != 0,
self.y_labeled_nums)
y_axis.add_numbers(*self.y_labeled_nums)
for mob in y_axis.numbers:
mob.next_to(mob.get_center(), LEFT, MED_SMALL_BUFF)
mob.shift(self.y_axis_numbers_nudge)
y_label = TextMobject(self.y_axis_label)
y_label.next_to(y_axis.get_tick_marks(), UP + RIGHT, buff=SMALL_BUFF)
y_label.shift_onto_screen()
y_axis.add(y_label)
self.y_axis_label_mob = y_label
if animate:
self.play(Write(VGroup(x_axis, y_axis)))
else:
self.add(x_axis, y_axis)
self.x_axis, self.y_axis = self.axes = VGroup(x_axis, y_axis)
self.default_graph_colors = it.cycle(self.default_graph_colors)
def construct(self):
CycloidScene.construct(self)
equation = TexMobject(
["\\dfrac{\\sin(\\theta)}{\\sqrt{y}}", "= \\text{constant}"])
sin_sqrt, const = equation.split()
new_eq = equation.copy()
new_eq.to_edge(UP, buff=1.3)
cycloid_word = TextMobject("Cycloid")
arrow = Arrow(2 * UP, cycloid_word)
arrow.reverse_points()
q_mark = TextMobject("?")
self.play(*map(ShimmerIn, equation.split()))
self.dither()
self.play(ApplyMethod(equation.shift, 2.2 * UP), ShowCreation(arrow))
q_mark.next_to(sin_sqrt)
self.play(ShimmerIn(cycloid_word))
self.dither()
self.grow_parts()
self.draw_cycloid()
self.dither()
extra_terms = [const, arrow, cycloid_word]
self.play(*[Transform(mob, q_mark) for mob in extra_terms])
self.remove(*extra_terms)
self.roll_back()
q_marks, arrows = self.get_q_marks_and_arrows(sin_sqrt)
self.draw_cycloid(3, ShowCreation(q_marks), ShowCreation(arrows))
self.dither()
def construct(self):
one_solution = TextMobject(["One ", "solution"])
two_insights = TextMobject(["Two ", " insights"])
two, insights = two_insights.split()
johann = ImageMobject("Johann_Bernoulli2", invert=False)
mark = ImageMobject("Mark_Levi", invert=False)
for mob in johann, mark:
mob.scale(0.4)
johann.next_to(insights, LEFT)
mark.next_to(johann, RIGHT)
name = TextMobject("Mark Levi").to_edge(UP)
self.play(*map(ShimmerIn, one_solution.split()))
self.dither()
for pair in zip(one_solution.split(), two_insights.split()):
self.play(Transform(*pair, path_func=path_along_arc(np.pi)))
self.dither()
self.clear()
self.add(two, insights)
for word, man in [(two, johann), (insights, mark)]:
self.play(Transform(word, Point(word.get_left())),
GrowFromCenter(man))
self.dither()
self.clear()
self.play(ApplyMethod(mark.center))
self.play(ShimmerIn(name))
self.dither()
def finite_analog(self, left_mob, arrow, right_mob):
self.clear()
self.add(left_mob, arrow, right_mob)
ex = TextMobject("\\times")
ex.highlight(RED)
# ex.shift(arrow.get_center())
middle = TexMobject("\\sum_{n=0}^N 2^n \\equiv -1 \\mod 2^{N+1}")
finite_analog = TextMobject("Finite analog")
finite_analog.scale(0.8)
brace = Brace(middle, UP)
finite_analog.next_to(brace, UP)
new_left = left_mob.copy().to_edge(LEFT)
new_right = right_mob.copy().to_edge(RIGHT)
left_arrow, right_arrow = [
Arrow(mob1.get_right()[0] * RIGHT,
mob2.get_left()[0] * RIGHT,
buff=0)
for mob1, mob2 in [(new_left, middle), (middle, new_right)]
]
for mob in ex, middle:
mob.sort_points(np.linalg.norm)
self.play(GrowFromCenter(ex))
self.wait()
self.play(Transform(left_mob, new_left),
Transform(arrow.copy(), left_arrow),
DelayByOrder(Transform(ex, middle)),
Transform(arrow, right_arrow),
Transform(right_mob, new_right))
self.play(GrowFromCenter(brace), ShimmerIn(finite_analog))
self.wait()
self.equivalence(left_mob, left_arrow,
Mobject(middle, brace, finite_analog))
def construct(self):
definition = TexMobject([
"\\text{HC}(", "x", ")",
"=\\lim_{n \\to \\infty}\\text{PHC}_n(", "x", ")"
])
definition.to_edge(UP)
definition.split()[1].highlight(BLUE)
definition.split()[-2].highlight(BLUE)
intro = TextMobject("Three things need to be proven")
prove_that = TextMobject("Prove that HC is $\\dots$")
prove_that.scale(0.7)
prove_that.to_edge(LEFT)
items = TextMobject([
"\\begin{enumerate}",
"\\item Well-defined: ",
"Points on Pseudo-Hilbert-curves really do converge",
"\\item A Curve: ",
"HC is continuous",
"\\item Space-filling: ",
"Each point in the unit square is an output of HC",
"\\end{enumerate}",
]).split()
items[1].highlight(GREEN)
items[3].highlight(YELLOW_C)
items[5].highlight(MAROON)
Mobject(*items).to_edge(RIGHT)
self.add(definition)
self.play(ShimmerIn(intro))
self.wait()
self.play(Transform(intro, prove_that))
for item in items[1:-1]:
self.play(ShimmerIn(item))
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.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 construct(self):
text = TextMobject("Which path minimizes travel time?")
