Merge branch 'master' of github.com:3b1b/manim into alt-calc

This commit is contained in:
Grant Sanderson 2018-05-14 18:42:48 -07:00
commit 53abc18be2
19 changed files with 890 additions and 210 deletions

View file

@ -3,7 +3,7 @@ from active_projects.eop.reusable_imports import *
class ShuffleThroughAllSequences(Scene):
CONFIG = {
"nb_coins" : 14,
"nb_coins" : 20,
"run_time" : 5,
"fps" : int(1.0/PRODUCTION_QUALITY_FRAME_DURATION),
"coin_size" : 0.5,
@ -31,7 +31,8 @@ class ShuffleThroughAllSequences(Scene):
radius = self.coin_size * 0.5,
spacing = self.coin_spacing)
self.add(idle_part, left_idle_part)
#self.add(idle_part, left_idle_part)
self.add(left_idle_part)
last_coin_seq = VGroup()
for i in range(2**nb_relevant_coins):
@ -46,7 +47,7 @@ class ShuffleThroughAllSequences(Scene):
spacing = self.coin_spacing)
coin_seq.next_to(idle_part, LEFT, buff = self.coin_spacing - self.coin_size)
left_idle_part.next_to(coin_seq, LEFT, buff = self.coin_spacing - self.coin_size)
all_coins = VGroup(left_idle_part, coin_seq, idle_part)
all_coins = VGroup(left_idle_part, coin_seq) #, idle_part)
all_coins.center()
self.remove(last_coin_seq)
self.add(coin_seq)

View file

@ -203,7 +203,7 @@ class IllustrateAreaModelBayes(Scene):
# solve formula for P(B|A)
rearranged_formula = TexMobject(["P(B\mid A)", "=", "{P(A\\text{ and }B) \over P(A)}"])
rearranged_formula = TexMobject("P(B\mid A)", "=", "{P(A\\text{ and }B) \over P(A)}")
rearranged_formula.move_to(indep_formula)
self.wait()

