def summarize_pattern(*radians):
sc = Scene()
circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
sc.add(circle)
points = [
(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
for angle in radians
]
dots = [Dot(point) for point in points]
last_num = None
for x in xrange(len(points)):
new_lines = Mobject(*[
Line(points[x], points[y]) for y in xrange(x)
])
num = TexMobject(str(moser_function(x + 1))).center()
sc.animate(
Transform(last_num, num) if last_num else ShowCreation(num),
FadeIn(new_lines),
FadeIn(dots[x]),
run_time = 0.5,
)
sc.remove(last_num)
last_num = num
sc.add(num, dots[x], new_lines)
sc.dither()
return sc
def next_few_videos(*radians):
sc = Scene()
circle = Circle(density=CIRCLE_DENSITY).scale(RADIUS)
points = [(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
for angle in radians]
dots = Mobject(*[Dot(point) for point in points])
lines = Mobject(*[
Line(point1, point2) for point1, point2 in it.combinations(points, 2)
])
thumbnail = Mobject(circle, dots, lines)
frame = VideoIcon().highlight("black",
lambda point: np.linalg.norm(point) < 0.5)
big_frame = deepcopy(frame).scale(SPACE_WIDTH)
frame.shift((-5, 0, 0))
sc.add(thumbnail)
sc.dither()
sc.animate(
Transform(big_frame, frame),
Transform(thumbnail,
deepcopy(thumbnail).scale(0.15).shift((-5, 0, 0))))
sc.add(frame, thumbnail)
sc.dither()
last = frame
for x in [-2, 1, 4]:
vi = VideoIcon().shift((x, 0, 0))
sc.animate(
Transform(deepcopy(last), vi),
Animation(thumbnail) #Keeps it from getting burried
)
sc.add(vi)
last = vi
return sc
def different_points(radians1, radians2):
sc = Scene()
circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
sc.add(circle)
points1, points2 = (
[
(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
for angle in radians
]
for radians in (radians1, radians2)
)
dots1, dots2 = (
Mobject(*[Dot(point) for point in points])
for points in (points1, points2)
)
lines1, lines2 = (
[
Line(point1, point2)
for point1, point2 in it.combinations(points, 2)
]
for points in (points1, points2)
)
sc.add(dots1, *lines1)
sc.animate(
Transform(dots1, dots2, run_time = 3),
*[
Transform(line1, line2, run_time = 3)
for line1, line2 in zip(lines1, lines2)
]
)
sc.dither()
return sc
def logo_to_circle():
from generate_logo import DARK_BROWN, LOGO_RADIUS
sc = Scene()
small_circle = Circle(density=CIRCLE_DENSITY,
color='skyblue').scale(LOGO_RADIUS).highlight(
DARK_BROWN, lambda (x, y, z): x < 0 and y > 0)
big_circle = Circle(density=CIRCLE_DENSITY).scale(RADIUS)
sc.add(small_circle)
sc.dither()
sc.animate(Transform(small_circle, big_circle))
return sc
def logo_to_circle():
from generate_logo import DARK_BROWN, LOGO_RADIUS
sc = Scene()
small_circle = Circle(
density = CIRCLE_DENSITY,
color = 'skyblue'
).scale(LOGO_RADIUS).highlight(
DARK_BROWN, lambda (x, y, z) : x < 0 and y > 0
)
big_circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
sc.add(small_circle)
sc.dither()`
sc.animate(Transform(small_circle, big_circle))
return sc
def interesting_problems():
sc = Scene()
locales = [(6, 2, 0), (6, -2, 0), (-5, -2, 0)]
fermat = Mobject(*TexMobjects(["x^n","+","y^n","=","z^n"]))
fermat.scale(0.5).shift((-2.5, 0.7, 0))
face = SimpleFace()
tb = ThoughtBubble().shift((-1.5, 1, 0))
sb = SpeechBubble().shift((-2.4, 1.3, 0))
fermat_copies, face_copies, tb_copies, sb_copies = (
Mobject(*[
deepcopy(mob).scale(0.5).shift(locale)
for locale in locales
])
for mob in [fermat, face, tb, sb]
)
sc.add(face, tb)
sc.animate(ShowCreation(fermat, run_time = 1))
sc.add(fermat)
sc.dither()
sc.animate(
Transform(
deepcopy(fermat).repeat(len(locales)),
fermat_copies
),
FadeIn(face_copies, run_time = 1.0)
)
sc.animate(FadeIn(tb_copies))
sc.dither()
sc.animate(
Transform(tb, sb),
Transform(tb_copies, sb_copies)
)
return sc
def response_invitation():
sc = Scene()
video_icon = VideoIcon()
mini_videos = Mobject(
*
[deepcopy(video_icon).scale(0.5).shift((3, y, 0)) for y in [-2, 0, 2]])
comments = Mobject(*[
