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):
n_terms = 4
def func((x, y, ignore)):
z = complex(x, y)
if (np.abs(x%1 - 0.5)<0.01 and y < 0.01) or np.abs(z)<0.01:
return ORIGIN
out_z = 1./(2*np.tan(np.pi*z)*(z**2))
return out_z.real*RIGHT - out_z.imag*UP
arrows = Mobject(*[
Arrow(ORIGIN, np.sqrt(2)*point)
for point in compass_directions(4, RIGHT+UP)
])
arrows.highlight(YELLOW)
arrows.ingest_submobjects()
all_arrows = Mobject(*[
arrows.copy().scale(0.3/(x)).shift(x*RIGHT)
for x in range(1, n_terms+2)
])
terms = TexMobject([
"\\dfrac{1}{%d^2} + "%(x+1)
for x in range(n_terms)
]+["\\cdots"])
terms.shift(2*UP)
plane = NumberPlane(color = BLUE_E)
axes = Mobject(NumberLine(), NumberLine().rotate(np.pi/2))
axes.highlight(WHITE)
for term in terms.split():
self.play(ShimmerIn(term, run_time = 0.5))
self.dither()
self.play(ShowCreation(plane), ShowCreation(axes))
self.play(*[
Transform(*pair)
for pair in zip(terms.split(), all_arrows.split())
])
self.play(PhaseFlow(
func, plane,
run_time = 5,
virtual_time = 8
))
class FluidFlow(Scene):
DEFAULT_CONFIG = {
"arrow_spacing" : 1,
"dot_spacing" : 0.5,
"dot_color" : BLUE_B,
"text_color" : WHITE,
"arrow_color" : GREEN_A,
"points_height" : SPACE_HEIGHT,
"points_width" : SPACE_WIDTH,
}
def use_function(self, function):
self.function = function
def get_points(self, spacing):
x_radius, y_radius = [
val-val%spacing
for val in self.points_width, self.points_height
]
return map(np.array, it.product(
np.arange(-x_radius, x_radius+spacing, spacing),
np.arange(-y_radius, y_radius+spacing, spacing),
[0]
))
def add_plane(self):
self.add(NumberPlane().fade())
def add_dots(self):
points = self.get_points(self.dot_spacing)
self.dots = Mobject(*map(Dot, points))
self.dots.highlight(self.dot_color)
self.play(ShowCreation(self.dots))
self.dither()
def add_arrows(self, true_length = False):
if not hasattr(self, "function"):
raise Exception("Must run use_function first")
points = self.get_points(self.arrow_spacing)
points = filter(
lambda p : np.linalg.norm(self.function(p)) > 0.01,
points
)
angles = map(angle_of_vector, map(self.function, points))
prototype = Arrow(
ORIGIN, RIGHT*self.arrow_spacing/2.,
color = self.arrow_color,
tip_length = 0.1,
buff = 0
)
arrows = []
for point in points:
arrow = prototype.copy()
output = self.function(point)
if true_length:
arrow.scale(np.linalg.norm(output))
arrow.rotate(angle_of_vector(output))
arrow.shift(point)
arrows.append(arrow)
self.arrows = Mobject(*arrows)
self.play(ShowCreation(self.arrows))
self.dither()
def add_paddle(self):
pass
def flow(self, **kwargs):
if not hasattr(self, "function"):
raise Exception("Must run use_function first")
self.play(ApplyToCenters(
PhaseFlow,
self.dots.split(),
function = self.function,
**kwargs
))
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)
class FormalDefinitionOfContinuity(Scene):
def construct(self):
self.setup()
self.label_spaces()
self.move_dot()
self.label_jump()
self.draw_circles()
self.vary_circle_sizes()
self.discontinuous_point()
def setup(self):
self.input_color = YELLOW_C
self.output_color = RED
def spiril(t):
theta = 2*np.pi*t
return t*np.cos(theta)*RIGHT+t*np.sin(theta)*UP
self.spiril1 = ParametricFunction(
lambda t : 1.5*RIGHT + DOWN + 2*spiril(t),
density = 5*DEFAULT_POINT_DENSITY_1D,
)
self.spiril2 = ParametricFunction(
lambda t : 5.5*RIGHT + UP - 2*spiril(1-t),
density = 5*DEFAULT_POINT_DENSITY_1D,
)
Mobject.align_data(self.spiril1, self.spiril2)
self.output = Mobject(self.spiril1, self.spiril2)
self.output.ingest_submobjects()
self.output.highlight(GREEN_A)
self.interval = UnitInterval()
self.interval.scale_to_fit_width(SPACE_WIDTH-1)
self.interval.to_edge(LEFT)
self.input_dot = Dot(color = self.input_color)
self.output_dot = self.input_dot.copy().highlight(self.output_color)
left, right = self.interval.get_left(), self.interval.get_right()
self.input_homotopy = lambda (x, y, z, t) : (x, y, t) + interpolate(left, right, t)
output_size = self.output.get_num_points()-1
output_points = self.output.points