View file

@ -152,7 +152,7 @@ class BrickRowScene(PiCreatureScene):
def merge_tallies(self, row, target_pos = UP):
r = row.subdiv_level
if np.all(target_pos == DOWN):
@ -218,7 +218,8 @@ class BrickRowScene(PiCreatureScene):
def construct(self):
self.force_skipping()
randy = self.get_primary_pi_creature()
randy = randy.scale(0.5).move_to(3*DOWN + 6*LEFT)
#self.add(randy)
@ -312,31 +313,57 @@ class BrickRowScene(PiCreatureScene):
new_tails[i].shift(COIN_SEQUENCE_SPACING * DOWN)
self.play(FadeIn(new_tails))
decimal_tallies = VGroup()
# introduce notion of tallies
for (i, rect) in enumerate(self.row.get_rects_for_level(2)):
tally = DecimalTally(2-i, i)
tally.next_to(rect, UP)
decimal_tallies.add(tally)
self.play(FadeIn(tally))
self.wait()
self.add_foreground_mobject(single_flip_labels)
self.add_foreground_mobject(new_heads)
self.add_foreground_mobject(single_flip_labels_copy)
self.add_foreground_mobject(new_tails)
# show individual outcomes
outcomes = self.row.get_outcome_rects_for_level(2, with_labels = False)
# get individual outcomes
outcomes = self.row.get_outcome_rects_for_level(2, with_labels = False,
inset = True)
grouped_outcomes = VGroup(outcomes[0], outcomes[1:3], outcomes[3])
decimal_tallies = VGroup()
# introduce notion of tallies
rects = self.row.get_rects_for_level(2)
rect = rects[0]
tally = DecimalTally(2,0)
tally.next_to(rect, UP)
decimal_tallies.add(tally)
self.play(
LaggedStart(FadeIn, outcomes)
FadeIn(tally),
FadeIn(grouped_outcomes[0])
)
self.wait()
rect = rects[1]
tally = DecimalTally(1,1)
tally.next_to(rect, UP)
decimal_tallies.add(tally)
self.play(
LaggedStart(FadeOut, outcomes),
FadeIn(tally),
FadeOut(grouped_outcomes[0]),
FadeIn(grouped_outcomes[1])
)
self.wait()
rect = rects[2]
tally = DecimalTally(0,2)
tally.next_to(rect, UP)
decimal_tallies.add(tally)
self.play(
FadeIn(tally),
FadeOut(grouped_outcomes[1]),
FadeIn(grouped_outcomes[2])
)
self.wait()
self.play(
FadeOut(grouped_outcomes[2])
)
self.wait()
self.wait()
self.play(
FadeOut(single_flip_labels),
@ -346,7 +373,6 @@ class BrickRowScene(PiCreatureScene):
)
self.wait()
self.tallies = VGroup()
for (i, rect) in enumerate(self.row.get_rects_for_level(2)):
tally = TallyStack(2-i, i, show_decimals = False)
@ -386,7 +412,8 @@ class BrickRowScene(PiCreatureScene):
# CALLBACK TO SEQUENCES #
# # # # # # # # # # # # #
outcomes = self.row.get_outcome_rects_for_level(2, with_labels = True)
outcomes = self.row.get_outcome_rects_for_level(2, with_labels = True,
inset = True)
subdivs = self.row.get_sequence_subdivs_for_level(2)
self.play(
FadeIn(outcomes),
@ -396,7 +423,8 @@ class BrickRowScene(PiCreatureScene):
self.wait()
rect_to_dice = outcomes[1]
rect_to_dice = self.row.get_outcome_rects_for_level(2, with_labels = False,
inset = False)[1]
N = 10
dice_width = rect_to_dice.get_width()/N
dice_height = rect_to_dice.get_height()/N
@ -419,9 +447,8 @@ class BrickRowScene(PiCreatureScene):
self.play(
LaggedStart(FadeIn, all_dice),
FadeOut(rect_to_dice.label)
FadeOut(outcomes[1])
)
self.wait()
table = Ellipse(width = 1.5, height = 1)
@ -455,7 +482,6 @@ class BrickRowScene(PiCreatureScene):
run_time = 0.05)
)
self.wait()
self.play(
@ -513,14 +539,17 @@ class BrickRowScene(PiCreatureScene):
self.clear()
self.add(randy, self.row, old_row)
self.add_foreground_mobject(self.tallies)
self.add_foreground_mobject(self.tallies_copy)
self.play(
self.row.fade, 0.7,
old_row.fade, 0.7,
FadeOut(self.tallies),
FadeOut(self.tallies_copy),
)
# # # # # # # # # # # # # # # # #
# SHOW SPLITTING WITH OUTCOMES #
# # # # # # # # # # # # # # # # #
@ -685,36 +714,35 @@ class BrickRowScene(PiCreatureScene):
#rate_func = there_and_back_with_pause,
run_time = 5))
self.wait()
braces = VGroup(*[Brace(rect, UP) for rect in self.row.rects])
counts = [choose(3, i) for i in range(4)]
probs = VGroup(*[TexMobject("{" + str(k) + "\over 8}") for k in counts])
for (brace, prob) in zip(braces, probs):
prob.next_to(brace, UP)
self.play(
LaggedStart(ShowCreation, braces),
LaggedStart(Write, probs)
)
self.wait()
self.play(LaggedStart(
FadeOut, outcomes,
#rate_func = there_and_back_with_pause,
run_time = 5))
self.wait()
self.play(FadeIn(self.tallies))
brace1 = Brace(self.row.rects[2], UP)
brace2 = Brace(self.row.rects[3], UP)
p1 = TexMobject("{3\over 8}").next_to(brace1, UP)
p2 = TexMobject("{1\over 8}").next_to(brace2, UP)
run_time = 5),
)
self.play(
ShowCreation(brace1),
ShowCreation(brace2),
Write(p1),
Write(p2),
FadeIn(self.tallies)
)
self.wait()
self.play(
FadeOut(brace1),
FadeOut(brace2),
FadeOut(p1),
FadeOut(p2),
FadeOut(braces),
FadeOut(probs)
)
self.wait()
# put visuals for other probability distribtuions here
@ -762,6 +790,9 @@ class BrickRowScene(PiCreatureScene):
self.wait()
self.row = self.merge_rects_by_subdiv(self.row)
self.revert_to_original_skipping_status()
self.wait()
@ -805,23 +836,16 @@ class BrickRowScene(PiCreatureScene):
index = 0
old_tally_sizes = [choose(n,i) for i in range(n + 1)]
new_tally_sizes = [choose(n + 1,i) for i in range(n + 2)]
for i in range(n + 2):
size = new_tally_sizes[i]
grouped_target_outcomes.add(VGroup(target_outcomes[index:index + size]))
index += size
self.play(
Transform(grouped_outcomes[k][0],grouped_target_outcomes[k][0][old_tally_sizes[k - 1]:])
)
self.play(
Transform(grouped_outcomes_copy[k][0],grouped_target_outcomes[k + 1][0][:old_tally_sizes[k]])
)
old_tally_sizes.append(0) # makes the edge cases work properly
# split the other tallies
for i in range(k) + range(k + 1, n + 1):
# split all tallies
for i in range(n + 1):
self.play(
Transform(grouped_outcomes[i][0],
grouped_target_outcomes[i][0][old_tally_sizes[i - 1]:]
@ -830,7 +854,7 @@ class BrickRowScene(PiCreatureScene):
grouped_target_outcomes[i + 1][0][:old_tally_sizes[i]]
