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):
words = TextMobject("Order 3 Pseudo-Hilbert Curve")
words.highlight(GREEN)
words.to_edge(UP)
grid4 = Mobject(Grid(2, 2), Grid(4, 4, point_thickness=2))
grid8 = Grid(8, 8, point_thickness=1)
order_3_curve = HilbertCurve(order=3)
mini_curves = [
HilbertCurve(order=2).scale(0.5).shift(1.5 * vect)
for vect in [LEFT + DOWN, LEFT + UP, RIGHT + UP, RIGHT + DOWN]
]
self.add(words, grid4)
self.dither()
self.play(ShowCreation(grid8))
self.dither()
self.play(*map(GrowFromCenter, mini_curves))
self.dither()
self.clear()
self.add(words, grid8, *mini_curves)
self.play(*[
ApplyMethod(curve.rotate_in_place, np.pi, axis)
for curve, axis in [(mini_curves[0],
UP + RIGHT), (mini_curves[3], UP + LEFT)]
])
self.play(ShowCreation(order_3_curve, run_time=5))
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):
words = TextMobject("Order 2 Pseudo-Hilbert Curve")
words.to_edge(UP, buff=0.3)
words.highlight(GREEN)
grid2 = Grid(2, 2)
grid4 = Grid(4, 4, point_thickness=2)
# order_1_curve = HilbertCurve(order = 1)
# squaggle_curve = order_1_curve.copy().apply_function(
# lambda (x, y, z) : (x + np.cos(3*y), y + np.sin(3*x), z)
# )
# squaggle_curve.show()
mini_curves = [
HilbertCurve(order=1).scale(0.5).shift(1.5 * vect)
for vect in [LEFT + DOWN, LEFT + UP, RIGHT + UP, RIGHT + DOWN]
]
last_curve = mini_curves[0]
naive_curve = Mobject(last_curve)
for mini_curve in mini_curves[1:]:
line = Line(last_curve.points[-1], mini_curve.points[0])
naive_curve.add(line, mini_curve)
last_curve = mini_curve
naive_curve.ingest_sub_mobjects()
naive_curve.gradient_highlight(RED, GREEN)
order_2_curve = HilbertCurve(order=2)
self.add(words, grid2)
self.dither()
self.play(ShowCreation(grid4))
self.play(*[ShowCreation(mini_curve) for mini_curve in mini_curves])
self.dither()
self.play(ShowCreation(naive_curve, run_time=5))
self.remove(*mini_curves)
self.dither()
self.play(Transform(naive_curve, order_2_curve))
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):
point_a = 3*LEFT+3*UP
point_b = 1.5*RIGHT+3*DOWN
midpoint = ORIGIN
lines, arcs, thetas = [], [], []
counter = it.count(1)
for point in point_a, point_b:
line = Line(point, midpoint, color = RED_D)
angle = np.pi/2-np.abs(np.arctan(line.get_slope()))
arc = Arc(angle, radius = 0.5).rotate(np.pi/2)
if point is point_b:
arc.rotate(np.pi)
line.reverse_points()
theta = TexMobject("\\theta_%d"%counter.next())
theta.scale(0.5)
theta.shift(2*arc.get_center())
arc.shift(midpoint)
theta.shift(midpoint)
lines.append(line)
arcs.append(arc)
thetas.append(theta)
vert_line = Line(2*UP, 2*DOWN)
vert_line.shift(midpoint)
path = Mobject(*lines).ingest_submobjects()
glass = Region(lambda x, y : y < 0, color = BLUE_E)
self.add(glass)
equation = TexMobject([
"\\dfrac{\\sin(\\theta_1)}{v_{\\text{air}}}",
"=",
"\\dfrac{\\sin(\\theta_2)}{v_{\\text{water}}}",
])
equation.to_corner(UP+RIGHT)
exp1, equals, exp2 = equation.split()
snells_law = TextMobject("Snell's Law:")
snells_law.highlight(YELLOW)