self.output_homotopy = lambda (x, y, z, t) : (x, y, z) + output_points[int(t*output_size)]
def get_circles_and_points(self, min_input, max_input):
input_left, input_right = [
self.interval.number_to_point(num)
for num in min_input, max_input
]
input_circle = Circle(
radius = np.linalg.norm(input_left-input_right)/2,
color = WHITE
)
input_circle.shift((input_left+input_right)/2)
input_points = Line(
input_left, input_right,
color = self.input_color
)
output_points = Mobject(color = self.output_color)
n = self.output.get_num_points()
output_points.add_points(
self.output.points[int(min_input*n):int(max_input*n)]
)
output_center = output_points.points[int(0.5*output_points.get_num_points())]
max_distance = np.linalg.norm(output_center-output_points.points[-1])
output_circle = Circle(
radius = max_distance,
color = WHITE
)
output_circle.shift(output_center)
return (
input_circle,
input_points,
output_circle,
output_points
)
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.wait()
def move_dot(self):
kwargs = {
"rate_func" : None,
"run_time" : 3
}
self.play(
Homotopy(self.input_homotopy, self.input_dot, **kwargs),
Homotopy(self.output_homotopy, self.output_dot, **kwargs),
ShowCreation(self.output, **kwargs)
)
self.wait()
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.wait()
self.remove(self.brace, self.jump)
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 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.wait()
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.wait()
self.remove(vary_circles.mobject, text, arrow)
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.wait()
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.wait()
self.play(ShimmerIn(text))
self.remove(input_circle, input_points, output_circle, input_points_copy)
self.play(vary_circles)
self.wait()
self.play(
ShimmerIn(discontinuous_at_A),
ShowCreation(discontinuous_arrow)
)
self.wait(3)
self.remove(vary_circles.mobject, discontinuous_at_A, discontinuous_arrow)
def continuous_point(self):
pass
class PiCreature(Mobject):
DEFAULT_CONFIG = {
"color" : BLUE_E
}
PART_NAMES = [
'arm',
'body',
'left_eye',
'right_eye',
'left_leg',
'right_leg',
'mouth',
]
WHITE_PART_NAMES = ['left_eye', 'right_eye', 'mouth']
MOUTH_NAMES = ["smile", "frown", "straight_mouth"]
def __init__(self, **kwargs):
Mobject.__init__(self, **kwargs)
for part_name in self.PART_NAMES:
mob = ImageMobject(
part_name_to_directory(part_name),
should_center = False
)
if part_name not in self.WHITE_PART_NAMES:
mob.highlight(self.color)
setattr(self, part_name, mob)
self.eyes = Mobject(self.left_eye, self.right_eye)
self.legs = Mobject(self.left_leg, self.right_leg)
mouth_center = self.get_mouth_center()
self.mouth.center()
self.smile = self.mouth
self.frown = self.mouth.copy().rotate(np.pi, RIGHT)
self.straight_mouth = TexMobject("-").scale(0.7)
for mouth in self.smile, self.frown, self.straight_mouth:
mouth.sort_points(lambda p : p[0])
mouth.highlight(self.color) ##to blend into background
mouth.shift(mouth_center)
self.digest_mobject_attrs()
self.give_smile()
self.add(self.mouth)
self.scale(PI_CREATURE_SCALE_VAL)
def get_parts(self):
return [getattr(self, pn) for pn in self.PART_NAMES]
def get_white_parts(self):
return [
getattr(self, pn)
for pn in self.WHITE_PART_NAMES+self.MOUTH_NAMES
]
def get_mouth_center(self):
result = self.body.get_center()
result[0] = self.eyes.get_center()[0]
return result
# left_center = self.left_eye.get_center()
# right_center = self.right_eye.get_center()
# l_to_r = right_center-left_center
# eyes_to_mouth = rotate_vector(l_to_r, -np.pi/2, OUT)
# eyes_to_mouth /= np.linalg.norm(eyes_to_mouth)
# return left_center/2 + right_center/2 + \
# PI_CREATURE_MOUTH_TO_EYES_DISTANCE*eyes_to_mouth
def highlight(self, color, condition = None):
for part in set(self.get_parts()).difference(self.get_white_parts()):
part.highlight(color, condition)
return self
def move_to(self, destination):
self.shift(destination-self.get_bottom())
return self
def change_mouth_to(self, mouth_name):