)
)
return
self.wait()
@ -894,6 +918,7 @@ class BrickRowScene(PiCreatureScene):
self.play(FadeOut(new_tallies))
self.clear()
self.row = BrickRow(3)
self.add(randy, self.row)
@ -923,6 +948,227 @@ class BrickRowScene(PiCreatureScene):
class ShowProbsInBrickRow3(BrickRowScene):
def construct(self):
randy = self.get_primary_pi_creature()
randy = randy.scale(0.5).move_to(3*DOWN + 6*LEFT)
#self.add(randy)
self.row = BrickRow(3, height = 2, width = 10)
self.wait()
self.add(self.row)
tallies = VGroup()
for (i, rect) in enumerate(self.row.get_rects_for_level(3)):
tally = TallyStack(3-i, i, show_decimals = False)
tally.move_to(rect)
tallies.add(tally)
self.add(tallies)
self.wait(6)
braces = VGroup(*[Brace(rect, UP) for rect in self.row.rects])
counts = [choose(3, i) for i in range(4)]
probs = VGroup(*[TexMobject("{" + str(k) + "\over 8}") for k in counts])
for (brace, prob) in zip(braces, probs):
prob.next_to(brace, UP)
self.wait()
self.play(
LaggedStart(ShowCreation, braces, run_time = 3),
LaggedStart(Write, probs, run_time = 3)
)
self.wait()
self.play(FadeOut(braces),FadeOut(probs))
class ShowOutcomesInBrickRow4(BrickRowScene):
def construct(self):
randy = self.get_primary_pi_creature()
randy = randy.scale(0.5).move_to(3*DOWN + 6*LEFT)
#self.add(randy)
self.row = BrickRow(3, height = 2, width = 10)
previous_row = self.row.copy()
v = 1.25 * self.row.height * UP
self.play(
previous_row.shift, v,
)
self.add(self.row)
self.add(previous_row)
self.wait()
previous_outcomes = previous_row.get_outcome_rects_for_level(3,
with_labels = True, inset = True)
previous_outcomes_copy = previous_outcomes.copy()
self.play(
LaggedStart(FadeIn, previous_outcomes),
LaggedStart(FadeIn, previous_outcomes_copy),
)
self.wait()
new_outcomes = self.row.get_outcome_rects_for_level(4,
with_labels = True, inset = True)
# remove each last coin
new_outcomes_left = VGroup(
new_outcomes[0],
new_outcomes[2],
new_outcomes[3],
new_outcomes[4],
new_outcomes[8],
new_outcomes[9],
new_outcomes[10],
new_outcomes[14]
)
new_outcomes_right = VGroup(
new_outcomes[1],
new_outcomes[5],
new_outcomes[6],
new_outcomes[7],
new_outcomes[11],
new_outcomes[12],
new_outcomes[13],
new_outcomes[15]
)
heads_labels = VGroup(*[outcome.label[-1] for outcome in new_outcomes_left])
tails_labels = VGroup(*[outcome.label[-1] for outcome in new_outcomes_right])
heads_labels.save_state()
tails_labels.save_state()
for outcome in new_outcomes:
outcome.label[-1].fade(1)
run_time = 0.5
self.play(Transform(previous_outcomes[0], new_outcomes_left[0], run_time = run_time))
self.play(Transform(previous_outcomes[1:4], new_outcomes_left[1:4], run_time = run_time))
self.play(Transform(previous_outcomes[4:7], new_outcomes_left[4:7], run_time = run_time))
self.play(Transform(previous_outcomes[7], new_outcomes_left[7], run_time = run_time))
self.play(heads_labels.restore)
self.play(Transform(previous_outcomes_copy[0], new_outcomes_right[0], run_time = run_time))
self.play(Transform(previous_outcomes_copy[1:4], new_outcomes_right[1:4], run_time = run_time))
self.play(Transform(previous_outcomes_copy[4:7], new_outcomes_right[4:7], run_time = run_time))
self.play(Transform(previous_outcomes_copy[7], new_outcomes_right[7], run_time = run_time))
self.play(tails_labels.restore)
self.wait()
anims = [FadeOut(previous_outcomes),FadeOut(previous_outcomes_copy)]
for outcome in new_outcomes_left:
anims.append(FadeOut(outcome.label[-1]))
for outcome in new_outcomes_right:
anims.append(FadeOut(outcome.label[-1]))
self.play(*anims)
self.wait()
class SplitTalliesIntoBrickRow4(BrickRowScene):
def construct(self):
randy = self.get_primary_pi_creature()
randy = randy.scale(0.5).move_to(3*DOWN + 6*LEFT)
#self.add(randy)
self.row = BrickRow(3, height = 2, width = 10)
previous_row = self.row.copy()
v = 1.25 * self.row.height * UP
self.play(
previous_row.shift, v,
)
tallies = VGroup()
for (i, rect) in enumerate(previous_row.get_rects_for_level(3)):
tally = TallyStack(3-i, i, show_decimals = True)
tally.move_to(rect)
tallies.add(tally)
moving_tallies_left = tallies.copy()
moving_tallies_right = tallies.copy()
self.add(self.row, previous_row)
self.add_foreground_mobject(tallies)
self.add_foreground_mobject(moving_tallies_left)
self.add_foreground_mobject(moving_tallies_right)
self.play(SplitRectsInBrickWall(self.row))
anims = []
for (tally, rect) in zip(moving_tallies_left, previous_row.rects):
anims.append(tally.move_to)
anims.append(rect.get_center() + rect.get_width() * 0.25 * LEFT)
self.play(*anims)
new_tallies_left = VGroup()
for (i, tally) in enumerate(moving_tallies_left):
new_tally = TallyStack(4-i,i, with_labels = True)
new_tally.move_to(tally)
new_tallies_left.add(new_tally)
self.play(Transform(moving_tallies_left, new_tallies_left))
anims = []
for (tally, rect) in zip(moving_tallies_right, previous_row.rects):
anims.append(tally.move_to)
anims.append(rect.get_center() + rect.get_width() * 0.25 * RIGHT)
self.play(*anims)
new_tallies_right = VGroup()
for (i, tally) in enumerate(moving_tallies_right):
new_tally = TallyStack(3-i,i+1, with_labels = True)
new_tally.move_to(tally)
new_tallies_right.add(new_tally)
self.play(Transform(moving_tallies_right, new_tallies_right))
hypothetical_new_row = BrickRow(4, height = 2, width = 10)
anims = []
for (tally, rect) in zip(moving_tallies_left[1:], hypothetical_new_row.rects[1:-1]):
anims.append(tally.move_to)
anims.append(rect)
for (tally, rect) in zip(moving_tallies_right[:-1], hypothetical_new_row.rects[1:-1]):
anims.append(tally.move_to)
anims.append(rect)
self.play(*anims)
self.wait()
self.row = self.merge_rects_by_subdiv(self.row)
self.wait()
self.row = self.merge_rects_by_coloring(self.row)
self.wait()