text.to_edge(UP)
self.generate_start_and_end_points()
point_a = Dot(self.start_point)
point_b = Dot(self.end_point)
A = TextMobject("A").next_to(point_a, UP)
B = TextMobject("B").next_to(point_b, DOWN)
paths = self.get_paths()
for point, letter in [(point_a, A), (point_b, B)]:
self.play(
ShowCreation(point),
ShimmerIn(letter)
)
self.play(ShimmerIn(text))
curr_path = paths[0].copy()
curr_path_copy = curr_path.copy().ingest_submobjects()
self.play(
self.photon_run_along_path(curr_path),
ShowCreation(curr_path_copy, rate_func = rush_into)
)
self.remove(curr_path_copy)
for path in paths[1:] + [paths[0]]:
self.play(Transform(curr_path, path, run_time = 4))
self.wait()
self.path = curr_path.ingest_submobjects()
def construct(self):
words, s = TextMobject(["Pseudo-Hilbert Curve", "s"]).split()
pre_words = TextMobject("Order 1")
pre_words.next_to(words, LEFT, buff = 0.5)
s.next_to(words, RIGHT, buff = 0.05, aligned_edge = DOWN)
cluster = Mobject(pre_words, words, s)
cluster.center()
cluster.scale(0.7)
cluster.to_edge(UP, buff = 0.3)
cluster.highlight(GREEN)
grid1 = Grid(1, 1)
grid2 = Grid(2, 2)
curve = HilbertCurve(order = 1)
self.add(words, s)
self.dither()
self.play(Transform(
s, pre_words,
path_func = path_along_arc(-np.pi/3)
))
self.dither()
self.play(ShowCreation(grid1))
self.dither()
self.play(ShowCreation(grid2))
self.dither()
kwargs = {
"run_time" : 5,
"rate_func" : None
}
self.play(ShowCreation(curve, **kwargs))
self.dither()
def construct(self):
grids = [
Grid(
2**order, 2**order,
stroke_width = 1
).shift(0.3*DOWN)
for order in 6, 7
]
grid = grids[0]
side_brace = Brace(grid, LEFT)
top_brace = Brace(grid, UP)
top_words = TextMobject("256")
new_top_words = TextMobject("512")
side_words = top_words.copy()
new_side_words = new_top_words.copy()
for words in top_words, new_top_words:
words.next_to(top_brace, UP, buff = 0.1)
for words in side_words, new_side_words:
words.next_to(side_brace, LEFT)
self.add(grid)
self.play(
GrowFromCenter(side_brace),
GrowFromCenter(top_brace),
ShimmerIn(top_words),
ShimmerIn(side_words)
)
self.dither()
self.play(
DelayByOrder(Transform(*grids)),
Transform(top_words, new_top_words),
Transform(side_words, new_side_words)
)
self.dither()
def setup_background(self):
glass = Region(lambda x, y : y < 0, color = BLUE_E)
self.generate_start_and_end_points()
point_a = Dot(self.start_point)
point_b = Dot(self.end_point)
A = TextMobject("A").next_to(point_a, UP)
B = TextMobject("B").next_to(point_b, DOWN)
self.add(glass, point_a, point_b, A, B)
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 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 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):
logo = MirekOlsakLogo(self.camera)
series_title = TextMobject(self.series_str).to_edge(UP)
self.add(series_title)
chapter_title = TextMobject(self.chapter_str)
chapter_title.scale(1.4)
self.play(Write(chapter_title))
self.play(ShowCreation(logo))
self.dither(self.dither_time)
self.play(FadeOut(VGroup(series_title, chapter_title, logo)))
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, with_words):
CycloidScene.construct(self)
randy = Randolph()