snells_law.to_edge(UP)
self.play(ShimmerIn(snells_law))
self.dither()
self.play(ShowCreation(path))
self.play(self.photon_run_along_path(path))
self.dither()
self.play(ShowCreation(vert_line))
self.play(*map(ShowCreation, arcs))
self.play(*map(GrowFromCenter, thetas))
self.dither()
self.play(ShimmerIn(exp1))
self.dither()
self.play(*map(ShimmerIn, [equals, exp2]))
self.dither()
def construct(self):
point_a = 3*LEFT+3*UP
point_b = 1.5*RIGHT+3*DOWN
midpoint = ORIGIN
lines, arcs, thetas = [], [], []
counter = it.count(1)
for point in point_a, point_b:
line = Line(point, midpoint, color = RED_D)
angle = np.pi/2-np.abs(np.arctan(line.get_slope()))
arc = Arc(angle, radius = 0.5).rotate(np.pi/2)
if point is point_b:
arc.rotate(np.pi)
line.reverse_points()
theta = TexMobject("\\theta_%d"%counter.next())
theta.scale(0.5)
theta.shift(2*arc.get_center())
arc.shift(midpoint)
theta.shift(midpoint)
lines.append(line)
arcs.append(arc)
thetas.append(theta)
vert_line = Line(2*UP, 2*DOWN)
vert_line.shift(midpoint)
path = Mobject(*lines).ingest_submobjects()
glass = Region(lambda x, y : y < 0, color = BLUE_E)
self.add(glass)
equation = TexMobject([
"\\dfrac{\\sin(\\theta_1)}{v_{\\text{air}}}",
"=",
"\\dfrac{\\sin(\\theta_2)}{v_{\\text{water}}}",
])
equation.to_corner(UP+RIGHT)
exp1, equals, exp2 = equation.split()
snells_law = TextMobject("Snell's Law:")
snells_law.highlight(YELLOW)
snells_law.to_edge(UP)
self.play(ShimmerIn(snells_law))
self.wait()
self.play(ShowCreation(path))
self.play(self.photon_run_along_path(path))
self.wait()
self.play(ShowCreation(vert_line))
self.play(*map(ShowCreation, arcs))
self.play(*map(GrowFromCenter, thetas))
self.wait()
self.play(ShimmerIn(exp1))
self.wait()
self.play(*map(ShimmerIn, [equals, exp2]))
self.wait()
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):
morty = Mortimer()
morty.next_to(ORIGIN, DOWN)
n_patrons = len(self.specific_patrons)
special_thanks = TextMobject("Special thanks")
special_thanks.highlight(YELLOW)
special_thanks.to_edge(UP)
patreon_logo = PatreonLogo()
patreon_logo.next_to(morty, UP, buff=MED_LARGE_BUFF)
patrons = map(TextMobject, self.specific_patrons)
patron_groups = []
index = 0
counter = 0
while index < len(patrons):
next_index = index + self.patron_group_size
group = VGroup(*patrons[index:next_index])
group.arrange_submobjects(DOWN, aligned_edge=LEFT)
if counter % 2 == 0:
group.to_edge(LEFT)
else:
group.to_edge(RIGHT)
patron_groups.append(group)
index = next_index
counter += 1
self.play(
morty.change_mode,
"gracious",
DrawBorderThenFill(patreon_logo),
)
self.play(Write(special_thanks, run_time=1))
for i, group in enumerate(patron_groups):
anims = [
FadeIn(
group,
run_time=2,
submobject_mode="lagged_start",
lag_factor=4,
),
morty.look_at,
group.get_top(),
]
if i >= 2:
anims.append(FadeOut(patron_groups[i - 2]))
self.play(*anims)
self.play(morty.look_at, group.get_bottom())
self.play(Blink(morty))
def construct(self):
mathy, bubble = get_mathy_and_bubble()
bubble.write("For a 256x256 pixel array...")