View file

@ -3,7 +3,12 @@ from big_ol_pile_of_manim_imports import *
from active_projects.eop.reusable_imports import *
from active_projects.eop.chapter1.brick_row_scene import BrickRowScene
class EntireBrickWall(BrickRowScene):
class EntireBrickWall(BrickRowScene, MovingCameraScene):
def setup(self):
super(BrickRowScene, self).setup()
super(PiCreatureScene, self).setup()
def construct(self):
@ -45,7 +50,6 @@ class EntireBrickWall(BrickRowScene):
rows.submobjects[-1] = self.merge_rects_by_coloring(rows[-1])
# draw indices under the last row for the number of tails
tails_counters = VGroup()
for (i, rect) in enumerate(rows[-1].rects):
@ -83,6 +87,7 @@ class EntireBrickWall(BrickRowScene):
last_row_rect = SurroundingRectangle(rows[-1], buff = 0)
last_row_rect.set_stroke(color = YELLOW, width = 6)
rows.save_state()
self.play(
rows.fade, 0.9,
ShowCreation(last_row_rect)
@ -102,24 +107,40 @@ class EntireBrickWall(BrickRowScene):
highlighted_brick(row = 20, nb_tails = i)
for i in range(20)
]
self.wait()
self.play(
FadeIn(highlighted_bricks[10])
)
self.wait()
self.play(
FadeOut(highlighted_bricks[10]),
FadeIn(highlighted_bricks[9]),
FadeIn(highlighted_bricks[11]),
)
self.wait()
self.play(
FadeOut(highlighted_bricks[9]),
FadeOut(highlighted_bricks[11]),
FadeIn(highlighted_bricks[8]),
FadeIn(highlighted_bricks[12]),
)
self.wait()
self.play(
FadeOut(highlighted_bricks[8]),
FadeOut(highlighted_bricks[12]),
FadeOut(last_row_rect),
rows.restore,
)
self.wait()
new_frame = self.camera_frame.copy()
new_frame.scale(0.0001).move_to(rows.get_corner(DR))
self.play(
Transform(self.camera_frame, new_frame,
run_time = 9,
rate_func = exponential_decay
)
)

View file

@ -42,8 +42,9 @@ class Introduction(TeacherStudentsScene):
self.wait()
self.get_teacher().change_mode("raise_right_hand")
self.play(
self.get_teacher().change_mode,"raise_right_hand"
)
self.wait()
self.wait(30)

View file

@ -41,17 +41,20 @@ class GenericMorphBrickRowIntoHistogram(Scene):
for rect in self.row.rects:
rect.set_stroke(color = WHITE, width = 3)
self.play(self.row.rects.space_out_submobjects, {"factor" : 1.3})
self.wait()
self.play(
self.row.rects.space_out_submobjects, {"factor" : 1.3},
FadeOut(tallies)
)
self.wait()
anims = []
for brick in self.row.rects:
anims.append(brick.rotate)
anims.append(TAU/4)
if self.show_tallies:
anims.append(FadeOut(tallies))
self.play(*anims)
self.wait()
anims = []
for (i,brick) in enumerate(self.row.rects):
@ -59,6 +62,7 @@ class GenericMorphBrickRowIntoHistogram(Scene):
anims.append(self.bar_anchors[i])
anims.append({"direction" : UP, "buff" : 0})
self.play(*anims)
self.wait()
self.bars.create_outline()
anims = [
@ -68,6 +72,8 @@ class GenericMorphBrickRowIntoHistogram(Scene):
anims.append(FadeIn(self.bars.outline))
self.play(*anims)
self.wait()
class MorphBrickRowIntoHistogram3(GenericMorphBrickRowIntoHistogram):
@ -83,6 +89,8 @@ class MorphBrickRowIntoHistogram3(GenericMorphBrickRowIntoHistogram):
def construct(self):
super(MorphBrickRowIntoHistogram3,self).construct()
@ -115,12 +123,14 @@ class MorphBrickRowIntoHistogram3(GenericMorphBrickRowIntoHistogram):
if i != 0:
y_guide.add(y_guide_label)
y_guides.add(y_guide)
self.wait()
self.play(
FadeIn(y_guides),
Animation(self.bars.outline),
Animation(self.bars)
)
self.wait()
self.play(
FadeIn(x_axis),
@ -137,10 +147,12 @@ class MorphBrickRowIntoHistogram3(GenericMorphBrickRowIntoHistogram):
total_area_group = VGroup(total_area_text, area_decimal)
total_area_group.move_to(2.7 * UP)
self.wait()
self.play(
FadeIn(total_area_text),
)
self.wait()
cumulative_areas = [0.125, 0.5, 0.875, 1]
covering_rects = self.bars.copy()
@ -165,6 +177,7 @@ class MorphBrickRowIntoHistogram3(GenericMorphBrickRowIntoHistogram):
FadeOut(covering_rects),
ShowCreation(total_area_rect)
)
self.wait()
@ -194,12 +207,14 @@ class MorphBrickRowIntoHistogram20(GenericMorphBrickRowIntoHistogram):
nb_tails_label = TextMobject("\# of tails")
nb_tails_label.move_to(5 * RIGHT + 2.5 * DOWN)
self.wait()
self.play(
FadeIn(x_axis),
FadeIn(x_labels),
FadeIn(nb_tails_label)
)
self.wait()
# draw y-guides
@ -221,6 +236,7 @@ class MorphBrickRowIntoHistogram20(GenericMorphBrickRowIntoHistogram):
self.bring_to_back(y_guides)
self.play(FadeIn(y_guides), Animation(self.bars))
self.wait()
histogram_width = self.bars.get_width()
histogram_height = self.bars.get_height()
@ -247,6 +263,7 @@ class MorphBrickRowIntoHistogram20(GenericMorphBrickRowIntoHistogram):
anims.append(ORIGIN)
self.play(*anims)
self.wait()
anims = []
for (guide, i, h) in zip(y_guides, prob_grid, y_guide_heights):
@ -265,6 +282,7 @@ class MorphBrickRowIntoHistogram20(GenericMorphBrickRowIntoHistogram):
anims.append(self.bars.get_bottom())
self.play(*anims)
self.wait()
class MorphBrickRowIntoHistogram100(MorphBrickRowIntoHistogram20):
CONFIG = {