randy.scale(RANDY_SCALE_FACTOR)
randy.shift(-randy.get_bottom())
central_randy = randy.copy()
start_randy = self.adjust_mobject_to_index(
randy.copy(), 1, self.cycloid.points
)
if with_words:
words1 = TextMobject("Trajectory due to gravity")
arrow = TexMobject("\\leftrightarrow")
words2 = TextMobject("Trajectory due \\emph{constantly} rotating wheel")
words1.next_to(arrow, LEFT)
words2.next_to(arrow, RIGHT)
words = Mobject(words1, arrow, words2)
words.scale_to_fit_width(2*SPACE_WIDTH-1)
words.to_edge(UP, buff = 0.2)
words.to_edge(LEFT)
self.play(ShowCreation(self.cycloid.copy()))
self.slide(randy, self.cycloid)
self.add(self.slider)
self.wait()
self.grow_parts()
self.draw_cycloid()
self.wait()
self.play(Transform(self.slider, start_randy))
self.wait()
self.roll_back()
self.wait()
if with_words:
self.play(*map(ShimmerIn, [words1, arrow, words2]))
self.wait()
self.remove(self.circle)
start_time = len(self.frames)*self.frame_duration
self.remove(self.slider)
self.slide(central_randy, self.cycloid)
end_time = len(self.frames)*self.frame_duration
self.play_over_time_range(
start_time,
end_time,
RollAlongVector(
self.circle,
self.cycloid.points[-1]-self.cycloid.points[0],
run_time = end_time-start_time,
rate_func = None
)
)
self.add(self.circle, self.slider)
self.wait()
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 construct(self):
name = TextMobject("Steven Strogatz")
name.to_edge(UP)
contributions = TextMobject("Frequent Contributions")
contributions.scale(0.5).to_edge(RIGHT).shift(2 * UP)
books_word = TextMobject("Books")
books_word.scale(0.5).to_edge(LEFT).shift(2 * UP)
radio_lab, sci_fri, cornell, book2, book3, book4 = [
ImageMobject(filename, invert=False, filter_color=WHITE)
for filename in [
"radio_lab",
"science_friday",
"cornell",
"strogatz_book2",
"strogatz_book3",
"strogatz_book4",
]
]
book1 = ImageMobject("strogatz_book1", invert=False)
nyt = ImageMobject("new_york_times")
logos = [radio_lab, nyt, sci_fri]
books = [book1, book2, book3, book4]
sample_size = Square(side_length=2)
last = contributions
for image in logos:
image.replace(sample_size)
image.next_to(last, DOWN)
last = image
sci_fri.scale_in_place(0.9)
shift_val = 0
sample_size.scale(0.75)
for book in books:
book.replace(sample_size)
book.next_to(books_word, DOWN)
book.shift(shift_val * (RIGHT + DOWN))
shift_val += 0.5
sample_size.scale(2)
cornell.replace(sample_size)
cornell.next_to(name, DOWN)
self.add(name)
self.play(FadeIn(cornell))
self.play(ShimmerIn(books_word))
for book in books:
book.shift(5 * LEFT)
self.play(ApplyMethod(book.shift, 5 * RIGHT))
self.play(ShimmerIn(contributions))
for logo in logos:
self.play(FadeIn(logo))
self.dither()
def add_rod_and_ring(self, rod, ring):
rod_word = TextMobject("Rod")
rod_word.next_to(Point(), UP)
ring_word = TextMobject("Ring")
ring_word.next_to(ring, UP)
self.wait()
self.add(rod)
self.play(ShimmerIn(rod_word))
self.wait()
self.remove(rod_word)
self.play(ShowCreation(ring))
self.play(ShimmerIn(ring_word))
self.wait()
self.remove(ring_word)
def construct(self):
words = TextMobject("""
It might come as a surprise how some well-known
fractals can be described with curves.
