def construct(self):
low_res = ImageMobject("low_resolution_lion", invert = False)
high_res = ImageMobject("Lion", invert = False)
grid = get_grid().scale(0.8)
for mob in low_res, high_res:
mob.replace(grid, stretch = True)
side_brace = Brace(low_res, LEFT)
top_brace = Brace(low_res, UP)
top_words = TextMobject("256 Px", size = "\\normal")
side_words = top_words.copy().rotate(np.pi/2)
top_words.next_to(top_brace, UP)
side_words.next_to(side_brace, LEFT)
self.add(high_res)
self.dither()
self.play(DelayByOrder(Transform(high_res, low_res)))
self.dither()
self.play(
GrowFromCenter(top_brace),
GrowFromCenter(side_brace),
ShimmerIn(top_words),
ShimmerIn(side_words)
)
self.dither()
for mob in grid, high_res:
mob.sort_points(np.linalg.norm)
self.play(DelayByOrder(Transform(high_res, grid)))
self.dither()
def construct(self, name):
run_time = 20
scale_factor = 0.8
image_array = get_image_array(name)
edge_mobject = self.get_edge_mobject(image_array)
full_picture = MobjectFromPixelArray(image_array)
for mob in edge_mobject, full_picture:
# mob.stroke_width = 4
mob.scale(scale_factor)
mob.show()
self.play(
DelayByOrder(FadeIn(
full_picture,
run_time = run_time,
rate_func = squish_rate_func(smooth, 0.7, 1)
)),
ShowCreation(
edge_mobject,
run_time = run_time,
rate_func = None
)
)
self.remove(edge_mobject)
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 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):
names = [
"Johann_Bernoulli2", "Jacob_Bernoulli",
"Gottfried_Wilhelm_von_Leibniz", "Newton"
]
guys = [ImageMobject(name, invert=False) for name in names]
johann = guys[0]
johann.scale(0.8)
pensive_johann = johann.copy()
pensive_johann.scale(0.25)
pensive_johann.to_corner(DOWN + LEFT)
comparitive_johann = johann.copy()
template = Square(side_length=2)
comparitive_johann.replace(template)
comparitive_johann.shift(UP + LEFT)
greater_than = TexMobject(">")
greater_than.next_to(comparitive_johann)
for guy, name in zip(guys, names)[1:]:
guy.replace(template)
guy.next_to(greater_than)
name_mob = TextMobject(name.replace("_", " "))
name_mob.scale(0.5)
name_mob.next_to(guy, DOWN)
guy.name_mob = name_mob
guy.sort_points(lambda p: np.dot(p, DOWN + RIGHT))
bubble = ThoughtBubble(initial_width=12)
bubble.stretch_to_fit_height(6)
bubble.ingest_submobjects()
bubble.pin_to(pensive_johann)
bubble.shift(DOWN)
point = Point(johann.get_corner(UP + RIGHT))
upper_point = Point(comparitive_johann.get_corner(UP + RIGHT))
lightbulb = ImageMobject("Lightbulb", invert=False)
lightbulb.scale(0.1)
lightbulb.sort_points(np.linalg.norm)
lightbulb.next_to(upper_point, RIGHT)
self.add(johann)
self.wait()
self.play(Transform(johann, pensive_johann),
Transform(point, bubble),
run_time=2)
self.remove(point)
self.add(bubble)
weakling = guys[1]
self.play(FadeIn(comparitive_johann), ShowCreation(greater_than),
FadeIn(weakling))
self.wait(2)
for guy in guys[2:]:
self.play(DelayByOrder(Transform(weakling, upper_point)))
self.play(FadeIn(guy), ShimmerIn(guy.name_mob))
self.wait(3)
self.remove(guy.name_mob)
weakling = guy
self.play(FadeOut(weakling), FadeOut(greater_than))
self.play(ShowCreation(lightbulb))
self.wait()
self.play(FadeOut(comparitive_johann), FadeOut(lightbulb))
self.play(ApplyMethod(Mobject(johann, bubble).scale, 10, run_time=3))
def construct(self):
grid = get_grid()
grid.sort_points(np.linalg.norm)
freq_line = get_freq_line()
freq_line.sort_points(lambda p : p[0])
red, blue = Color(RED), Color(BLUE)
freq_line.gradient_highlight(red, blue)
colors = [
Color(rgb = interpolate(
np.array(red.rgb),
np.array(blue.rgb),
alpha
))
for alpha in np.arange(4)/3.
]
string = Line(3*LEFT, 3*RIGHT, color = colors[1])
vibration = Vibrate(string)
vibration_copy = vibration.copy()
vibration_copy.mobject.stroke_width = 1
sub_vibrations = [
Vibrate(
string.copy().shift((n-1)*UP).highlight(colors[n]),
overtones = 1,
spatial_period = 6./(n+1),
temporal_period = 1./(n+1),
amplitude = 0.5/(n+1)
)
for n in range(4)
]
words = TexMobject("&\\vdots \\\\ \\text{thousands }& \\text{of frequencies} \\\\ &\\vdots")
words.to_edge(UP, buff = 0.1)
self.add(grid)
self.dither()
self.play(DelayByOrder(ApplyMethod(
grid.gradient_highlight, red, blue
)))
self.play(Transform(grid, freq_line))
self.dither()
self.play(
ShimmerIn(
words,
rate_func = squish_rate_func(smooth, 0, 0.2)
),
*sub_vibrations,
run_time = 5
)
self.play(
*[
TransformAnimations(
sub_vib, vibration
)
for sub_vib in sub_vibrations
]+[FadeOut(words)]
)
self.clear()
self.add(freq_line)
self.play(vibration)
def show_infinite_objects(self):
sigma, summand, equals, result = TexMobject([
"\\sum_{n = 1}^{\\infty}",
"\\dfrac{1}{n^2}",
"=",
"\\dfrac{\pi^2}{6}"
]).split()
alt_summand = TexMobject("n").replace(summand)
alt_result = TexMobject("-\\dfrac{1}{12}").replace(result)
rationals, other_equals, naturals = TexMobject([
"|\\mathds{Q}|",
"=",
"|\\mathds{N}|"
]).scale(2).split()
infinity = TexMobject("\\infty").scale(2)
local_mobjects = filter(
lambda m : isinstance(m, Mobject),
locals().values(),
)
for mob in local_mobjects:
mob.sort_points(np.linalg.norm)
self.play(ShimmerIn(infinity))
self.dither()
self.play(
ShimmerIn(summand),
ShimmerIn(equals),
ShimmerIn(result),
DelayByOrder(Transform(infinity, sigma))
)
self.dither()
self.play(
Transform(summand, alt_summand),
Transform(result, alt_result),
)
self.dither()
self.remove(infinity)
self.play(*[
CounterclockwiseTransform(
Mobject(summand, equals, result, sigma),
Mobject(rationals, other_equals, naturals)
)
])
self.dither()
self.clear()
self.add(self.bubble)