View file

@ -17,19 +17,9 @@ class ProbabilityDistributions(PiCreatureScene):
run_time = 3
text = TextMobject("Probability distributions", color = YELLOW)
text.to_edge(UP)
text_rect = SurroundingRectangle(text, buff = MED_SMALL_BUFF)
self.play(
FadeIn(text),
ShowCreation(text_rect)
)
# WEATHER FORECAST
unit_rect = Rectangle(
height = 3, width = 3
).shift(DOWN)
@ -48,9 +38,9 @@ class ProbabilityDistributions(PiCreatureScene):
sun_rect.set_fill(color = YELLOW, opacity = opacity)
sun_rect.set_stroke(width = 0)
self.play(FadeIn(VGroup(unit_rect, rain_rect, sun_rect)))
self.add(unit_rect, rain_rect, sun_rect)
rain = SVGMobject(file_name = "rain").scale(0.35)
rain = SVGMobject(file_name = "rain").scale(0.25)
sun = SVGMobject(file_name = "sun").scale(0.35)
rain.flip().move_to(rain_rect)
@ -58,6 +48,7 @@ class ProbabilityDistributions(PiCreatureScene):
self.add(rain, sun)
text_scale = 0.7
brace_rain = Brace(rain_rect, UP)
@ -76,72 +67,73 @@ class ProbabilityDistributions(PiCreatureScene):
self.add(brace_rain, p_rain_whole_label, brace_sun, p_sun_whole_label)
self.wait(6)
new_p_rain = 0.68
new_p_sun = 1 - new_p_rain
# new_p_rain = 0.68
# new_p_sun = 1 - new_p_rain
new_rain_rect = unit_rect.copy().stretch(new_p_rain, 0)
new_rain_rect.align_to(unit_rect, LEFT)
new_rain_rect.set_fill(color = BLUE, opacity = opacity)
new_rain_rect.set_stroke(width = 0)
# new_rain_rect = unit_rect.copy().stretch(new_p_rain, 0)
# new_rain_rect.align_to(unit_rect, LEFT)
# new_rain_rect.set_fill(color = BLUE, opacity = opacity)
# new_rain_rect.set_stroke(width = 0)
new_sun_rect = unit_rect.copy().stretch(new_p_sun, 0)
new_sun_rect.next_to(new_rain_rect, RIGHT, buff = 0)
new_sun_rect.set_fill(color = YELLOW, opacity = opacity)
new_sun_rect.set_stroke(width = 0)
# new_sun_rect = unit_rect.copy().stretch(new_p_sun, 0)
# new_sun_rect.next_to(new_rain_rect, RIGHT, buff = 0)
# new_sun_rect.set_fill(color = YELLOW, opacity = opacity)
# new_sun_rect.set_stroke(width = 0)
new_rain = SVGMobject(file_name = "rain").scale(0.35)
new_sun = SVGMobject(file_name = "sun").scale(0.35)
# new_rain = SVGMobject(file_name = "rain").scale(0.35)
# new_sun = SVGMobject(file_name = "sun").scale(0.35)
new_rain.flip().move_to(new_rain_rect)
new_sun.move_to(new_sun_rect)
# new_rain.flip().move_to(new_rain_rect)
# new_sun.move_to(new_sun_rect)
new_brace_rain = Brace(new_rain_rect, UP)
new_p_rain_label = TextMobject("$P($rain$)=$").scale(text_scale)
new_p_rain_decimal = DecimalNumber(new_p_rain).scale(text_scale)
new_p_rain_decimal.next_to(new_p_rain_label)
new_p_rain_whole_label = VGroup(new_p_rain_label, new_p_rain_decimal)
new_p_rain_whole_label.next_to(new_brace_rain, UP)
# new_brace_rain = Brace(new_rain_rect, UP)
# new_p_rain_label = TextMobject("$P($rain$)=$").scale(text_scale)
# new_p_rain_decimal = DecimalNumber(new_p_rain).scale(text_scale)
# new_p_rain_decimal.next_to(new_p_rain_label)
# new_p_rain_whole_label = VGroup(new_p_rain_label, new_p_rain_decimal)
# new_p_rain_whole_label.next_to(new_brace_rain, UP)
new_brace_sun = Brace(new_sun_rect, DOWN)
new_p_sun_label = TextMobject("$P($sunshine$)=$").scale(text_scale)
new_p_sun_decimal = DecimalNumber(new_p_sun).scale(text_scale)
new_p_sun_decimal.next_to(new_p_sun_label)
new_p_sun_whole_label = VGroup(new_p_sun_label, new_p_sun_decimal)
new_p_sun_whole_label.next_to(new_brace_sun, DOWN)
# new_brace_sun = Brace(new_sun_rect, DOWN)
# new_p_sun_label = TextMobject("$P($sunshine$)=$").scale(text_scale)
# new_p_sun_decimal = DecimalNumber(new_p_sun).scale(text_scale)
# new_p_sun_decimal.next_to(new_p_sun_label)
# new_p_sun_whole_label = VGroup(new_p_sun_label, new_p_sun_decimal)
# new_p_sun_whole_label.next_to(new_brace_sun, DOWN)
def rain_update_func(alpha):
return alpha * new_p_rain + (1 - alpha) * p_rain
# def rain_update_func(alpha):
# return alpha * new_p_rain + (1 - alpha) * p_rain
def sun_update_func(alpha):
return 1 - rain_update_func(alpha)
# def sun_update_func(alpha):
# return 1 - rain_update_func(alpha)
update_p_rain = ChangingDecimal(
p_rain_decimal, rain_update_func,
tracked_mobject = p_rain_label,
run_time = run_time
)
update_p_sun = ChangingDecimal(
p_sun_decimal, sun_update_func,
tracked_mobject = p_sun_label,
run_time = run_time
)
# update_p_rain = ChangingDecimal(
# p_rain_decimal, rain_update_func,
# tracked_mobject = p_rain_label,
# run_time = run_time
# )
# update_p_sun = ChangingDecimal(
# p_sun_decimal, sun_update_func,
# tracked_mobject = p_sun_label,
# run_time = run_time
# )
self.play(
Transform(rain_rect, new_rain_rect, run_time = run_time),