""")
words.to_edge(UP)
self.setup(Sierpinski)
self.add(TextMobject("Speaking of other fractals\\dots"))
self.wait(3)
self.clear()
self.play(ShimmerIn(words))
for x in range(9):
self.increase_order()
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):
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 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):
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.dither()
def construct(self):
rect = Rectangle(height=4, width=6, color=WHITE)
words = TextMobject("Details of proof")
words.to_edge(UP)
self.play(ShowCreation(rect), ShimmerIn(words))
self.wait()
def construct(self):
point_a, point_b = 3 * LEFT, 3 * RIGHT
dots = []
for point, char in [(point_a, "A"), (point_b, "B")]:
dot = Dot(point)
letter = TexMobject(char)
letter.next_to(dot, UP + LEFT)
dot.add(letter)
dots.append(dot)
path = ParametricFunction(lambda t:
(t / 2 + np.cos(t)) * RIGHT + np.sin(t) * UP,
start=-2 * np.pi,
end=2 * np.pi)
path.scale(6 / (2 * np.pi))
path.shift(point_a - path.points[0])
path.highlight(RED)
line = Line(point_a, point_b)
words = TextMobject("Shortest path from $A$ to $B$")
words.to_edge(UP)
self.play(ShimmerIn(words), *map(GrowFromCenter, dots))
self.play(ShowCreation(path))
self.play(Transform(path, line, path_func=path_along_arc(np.pi)))
self.wait()
def construct(self):
t_axis = NumberLine()
theta_axis = NumberLine().rotate(np.pi / 2)
theta_mob = TexMobject("\\theta(t)")
t_mob = TexMobject("t")
theta_mob.next_to(theta_axis, RIGHT)
theta_mob.to_edge(UP)
t_mob.next_to(t_axis, UP)
t_mob.to_edge(RIGHT)
graph = ParametricFunction(
lambda t: 4 * t * RIGHT + 2 * smooth(t) * UP)
line = Line(graph.points[0], graph.points[-1], color=WHITE)
q_mark = TextMobject("?")
q_mark.next_to(Point(graph.get_center()), LEFT)
stars = Stars(color=BLACK)
stars.scale(0.1).shift(q_mark.get_center())
squiggle = ParametricFunction(lambda t: t * RIGHT + 0.2 * t * (5 - t) *
(np.sin(t)**2) * UP,
start=0,
end=5)
self.play(ShowCreation(t_axis), ShowCreation(theta_axis),
ShimmerIn(theta_mob), ShimmerIn(t_mob))
self.play(ShimmerIn(q_mark), ShowCreation(graph))
self.wait()
self.play(Transform(q_mark, stars), Transform(graph, line))
self.wait()
self.play(Transform(graph, squiggle))
self.wait()
def construct(self):
europe = ImageMobject("Europe", use_cache = False)
self.add(europe)
self.freeze_background()
mathematicians = [
("Newton", [-1.75, -0.75, 0]),
("Jacob_Bernoulli",[-0.75, -1.75, 0]),
("Ehrenfried_von_Tschirnhaus",[0.5, -0.5, 0]),
("Gottfried_Wilhelm_von_Leibniz",[0.2, -1.75, 0]),
("Guillaume_de_L'Hopital", [-1.75, -1.25, 0]),
]
for name, point in mathematicians:
man = ImageMobject(name, invert = False)
if name == "Newton":
name = "Isaac_Newton"
name_mob = TextMobject(name.replace("_", " "))
name_mob.to_corner(UP+LEFT, buff=0.75)
self.add(name_mob)
man.scale_to_fit_height(4)
mobject = Point(man.get_corner(UP+LEFT))
self.play(Transform(mobject, man))
man.scale(0.2)
man.shift(point)
self.play(Transform(mobject, man))
self.remove(name_mob)
def show_diameter(self):
exceptions = [
self.circle, self.tangent_line, self.pc_line,
self.right_angle_symbol
]
everything = set(self.mobjects).difference(exceptions)
everything_copy = Mobject(*everything).copy()
light_everything = everything_copy.copy()
dark_everything = everything_copy.copy()
dark_everything.fade(0.8)
bottom_point = np.array(self.c_point)
bottom_point += 2 * self.radius * DOWN
diameter = Line(bottom_point, self.c_point)
brace = Brace(diameter, RIGHT)
diameter_word = TextMobject("Diameter")
d_mob = TexMobject("D")
diameter_word.next_to(brace)
d_mob.next_to(diameter)
self.remove(*everything)
self.play(Transform(everything_copy, dark_everything))
self.dither()
self.play(ShowCreation(diameter))
self.play(GrowFromCenter(brace))
self.play(ShimmerIn(diameter_word))
self.dither()
self.play(*[Transform(mob, d_mob) for mob in brace, diameter_word])
self.remove(brace, diameter_word)
self.add(d_mob)
self.play(Transform(everything_copy, light_everything))
self.remove(everything_copy)
self.add(*everything)
self.d_mob = d_mob
self.bottom_point = bottom_point