#TODO, This is poorly implemented
self.mouth = getattr(self, mouth_name)
self.sub_mobjects = list_update(
self.sub_mobjects,
self.get_parts()
)
self.mouth.highlight(WHITE)
return self
def give_smile(self):
return self.change_mouth_to("smile")
def give_frown(self):
return self.change_mouth_to("frown")
def give_straight_face(self):
return self.change_mouth_to("straight_mouth")
def get_eye_center(self):
return self.eyes.get_center()
def make_mean(self):
eye_x, eye_y = self.get_eye_center()[:2]
def should_delete((x, y, z)):
return y - eye_y > 0.3*abs(x - eye_x)
self.eyes.highlight("black", should_delete)
self.give_straight_face()
return self
def make_sad(self):
eye_x, eye_y = self.get_eye_center()[:2]
eye_y += 0.15
def should_delete((x, y, z)):
return y - eye_y > -0.3*abs(x - eye_x)
self.eyey.highlight("black", should_delete)
self.give_frown()
return self
def get_step_intermediate(self, pi_creature):
vect = pi_creature.get_center() - self.get_center()
result = self.copy().shift(vect / 2.0)
left_forward = vect[0] > 0
if self.right_leg.get_center()[0] < self.left_leg.get_center()[0]:
#For Mortimer's case
left_forward = not left_forward
if left_forward:
result.left_leg.wag(vect/2.0, DOWN)
result.right_leg.wag(-vect/2.0, DOWN)
else:
result.right_leg.wag(vect/2.0, DOWN)
result.left_leg.wag(-vect/2.0, DOWN)
return result
def blink(self):
bottom = self.eyes.get_bottom()
self.eyes.apply_function(
lambda (x, y, z) : (x, bottom[1], z)
)
return self
def shift_eyes(self):
for eye in self.left_eye, self.right_eye:
eye.rotate_in_place(np.pi, UP)
return self
def to_symbol(self):
Mobject.__init__(
self,
*list(set(self.get_parts()).difference(self.get_white_parts()))
)
class PiCreature(Mobject):
DEFAULT_CONFIG = {"color": BLUE_E}
PART_NAMES = [
'arm',
'body',
'left_eye',
'right_eye',
'left_leg',
'right_leg',
'mouth',
]
WHITE_PART_NAMES = ['left_eye', 'right_eye', 'mouth']
MOUTH_NAMES = ["smile", "frown", "straight_mouth"]
def __init__(self, **kwargs):
Mobject.__init__(self, **kwargs)
for part_name in self.PART_NAMES:
mob = ImageMobject(part_name_to_directory(part_name),
should_center=False)
if part_name not in self.WHITE_PART_NAMES:
mob.highlight(self.color)
setattr(self, part_name, mob)
self.eyes = Mobject(self.left_eye, self.right_eye)
self.legs = Mobject(self.left_leg, self.right_leg)
mouth_center = self.get_mouth_center()
self.mouth.center()
self.smile = self.mouth
self.frown = self.mouth.copy().rotate(np.pi, RIGHT)
self.straight_mouth = TexMobject("-").scale(0.7)
for mouth in self.smile, self.frown, self.straight_mouth:
mouth.sort_points(lambda p: p[0])
mouth.highlight(self.color) ##to blend into background
mouth.shift(mouth_center)
self.digest_mobject_attrs()
self.give_smile()
self.add(self.mouth)
self.scale(PI_CREATURE_SCALE_VAL)
def get_parts(self):
return [getattr(self, pn) for pn in self.PART_NAMES]
def get_white_parts(self):
return [
getattr(self, pn)
for pn in self.WHITE_PART_NAMES + self.MOUTH_NAMES
]
def get_mouth_center(self):
result = self.body.get_center()
result[0] = self.eyes.get_center()[0]
return result
# left_center = self.left_eye.get_center()
# right_center = self.right_eye.get_center()
# l_to_r = right_center-left_center
# eyes_to_mouth = rotate_vector(l_to_r, -np.pi/2, OUT)
# eyes_to_mouth /= np.linalg.norm(eyes_to_mouth)
# return left_center/2 + right_center/2 + \
# PI_CREATURE_MOUTH_TO_EYES_DISTANCE*eyes_to_mouth
def highlight(self, color, condition=None):
for part in set(self.get_parts()).difference(self.get_white_parts()):
part.highlight(color, condition)
return self
def move_to(self, destination):
self.shift(destination - self.get_bottom())
return self
def change_mouth_to(self, mouth_name):
#TODO, This is poorly implemented
self.mouth = getattr(self, mouth_name)
self.sub_mobjects = list_update(self.sub_mobjects, self.get_parts())
self.mouth.highlight(WHITE)
return self
def give_smile(self):
return self.change_mouth_to("smile")
def give_frown(self):
return self.change_mouth_to("frown")
def give_straight_face(self):