Line((-1.2, y, 0), (1.2, y, 0), color='white')
for y in [-1.5, -1.75, -2]
])
sc.add(video_icon)
sc.dither()
sc.animate(Transform(deepcopy(video_icon).repeat(3), mini_videos))
sc.add(mini_videos)
sc.dither()
sc.animate(ShowCreation(comments, run_time=1.0))
return sc
def next_few_videos(*radians):
sc = Scene()
circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
points = [
(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
for angle in radians
]
dots = Mobject(*[
Dot(point) for point in points
])
lines = Mobject(*[
Line(point1, point2)
for point1, point2 in it.combinations(points, 2)
])
thumbnail = Mobject(circle, dots, lines)
frame = VideoIcon().highlight(
"black",
lambda point : np.linalg.norm(point) < 0.5
)
big_frame = deepcopy(frame).scale(SPACE_WIDTH)
frame.shift((-5, 0, 0))
sc.add(thumbnail)
sc.dither()
sc.animate(
Transform(big_frame, frame),
Transform(
thumbnail,
deepcopy(thumbnail).scale(0.15).shift((-5, 0, 0))
)
)
sc.add(frame, thumbnail)
sc.dither()
last = frame
for x in [-2, 1, 4]:
vi = VideoIcon().shift((x, 0, 0))
sc.animate(
Transform(deepcopy(last), vi),
Animation(thumbnail)#Keeps it from getting burried
)
sc.add(vi)
last = vi
return sc
def response_invitation():
sc = Scene()
video_icon = VideoIcon()
mini_videos = Mobject(*[
deepcopy(video_icon).scale(0.5).shift((3, y, 0))
for y in [-2, 0, 2]
])
comments = Mobject(*[
Line((-1.2, y, 0), (1.2, y, 0), color = 'white')
for y in [-1.5, -1.75, -2]
])
sc.add(video_icon)
sc.dither()
sc.animate(Transform(deepcopy(video_icon).repeat(3), mini_videos))
sc.add(mini_videos)
sc.dither()
sc.animate(ShowCreation(comments, run_time = 1.0))
return sc
def connect_points(*radians):
sc = Scene()
circle = Circle(density=CIRCLE_DENSITY).scale(RADIUS)
sc.add(circle)
points = [(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
for angle in radians]
dots = [Dot(point) for point in points]
sc.add(*dots)
anims = []
all_lines = []
for x in xrange(len(points)):
lines = [Line(points[x], points[y]) for y in range(len(points))]
lines = Mobject(*lines)
anims.append(Transform(deepcopy(dots[x]), lines, run_time=3.0))
all_lines.append(lines)
sc.animate(*anims)
sc.add(*all_lines)
sc.dither()
return sc
def connect_points(*radians):
sc = Scene()
circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
sc.add(circle)
points = [
(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
for angle in radians
]
dots = [Dot(point) for point in points]
sc.add(*dots)
anims = []
all_lines = []
for x in xrange(len(points)):
lines = [Line(points[x], points[y]) for y in range(len(points))]
lines = Mobject(*lines)
anims.append(Transform(deepcopy(dots[x]), lines, run_time = 3.0))
all_lines.append(lines)
sc.animate(*anims)
sc.add(*all_lines)
sc.dither()
return sc
def count_sections(*radians):
sc = Scene()
circle = Circle(density = CIRCLE_DENSITY).scale(RADIUS)
sc.add(circle)
points = [
(RADIUS * np.cos(angle), RADIUS * np.sin(angle), 0)
for angle in radians
]
dots = [Dot(point) for point in points]
interior = Region(lambda x, y : x**2 + y**2 < RADIUS**2)
for x in xrange(1, len(points)):
if x == 1:
sc.animate(ShowCreation(dots[0]), ShowCreation(dots[1]))
sc.add(dots[0], dots[1])
else:
sc.animate(ShowCreation(dots[x]))
sc.add(dots[x])
new_lines = Mobject(*[
Line(points[x], points[y]) for y in xrange(x)
])
sc.animate(Transform(deepcopy(dots[x]), new_lines, run_time = 2.0))
sc.add(new_lines)
sc.dither()
regions = plane_partition_from_points(*points[:x+1])
for reg in regions:
reg.intersect(interior)
regions = filter(lambda reg : reg.bool_grid.any(), regions)
last_num = None
for reg, count in zip(regions, it.count(1)):
number = TexMobject(str(count)).shift((RADIUS, 3, 0))
sc.highlight_region(reg)
rt = 1.0 / (x**0.8)
sc.add(number)
sc.remove(last_num)
last_num = number
sc.dither(rt)
sc.reset_background()
sc.remove(last_num)
sc.animate(Transform(last_num, deepcopy(last_num).center()))
sc.dither()
sc.remove(last_num)
return sc