words = TextMobject("Order 8 Pseudo-Hilbert Curve")
words.highlight(GREEN)
words.to_edge(UP, buff=0.3)
curve = HilbertCurve(order=8)
self.add(mathy, bubble)
self.play(ShimmerIn(bubble.content))
self.dither()
self.clear()
self.add(words)
self.play(ShowCreation(curve, run_time=7, rate_func=None))
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.dither()
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.dither()
self.equivalence(
left_mob,
left_arrow,
Mobject(middle, brace, finite_analog)
)
def construct(self):
morty = Mortimer()
morty.next_to(ORIGIN, DOWN)
n_patrons = len(self.specific_patrons)
special_thanks = TextMobject("Special thanks")
special_thanks.highlight(YELLOW)
special_thanks.to_edge(UP)
patreon_logo = PatreonLogo()
patreon_logo.next_to(morty, UP, buff=MED_LARGE_BUFF)
patrons = map(TextMobject, self.specific_patrons)
num_groups = float(len(patrons)) / self.patron_group_size
proportion_range = np.linspace(0, 1, num_groups + 1)
indices = (len(patrons) * proportion_range).astype('int')
patron_groups = [
VGroup(*patrons[i:j]) for i, j in zip(indices, indices[1:])
]
for i, group in enumerate(patron_groups):
group.arrange_submobjects(DOWN, aligned_edge=LEFT)
group.scale(self.patron_scale_val)
group.to_edge(LEFT if i % 2 == 0 else RIGHT)
self.play(
morty.change_mode,
"gracious",
DrawBorderThenFill(patreon_logo),
)
self.play(Write(special_thanks, run_time=1))
print len(patron_groups)
for i, group in enumerate(patron_groups):
anims = [
FadeIn(
group,
run_time=2,
submobject_mode="lagged_start",
lag_factor=4,
),
morty.look_at,
group.get_top(),
]
if i >= 2:
anims.append(FadeOut(patron_groups[i - 2]))
self.play(*anims)
self.play(morty.look_at, group.get_bottom())
self.play(Blink(morty))
def construct(self):
morty = Mortimer()
morty.next_to(ORIGIN, DOWN)
n_patrons = len(self.specific_patrons)
special_thanks = TextMobject("Special thanks")
special_thanks.highlight(YELLOW)
special_thanks.to_edge(UP)
patreon_logo = PatreonLogo()
patreon_logo.next_to(morty, UP, buff=MED_LARGE_BUFF)
left_patrons = VGroup(
*map(TextMobject, self.specific_patrons[:n_patrons / 2]))
right_patrons = VGroup(
*map(TextMobject, self.specific_patrons[n_patrons / 2:]))
for patrons in left_patrons, right_patrons:
patrons.arrange_submobjects(DOWN,
aligned_edge=LEFT,
buff=1.5 * MED_SMALL_BUFF)
all_patrons = VGroup(left_patrons, right_patrons)
all_patrons.scale(0.7)
for patrons, vect in (left_patrons, LEFT), (right_patrons, RIGHT):
patrons.to_corner(UP + vect, buff=MED_SMALL_BUFF)
shift_distance = max(0, 1 - SPACE_HEIGHT - all_patrons.get_bottom()[1])
velocity = shift_distance / 9.0
def get_shift_anim():
return ApplyMethod(all_patrons.shift,
velocity * UP,
rate_func=None)
self.play(
morty.change_mode,
"gracious",
DrawBorderThenFill(patreon_logo),
)
self.play(Write(special_thanks, run_time=1))
self.play(Write(left_patrons), morty.look_at, left_patrons)
self.play(Write(right_patrons), morty.look_at, right_patrons)
self.play(Blink(morty), get_shift_anim())
for patrons in left_patrons, right_patrons:
for index in 0, -1:
self.play(morty.look_at, patrons[index], get_shift_anim())
self.play(get_shift_anim())
def construct(self):
mathy, bubble = get_mathy_and_bubble()
bubble.write("For a 256x256 pixel array...")
