def __init__(self,
mobject1,
mobject2,
run_time=DEFAULT_TRANSFORM_RUN_TIME,
interpolation_function=straight_path,
black_out_extra_points=False,
*args,
**kwargs):
self.interpolation_function = interpolation_function
count1, count2 = mobject1.get_num_points(), mobject2.get_num_points()
if count2 == 0:
mobject2 = Point((SPACE_WIDTH, SPACE_HEIGHT, 0))
count2 = mobject2.get_num_points()
Mobject.align_data(mobject1, mobject2)
Animation.__init__(self, mobject1, run_time=run_time, *args, **kwargs)
self.ending_mobject = mobject2
self.mobject.SHOULD_BUFF_POINTS = \
mobject1.SHOULD_BUFF_POINTS and mobject2.SHOULD_BUFF_POINTS
self.reference_mobjects.append(mobject2)
self.name += "To" + str(mobject2)
if black_out_extra_points and count2 < count1:
#Ensure redundant pixels fade to black
indices = np.arange(0, count1 - 1,
float(count1) / count2).astype('int')
temp = np.zeros(mobject2.points.shape)
temp[indices] = mobject2.rgbs[indices]
mobject2.rgbs = temp
self.non_redundant_m2_indices = indices
def __init__(self, mobject1, mobject2,
run_time = DEFAULT_TRANSFORM_RUN_TIME,
interpolation_function = straight_path,
black_out_extra_points = False,
*args, **kwargs):
self.interpolation_function = interpolation_function
count1, count2 = mobject1.get_num_points(), mobject2.get_num_points()
if count2 == 0:
mobject2 = Point((SPACE_WIDTH, SPACE_HEIGHT, 0))
count2 = mobject2.get_num_points()
Mobject.align_data(mobject1, mobject2)
Animation.__init__(self, mobject1, run_time = run_time, *args, **kwargs)
self.ending_mobject = mobject2
self.mobject.SHOULD_BUFF_POINTS = \
mobject1.SHOULD_BUFF_POINTS and mobject2.SHOULD_BUFF_POINTS
self.reference_mobjects.append(mobject2)
self.name += "To" + str(mobject2)
if black_out_extra_points and count2 < count1:
#Ensure redundant pixels fade to black
indices = np.arange(
0, count1-1, float(count1) / count2
).astype('int')
temp = np.zeros(mobject2.points.shape)
temp[indices] = mobject2.rgbs[indices]
mobject2.rgbs = temp
self.non_redundant_m2_indices = indices
def construct(self):
curve = PeanoCurve(order=5)
curve.stretch_to_fit_width(2 * SPACE_WIDTH)
curve.stretch_to_fit_height(2 * SPACE_HEIGHT)
curve_start = curve.copy()
curve_start.apply_over_attr_arrays(lambda arr: arr[:200])
time_line = get_time_line()
time_line.shift(-time_line.number_to_point(2000))
self.add(time_line)
self.play(
ApplyMethod(time_line.shift,
-time_line.number_to_point(1900),
run_time=3))
brace = Brace(
Mobject(
Point(time_line.number_to_point(1865)),
Point(time_line.number_to_point(1888)),
), UP)
words = TextMobject("""
Cantor drives himself (and the \\\\
mathematical community at large) \\\\
crazy with research on infinity.
""")
words.next_to(brace, UP)
self.play(GrowFromCenter(brace), ShimmerIn(words))
self.dither()
self.play(Transform(time_line, curve_start), FadeOut(brace),
FadeOut(words))
self.play(ShowCreation(curve, run_time=5, rate_func=None))
self.dither()
def __init__(self, mobject, point, **kwargs):
digest_config(self, kwargs)
target = mobject.copy()
point_mob = Point(point)
if self.point_color:
point_mob.highlight(self.point_color)
mobject.replace(point_mob)
mobject.highlight(point_mob.get_color())
Transform.__init__(self, mobject, target, **kwargs)
def label_jump(self):
jump_points = Mobject(Point(self.spiril1.points[-1]),
Point(self.spiril2.points[0]))
self.brace = Brace(jump_points, RIGHT)
self.jump = TextMobject("Jump")
self.jump.next_to(self.brace, RIGHT)
self.play(GrowFromCenter(self.brace), ShimmerIn(self.jump))
self.dither()
self.remove(self.brace, self.jump)
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 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):
words = TextMobject("Would this actually work?")