Transform(sun_rect, new_sun_rect, run_time = run_time),
Transform(rain, new_rain, run_time = run_time),
Transform(sun, new_sun, run_time = run_time),
Transform(brace_rain, new_brace_rain, run_time = run_time),
Transform(brace_sun, new_brace_sun, run_time = run_time),
Transform(p_rain_label, new_p_rain_label, run_time = run_time),
Transform(p_sun_label, new_p_sun_label, run_time = run_time),
update_p_rain,
update_p_sun
)
# self.play(
# Transform(rain_rect, new_rain_rect, run_time = run_time),
# Transform(sun_rect, new_sun_rect, run_time = run_time),
# Transform(rain, new_rain, run_time = run_time),
# Transform(sun, new_sun, run_time = run_time),
# Transform(brace_rain, new_brace_rain, run_time = run_time),
# Transform(brace_sun, new_brace_sun, run_time = run_time),
# Transform(p_rain_label, new_p_rain_label, run_time = run_time),
# Transform(p_sun_label, new_p_sun_label, run_time = run_time),
# update_p_rain,
# update_p_sun
# )
@ -164,51 +156,7 @@ class ProbabilityDistributions(PiCreatureScene):
FadeOut(p_sun_whole_label),
)
# COIN FLIP
coin_flip_rect = BrickRow(3, height = 2, width = 10)
for (i, brick) in enumerate(coin_flip_rect.rects):
tally = TallyStack(3 - i, i)
tally.move_to(brick)
coin_flip_rect.add(tally)
coin_flip_rect.scale(0.8).shift(2*RIGHT)
self.play(FadeIn(coin_flip_rect))
counts = [1, 3, 3, 1]
braces = VGroup()
labels = VGroup()
for (rect, count) in zip(coin_flip_rect.rects, counts):
label = TexMobject("{" + str(count) + "\over 8}").scale(0.5)
brace = Brace(rect, DOWN)
label.next_to(brace, DOWN)
braces.add(brace)
labels.add(label)
self.play(
LaggedStart(ShowCreation, braces, lag_ratio = lag_ratio, run_time = run_time),
LaggedStart(Write, labels, lag_ratio = lag_ratio, run_time = run_time)
)
coin_flip_rect.add(braces, labels)
coin_flip_rect.target = coin_flip_rect.copy().scale(0.6)
coin_flip_rect.target.to_corner(UR, buff = MED_LARGE_BUFF)
coin_flip_rect.target.shift(DOWN)
self.play(
MoveToTarget(coin_flip_rect)
)
self.play(
FadeOut(braces),
FadeOut(labels)
)
self.wait(3)
# DOUBLE DICE THROW
@ -241,24 +189,25 @@ class ProbabilityDistributions(PiCreatureScene):
for k in range(5 - i)
]))
self.play(
FadeIn(dice_unit_rect),
FadeIn(dice_table.rows)
)
# self.play(
# FadeIn(dice_unit_rect),
# FadeIn(dice_table.rows)
# )
for (cell, label) in zip(dice_table.cells, dice_table.labels):
cell.add(label)
# self.play(
# LaggedStart(FadeIn, dice_table_grouped_cells,
# lag_ratio = lag_ratio, run_time = run_time)
# )
self.play(
LaggedStart(FadeIn, dice_table_grouped_cells,
lag_ratio = lag_ratio, run_time = run_time)
FadeIn(dice_table_grouped_cells),
FadeIn(dice_unit_rect),
FadeIn(dice_table.rows)
)
self.wait()
self.play(
FadeOut(dice_table.rows),
FadeOut(dice_unit_rect),
)
self.wait(3)
self.play(
@ -266,3 +215,104 @@ class ProbabilityDistributions(PiCreatureScene):
rate_func=there_and_back_with_pause,
run_time=run_time
)
dice_table.add(dice_unit_rect)
dice_table_target = dice_table.copy()
dice_table_target.scale(0.5).to_corner(UR, buff = LARGE_BUFF)
dice_table_target.shift(0.4*UP)
self.play(Transform(dice_table, dice_table_target))
self.play(
FadeOut(dice_table.rows),
FadeOut(dice_unit_rect),
)
self.wait(3)
# TITLE
text = TextMobject("Probability distributions", color = YELLOW)
text.to_edge(UP)
text_rect = SurroundingRectangle(text, buff = MED_SMALL_BUFF)
self.play(
FadeIn(text),
ShowCreation(text_rect)
)
self.wait(3)
# COIN FLIP
brick_row = BrickRow(3, height = 2, width = 10)
coin_flip_rect = VGroup(brick_row)
tallies = VGroup()
for (i, brick) in enumerate(brick_row.rects):
tally = TallyStack(3 - i, i)
tally.move_to(brick)
tallies.add(tally)
coin_flip_rect.add(tallies)
coin_flip_rect.scale(0.65).shift(RIGHT)
self.play(FadeIn(coin_flip_rect))
counts = [1, 3, 3, 1]
braces = VGroup()
labels = VGroup()
for (rect, count) in zip(brick_row.rects, counts):
label = TexMobject("{" + str(count) + "\over 8}").scale(0.5)
brace = Brace(rect, DOWN)
label.next_to(brace, DOWN)
braces.add(brace)
labels.add(label)
self.play(
FadeIn(braces),
FadeIn(labels)
)
coin_flip_rect.add(braces, labels)
self.wait(6)
outcomes = brick_row.get_outcome_rects_for_level(3, with_labels = True,
inset = True)
outcomes.scale(0.65)
outcomes.move_to(brick_row.get_center())
outcome_braces = VGroup(*[
Brace(outcome, DOWN) for outcome in outcomes
])
outcome_labels = VGroup(*[
TexMobject("{1\over 8}").scale(0.5).next_to(brace, DOWN)
for brace in outcome_braces
])
self.play(
FadeOut(tallies),
FadeIn(outcomes),
FadeOut(braces),
FadeOut(labels),
FadeIn(outcome_braces),
FadeIn(outcome_labels)
)
self.wait(10)