words = TextMobject("Order 8 Pseudo-Hilbert Curve")
words.highlight(GREEN)
words.to_edge(UP, buff = 0.3)
curve = HilbertCurve(order = 8)
self.add(mathy, bubble)
self.play(ShimmerIn(bubble.content))
self.dither()
self.clear()
self.add(words)
self.play(ShowCreation(
curve, run_time = 7, rate_func = None
))
self.dither()
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 get_corner_numbers(self, value, symbol):
value_mob = TextMobject(value)
width = self.get_width() / self.card_width_to_corner_num_width
height = self.get_height() / self.card_height_to_corner_num_height
value_mob.scale_to_fit_width(width)
value_mob.stretch_to_fit_height(height)
value_mob.next_to(self.get_corner(UP + LEFT),
DOWN + RIGHT,
buff=MED_LARGE_BUFF * width)
value_mob.highlight(symbol.get_color())
corner_symbol = symbol.copy()
corner_symbol.scale_to_fit_width(width)
corner_symbol.next_to(value_mob, DOWN, buff=MED_SMALL_BUFF * width)
corner_group = VGroup(value_mob, corner_symbol)
opposite_corner_group = corner_group.copy()
opposite_corner_group.rotate(np.pi, about_point=self.get_center())
return VGroup(corner_group, opposite_corner_group)
def label(self, text, time = 5):
mob = TextMobject(text)
mob.scale(1.5)
mob.to_edge(UP)
rectangle = region_from_polygon_vertices(*[
mob.get_corner(vect) + 0.3*vect
for vect in [
UP+RIGHT,
UP+LEFT,
DOWN+LEFT,
DOWN+RIGHT
]
])
mob.highlight(self.text_color)
rectangle = MobjectFromRegion(rectangle, "#111111")
rectangle.point_thickness = 3
self.add(rectangle, mob)
self.dither(time)
self.remove(mob, rectangle)
def construct(self):
words = TextMobject("Order 2 Pseudo-Hilbert Curve")
words.to_edge(UP, buff = 0.3)
words.highlight(GREEN)
grid2 = Grid(2, 2)
grid4 = Grid(4, 4, stroke_width = 2)
# order_1_curve = HilbertCurve(order = 1)
# squaggle_curve = order_1_curve.copy().apply_function(
# lambda (x, y, z) : (x + np.cos(3*y), y + np.sin(3*x), z)
# )
# squaggle_curve.show()
mini_curves = [
HilbertCurve(order = 1).scale(0.5).shift(1.5*vect)
for vect in [
LEFT+DOWN,
LEFT+UP,
RIGHT+UP,
RIGHT+DOWN
]
]
last_curve = mini_curves[0]
naive_curve = Mobject(last_curve)
for mini_curve in mini_curves[1:]:
line = Line(last_curve.points[-1], mini_curve.points[0])
naive_curve.add(line, mini_curve)
last_curve = mini_curve
naive_curve.ingest_submobjects()
naive_curve.gradient_highlight(RED, GREEN)
order_2_curve = HilbertCurve(order = 2)
self.add(words, grid2)
self.dither()
self.play(ShowCreation(grid4))
self.play(*[
ShowCreation(mini_curve)
for mini_curve in mini_curves
])
self.dither()
self.play(ShowCreation(naive_curve, run_time = 5))
self.remove(*mini_curves)
self.dither()
self.play(Transform(naive_curve, order_2_curve))
self.dither()
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 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):
words = TextMobject("Order 3 Pseudo-Hilbert Curve")
words.highlight(GREEN)
words.to_edge(UP)
grid4 = Mobject(
Grid(2, 2),
Grid(4, 4, stroke_width = 2)
)
grid8 = Grid(8, 8, stroke_width = 1)
order_3_curve = HilbertCurve(order = 3)
mini_curves = [
HilbertCurve(order = 2).scale(0.5).shift(1.5*vect)
for vect in [
LEFT+DOWN,
LEFT+UP,
RIGHT+UP,
RIGHT+DOWN
]
]
self.add(words, grid4)