grid = get_grid()
grid.scale_to_fit_width(6)
grid.to_edge(LEFT)
freq_line = get_freq_line()
freq_line.scale_to_fit_width(6)
freq_line.center().to_edge(RIGHT)
mapping = Mobject(grid, freq_line, Arrow(grid, freq_line))
mapping.ingest_sub_mobjects()
lower_left = Point().to_corner(DOWN + LEFT, buff=0)
lower_right = Point().to_corner(DOWN + RIGHT, buff=0)
self.add(words)
self.dither()
self.play(Transform(words, lower_right),
Transform(lower_left, mapping))
self.dither()
def construct(self):
val = 0.3
text = TextMobject([
"PHC", "$_n", "(", "%3.1f"%val, ")$",
" has a ", "limit point ", "as $n \\to \\infty$"
])
func_parts = text.copy().split()[:5]
Mobject(*func_parts).center().to_edge(UP)
num_str, val_str = func_parts[1], func_parts[3]
curve = UnitInterval()
curve.sort_points(lambda p : p[0])
dot = Dot().shift(curve.number_to_point(val))
arrow = Arrow(val_str, dot, buff = 0.1)
curve.add_numbers(0, 1)
self.play(ShowCreation(curve))
self.play(
ShimmerIn(val_str),
ShowCreation(arrow),
ShowCreation(dot)
)
self.wait()
self.play(
FadeOut(arrow),
*[
FadeIn(func_parts[i])
for i in 0, 1, 2, 4
]
)
for num in range(2,9):
new_curve = HilbertCurve(order = num)
new_curve.scale(0.8)
new_dot = Dot(new_curve.points[int(val*new_curve.get_num_points())])
new_num_str = TexMobject(str(num)).replace(num_str)
self.play(
Transform(curve, new_curve),
Transform(dot, new_dot),
Transform(num_str, new_num_str)
)
self.wait()
text.to_edge(UP)
text_parts = text.split()
for index in 1, -1:
text_parts[index].highlight()
starters = Mobject(*func_parts + [
Point(mob.get_center(), stroke_width=1)
for mob in text_parts[5:]
])
self.play(Transform(starters, text))
arrow = Arrow(text_parts[-2].get_bottom(), dot, buff = 0.1)
self.play(ShowCreation(arrow))
self.wait()
def construct(self):
mathy, bubble = get_mathy_and_bubble()
squiggle_mouth = mathy.mouth.copy()
squiggle_mouth.apply_function(
lambda (x, y, z) : (x, y+0.02*np.sin(50*x), z)
)
bubble.ingest_submobjects()
bubble.write("Why not use a Hilbert curve \\textinterrobang ")
words1 = bubble.content
bubble.write("So, it's not one curve but an infinite family of curves \\dots")
words2 = bubble.content
bubble.write("Well, no, it \\emph{is} just one thing, but I need \\\\ \
to tell you about a certain infinite family first.")
words3 = bubble.content
description = TextMobject("Mathematician friend", size = "\\small")
description.next_to(mathy, buff = 2)
arrow = Arrow(description, mathy)
self.add(mathy)
self.play(
ShowCreation(arrow),
ShimmerIn(description)
)
self.dither()
point = Point(bubble.get_tip())
self.play(
Transform(point, bubble),
)
self.remove(point)
self.add(bubble)
self.play(ShimmerIn(words1))
self.dither()
self.remove(description, arrow)
self.play(
Transform(mathy.mouth, squiggle_mouth),
ApplyMethod(mathy.arm.wag, 0.2*RIGHT, LEFT),
)
self.remove(words1)
self.add(words2)
self.dither(2)
self.remove(words2)
self.add(words3)
self.dither(2)
self.play(
ApplyPointwiseFunction(
lambda p : 15*p/np.linalg.norm(p),
bubble
),
ApplyMethod(mathy.shift, 5*(DOWN+LEFT)),
FadeOut(words3),
run_time = 3
)
def construct(self):
image = ImageMobject("lion", invert=False)
image.scale(0.5)
image.shift(2 * LEFT)
self.add(image)
for vect, num in zip([DOWN, RIGHT], [1, 2]):
brace = Brace(image, vect)
words_mob = TextMobject("Dimension %d" % num)
words_mob.next_to(image, vect, buff=1)
self.play(Transform(Point(brace.get_center()), brace),
ShimmerIn(words_mob),
run_time=2)
self.dither()
def construct(self):
mathy, bubble = get_mathy_and_bubble()
bubble.stretch_to_fit_width(4)
mathy.to_corner(DOWN + LEFT)
bubble.pin_to(mathy)
bubble.shift(LEFT)
morty = Mortimer()
morty.to_corner(DOWN + RIGHT)
morty_bubble = SpeechBubble()
morty_bubble.stretch_to_fit_width(4)
morty_bubble.pin_to(morty)
bubble.write("""
Did you know a curve \\\\
can fill all space?
""")
morty_bubble.write("Who cares?")
self.add(mathy, morty)
for bub, buddy in [(bubble, mathy), (morty_bubble, morty)]:
self.play(Transform(Point(bub.get_tip()), bub))
self.play(ShimmerIn(bub.content))
self.play(
ApplyMethod(buddy.blink,
rate_func=squish_rate_func(there_and_back)))
def __init__(self, mobject, point, **kwargs):
target = mobject.copy()
point_mob = Point(point)
mobject.replace(point_mob)
mobject.highlight(point_mob.get_color())
Transform.__init__(self, mobject, target, **kwargs)
def __init__(self, mobject, **kwargs):
Transform.__init__(self, mobject, Point(mobject.get_center()),
**kwargs)
def __init__(self, mobject, **kwargs):
target = mobject.copy()
point = Point(mobject.get_center())
mobject.replace(point)
mobject.highlight(point.get_color())
Transform.__init__(self, mobject, target, **kwargs)