View file

@ -71,9 +71,11 @@ class QuizResult(PiCreatureScene):
all_quizzes.add(quiz_copy)
master_quiz = get_example_quiz()
self.play(ShowCreation(master_quiz))
self.play(ShowCreation(master_quiz), run_time = 2)
self.wait()
self.play(Transform(master_quiz, all_quizzes[0]))
self.wait()
self.play(LaggedStart(FadeIn,all_quizzes))
grades_mob = VGroup()
@ -83,6 +85,7 @@ class QuizResult(PiCreatureScene):
grades_mob.add(grade_mob)
self.remove(master_quiz)
self.wait()
self.play(
FadeOut(all_quizzes),
FadeIn(grades_mob)
@ -99,13 +102,53 @@ class QuizResult(PiCreatureScene):
slot.scale(0.5).move_to(quiz)
students_points_mob.add(slot)
self.wait()
self.play(
#all_students.fade, 0,
FadeOut(grades_mob),
FadeIn(students_points_mob)
)
all_students.save_state()
students_points_mob.save_state()
self.wait()
randy = all_students[0]
morty = all_students[nb_students_y]
all_other_students = VGroup(*all_students)
all_other_students.remove(randy, morty)
randy_points = students_points_mob[0]
morty_points = students_points_mob[nb_students_y]
all_other_points = VGroup(*students_points_mob)
all_other_points.remove(randy_points, morty_points)
self.play(
all_other_students.fade, 0.8,
all_other_points.fade, 0.8,
)
self.wait()
scale = 1.5
self.play(randy_points.scale,scale)
self.play(randy_points.scale,1.0/scale, morty_points.scale,scale)
self.play(morty_points.scale,1.0/scale)
self.wait()
self.play(
all_students.restore,
students_points_mob.restore,
)
self.wait()
anims = []
for points in students_points_mob:
anims.append(points.scale)
anims.append(scale)
self.play(*anims)
self.wait()
anims = []
for points in students_points_mob:
anims.append(points.scale)
anims.append(1.0/scale)
self.play(*anims)
anims = []
anchor_point = 3 * DOWN + 1 * LEFT
@ -114,6 +157,7 @@ class QuizResult(PiCreatureScene):
anims.append(anchor_point + grade * RIGHT + grades_count * UP)
anims.append(FadeOut(students_points_mob))
self.wait()
self.play(*anims)
grade_labels = VGroup()
@ -125,6 +169,7 @@ class QuizResult(PiCreatureScene):
out_of_label = TextMobject("out of 3", color = highlight_color)
out_of_label.next_to(grade_labels, RIGHT, buff = MED_LARGE_BUFF)
grade_labels.add(out_of_label)
self.wait()
self.play(Write(grade_labels))
grade_hist = Histogram(
@ -138,6 +183,7 @@ class QuizResult(PiCreatureScene):
)
grade_hist.move_to(all_students)
self.wait()
self.play(
FadeIn(grade_hist),
FadeOut(all_students)
@ -145,12 +191,13 @@ class QuizResult(PiCreatureScene):
nb_students_label = TextMobject("\# of students", color = highlight_color)
nb_students_label.move_to(5 * LEFT + 2 * UP)
nb_students_label.move_to(5 * RIGHT + 1 * UP)
arrows = VGroup(*[
Arrow(nb_students_label.get_right(), grade_hist.bars[i].get_center(),
Arrow(nb_students_label.get_left(), grade_hist.bars[i].get_center(),
color = highlight_color)
for i in range(4)
])
self.wait()
self.play(Write(nb_students_label), LaggedStart(GrowArrow,arrows))
percentage_label = TextMobject("\% of students", color = highlight_color)
@ -167,6 +214,7 @@ class QuizResult(PiCreatureScene):
new_label.move_to(label)
anims.append(Transform(label, new_label))
anims.append(ReplacementTransform(nb_students_label, percentage_label))
self.wait()
self.play(*anims)
self.remove(all_quizzes)
@ -177,10 +225,12 @@ class QuizResult(PiCreatureScene):
pi.move_to(x * RIGHT + y * UP)
all_students.scale(0.8)
all_students.to_corner(DOWN + LEFT)
self.wait()
self.play(FadeIn(all_students))
prob_label = TextMobject("probability", color = highlight_color)
prob_label.move_to(percentage_label)
self.wait()
self.play(
all_students[8].set_color, MAROON_E,
#all_students[:8].fade, 0.6,
@ -188,6 +238,7 @@ class QuizResult(PiCreatureScene):
ReplacementTransform(percentage_label, prob_label)
)
self.wait()
self.play(
FadeOut(prob_label),
FadeOut(arrows)
@ -210,6 +261,7 @@ class QuizResult(PiCreatureScene):
rate_func = linear
)
self.wait()
for i in range(3):
self.play(flash_hist, flash_class)
self.remove(flash_hist.prototype_cell)