self.dither()
self.play(ShowCreation(grid8))
self.dither()
self.play(*map(GrowFromCenter, mini_curves))
self.dither()
self.clear()
self.add(words, grid8, *mini_curves)
self.play(*[
ApplyMethod(curve.rotate_in_place, np.pi, axis)
for curve, axis in [
(mini_curves[0], UP+RIGHT),
(mini_curves[3], UP+LEFT)
]
])
self.play(ShowCreation(order_3_curve, run_time = 5))
self.dither()
def get_corner_numbers(self, value, symbol):
value_mob = TextMobject(value)
width = self.get_width()/self.card_width_to_corner_num_width
height = self.get_height()/self.card_height_to_corner_num_height
value_mob.scale_to_fit_width(width)
value_mob.stretch_to_fit_height(height)
value_mob.next_to(
self.get_corner(UP+LEFT), DOWN+RIGHT,
buff = MED_LARGE_BUFF*width
)
value_mob.highlight(symbol.get_color())
corner_symbol = symbol.copy()
corner_symbol.scale_to_fit_width(width)
corner_symbol.next_to(
value_mob, DOWN,
buff = MED_SMALL_BUFF*width
)
corner_group = VGroup(value_mob, corner_symbol)
opposite_corner_group = corner_group.copy()
opposite_corner_group.rotate(
np.pi, about_point = self.get_center()
)
return VGroup(corner_group, opposite_corner_group)
def get_author(self, quote):
author = TextMobject("-" + self.author)
author.next_to(quote, DOWN)
author.highlight(YELLOW)
return author
def construct(self):
morty = Mortimer()
morty.next_to(ORIGIN, DOWN)
n_patrons = len(self.specific_patrons)
special_thanks = TextMobject("Special thanks")
special_thanks.highlight(YELLOW)
special_thanks.to_edge(UP)
patreon_logo = PatreonLogo()
patreon_logo.next_to(morty, UP, buff = MED_LARGE_BUFF)
left_patrons = VGroup(*map(TextMobject,
self.specific_patrons[:n_patrons/2]
))
right_patrons = VGroup(*map(TextMobject,
self.specific_patrons[n_patrons/2:]
))
for patrons in left_patrons, right_patrons:
patrons.arrange_submobjects(
DOWN, aligned_edge = LEFT,
buff = 1.5*MED_SMALL_BUFF
)
all_patrons = VGroup(left_patrons, right_patrons)
all_patrons.scale(self.patron_scale_val)
for patrons, vect in (left_patrons, LEFT), (right_patrons, RIGHT):
patrons.to_edge(vect, buff = MED_SMALL_BUFF)
if patrons.get_height() > 2*SPACE_HEIGHT - LARGE_BUFF:
patrons.to_edge(UP, buff = MED_SMALL_BUFF)
shift_distance = max(
0, (all_patrons.get_height() - 2*SPACE_HEIGHT)
)
if shift_distance > 0:
shift_distance += 1
velocity = shift_distance/9.0
def get_shift_anim():
return ApplyMethod(
all_patrons.shift, velocity*UP,
rate_func = None
)
self.play(
morty.change_mode, "gracious",
DrawBorderThenFill(patreon_logo),
)
self.play(Write(special_thanks, run_time = 1))
self.play(
Write(left_patrons),
morty.look_at, left_patrons
)
self.play(
Write(right_patrons),
morty.look_at, right_patrons
)
self.play(Blink(morty), get_shift_anim())
for patrons in left_patrons, right_patrons:
for index in 0, -1:
self.play(
morty.look_at, patrons[index],
get_shift_anim()
)
self.play(get_shift_anim())
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):
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()
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 get_author(self, quote):
author = TextMobject("-" + self.author)
author.next_to(quote, DOWN)
author.highlight(YELLOW)
return author