return self.change_mouth_to("straight_mouth")
def get_eye_center(self):
return self.eyes.get_center()
def make_mean(self):
eye_x, eye_y = self.get_eye_center()[:2]
def should_delete((x, y, z)):
return y - eye_y > 0.3 * abs(x - eye_x)
self.eyes.highlight("black", should_delete)
self.give_straight_face()
return self
def make_sad(self):
eye_x, eye_y = self.get_eye_center()[:2]
eye_y += 0.15
def should_delete((x, y, z)):
return y - eye_y > -0.3 * abs(x - eye_x)
self.eyey.highlight("black", should_delete)
self.give_frown()
return self
def get_step_intermediate(self, pi_creature):
vect = pi_creature.get_center() - self.get_center()
result = self.copy().shift(vect / 2.0)
left_forward = vect[0] > 0
if self.right_leg.get_center()[0] < self.left_leg.get_center()[0]:
#For Mortimer's case
left_forward = not left_forward
if left_forward:
result.left_leg.wag(vect / 2.0, DOWN)
result.right_leg.wag(-vect / 2.0, DOWN)
else:
result.right_leg.wag(vect / 2.0, DOWN)
result.left_leg.wag(-vect / 2.0, DOWN)
return result
def blink(self):
bottom = self.eyes.get_bottom()
self.eyes.apply_function(lambda (x, y, z): (x, bottom[1], z))
return self
def shift_eyes(self):
for eye in self.left_eye, self.right_eye:
eye.rotate_in_place(np.pi, UP)
return self
def to_symbol(self):
Mobject.__init__(
self,
*list(set(self.get_parts()).difference(self.get_white_parts())))
class FormalDefinitionOfContinuity(Scene):
def construct(self):
self.setup()
self.label_spaces()
self.move_dot()
self.label_jump()
self.draw_circles()
self.vary_circle_sizes()
self.discontinuous_point()
def setup(self):
self.input_color = YELLOW_C
self.output_color = RED
def spiril(t):
theta = 2*np.pi*t
return t*np.cos(theta)*RIGHT+t*np.sin(theta)*UP
self.spiril1 = ParametricFunction(
lambda t : 1.5*RIGHT + DOWN + 2*spiril(t),
density = 5*DEFAULT_POINT_DENSITY_1D,
)
self.spiril2 = ParametricFunction(
lambda t : 5.5*RIGHT + UP - 2*spiril(1-t),
density = 5*DEFAULT_POINT_DENSITY_1D,
)
Mobject.align_data(self.spiril1, self.spiril2)
self.output = Mobject(self.spiril1, self.spiril2)
self.output.ingest_sub_mobjects()
self.output.highlight(GREEN_A)
self.interval = UnitInterval()
self.interval.scale_to_fit_width(SPACE_WIDTH-1)
self.interval.to_edge(LEFT)
self.input_dot = Dot(color = self.input_color)
self.output_dot = self.input_dot.copy().highlight(self.output_color)
left, right = self.interval.get_left(), self.interval.get_right()
self.input_homotopy = lambda (x, y, z, t) : (x, y, t) + interpolate(left, right, t)
output_size = self.output.get_num_points()-1
output_points = self.output.points
self.output_homotopy = lambda (x, y, z, t) : (x, y, z) + output_points[int(t*output_size)]
def get_circles_and_points(self, min_input, max_input):
input_left, input_right = [
self.interval.number_to_point(num)
for num in min_input, max_input
]
input_circle = Circle(
radius = np.linalg.norm(input_left-input_right)/2,
color = WHITE
)
input_circle.shift((input_left+input_right)/2)
input_points = Line(
input_left, input_right,
color = self.input_color
)
output_points = Mobject(color = self.output_color)
n = self.output.get_num_points()
output_points.add_points(
self.output.points[int(min_input*n):int(max_input*n)]
)
output_center = output_points.points[int(0.5*output_points.get_num_points())]
max_distance = np.linalg.norm(output_center-output_points.points[-1])
output_circle = Circle(
radius = max_distance,
color = WHITE
)
output_circle.shift(output_center)
return (
input_circle,
input_points,
output_circle,
output_points
)
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 move_dot(self):
kwargs = {
"rate_func" : None,
"run_time" : 3
}
self.play(
Homotopy(self.input_homotopy, self.input_dot, **kwargs),
Homotopy(self.output_homotopy, self.output_dot, **kwargs),
ShowCreation(self.output, **kwargs)
)
self.dither()
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 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 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 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 continuous_point(self):
pass