View file

@ -0,0 +1,145 @@
from big_ol_pile_of_manim_imports import *
class ProbabilityRect(VMobject):
CONFIG = {
"unit_width" : 2,
"unit_height" : 2,
"alignment" : LEFT,
"color": YELLOW,
"opacity": 1.0,
"num_decimal_places": 2,
"use_percent" : False
}
def __init__(self, p0, **kwargs):
VMobject.__init__(self, **kwargs)
self.unit_rect = Rectangle(
width = self.unit_width,
height = self.unit_height,
stroke_color = self.color
)
self.p = p0
self.prob_rect = self.create_prob_rect(p0)
self.prob_label = self.create_prob_label(p0)
self.add(self.unit_rect, self.prob_rect, self.prob_label)
def create_prob_rect(self, p):
prob_width, prob_height = self.unit_width, self.unit_height
if self.alignment in [LEFT, RIGHT]:
prob_width *= p
elif self.alignment in [UP, DOWN]:
prob_height *= p
else:
raise Exception("Aligment must be LEFT, RIGHT, UP or DOWN")
prob_rect = Rectangle(
width = prob_width,
height = prob_height,
fill_color = self.color,
fill_opacity = self.opacity,
stroke_color = self.color
)
prob_rect.align_to(self.unit_rect, direction = self.alignment)
return prob_rect
def create_prob_label(self, p):
if self.use_percent:
prob_label = DecimalNumber(
p * 100,
color = BLACK,
num_decimal_places = self.num_decimal_places,
unit = "\%"
)
else:
prob_label = DecimalNumber(
p,
color = BLACK,
num_decimal_places = self.num_decimal_places,
)
prob_label.move_to(self.prob_rect)
return prob_label
class ChangeProbability(Animation):
def __init__(self, prob_mob, p1, **kwargs):
if not isinstance(prob_mob, ProbabilityRect):
raise Exception("ChangeProportion's mobject must be a ProbabilityRect")
self.p1 = p1
self.p0 = prob_mob.p
Animation.__init__(self, prob_mob, **kwargs)
def update_mobject(self, alpha):
p = (1 - alpha) * self.p0 + alpha * self.p1
self.mobject.remove(self.mobject.prob_rect, self.mobject.prob_label)
self.mobject.prob_rect = self.mobject.create_prob_rect(p)
self.mobject.prob_label = self.mobject.create_prob_label(p)
self.mobject.add(self.mobject.prob_rect, self.mobject.prob_label)
def clean_up(self, surrounding_scene=None):
self.mobject.p = self.p1
super(ChangeProbability, self).clean_up(surrounding_scene = surrounding_scene)
class ShowProbAsProportion(Scene):
def construct(self):
p0 = 0.3
p1 = 1
p2 = 0.18
p3 = 0.64
prob_mob = ProbabilityRect(p0,
unit_width = 4,
unit_height = 2,
use_percent = False,
num_decimal_places = 2
)
self.add(prob_mob)
self.wait()
self.play(
ChangeProbability(prob_mob, p1,
run_time = 3)
)
self.wait(0.5)
self.play(
ChangeProbability(prob_mob, p2,
run_time = 3)
)
self.wait(0.5)
self.play(
ChangeProbability(prob_mob, p3,
run_time = 3)
)

View file

@ -0,0 +1,29 @@
from big_ol_pile_of_manim_imports import *
from active_projects.eop.reusable_imports import *
class StackingCoins(Scene):
def construct(self):
h = t = 0
heads_stack = HeadsStack(size = h)
heads_stack.next_to(0.5*LEFT + 3*DOWN, UP)
tails_stack = TailsStack(size = t)
tails_stack.next_to(0.5*RIGHT + 3*DOWN, UP)
self.add(heads_stack, tails_stack)
for i in range(120):
flip = np.random.choice(["H", "T"])
if flip == "H":
h += 1
new_heads_stack = HeadsStack(size = h)
new_heads_stack.next_to(0.5*LEFT + 3*DOWN, UP)
self.play(Transform(heads_stack, new_heads_stack,
run_time = 0.2))
elif flip == "T":
t += 1
new_tails_stack = TailsStack(size = t)
new_tails_stack.next_to(0.5*RIGHT + 3*DOWN, UP)
self.play(Transform(tails_stack, new_tails_stack,
run_time = 0.2))

View file

@ -0,0 +1,31 @@
from big_ol_pile_of_manim_imports import *
from active_projects.eop.reusable_imports import *
class RandyThinksAboutCoin(PiCreatureScene):
def construct(self):
randy = self.get_primary_pi_creature()
randy.center()
self.add(randy)
self.wait()
h_or_t = BinaryOption(UprightHeads().scale(3), UprightTails().scale(3),
text_scale = 1.5)
self.think(h_or_t, direction = LEFT)
v = 0.3
self.play(
h_or_t[0].shift,v*UP,
h_or_t[2].shift,v*DOWN,
)
self.play(
h_or_t[0].shift,2*v*DOWN,
h_or_t[2].shift,2*v*UP,
)
self.play(
h_or_t[0].shift,v*UP,
h_or_t[2].shift,v*DOWN,
)
self.wait()

View file

@ -0,0 +1,46 @@
from big_ol_pile_of_manim_imports import *
class WhatDoesItReallyMean(TeacherStudentsScene):
CONFIG = {
"default_pi_creature_kwargs": {
"color": MAROON_E,
"flip_at_start": True,
},
}
def construct(self):
student_q = TextMobject("What does", "``probability''", "\emph{actually}", "mean?")
student_q.set_color_by_tex("probability", YELLOW)
self.student_says(student_q, target_mode = "sassy")
self.wait()
self.play(
self.students[1].change_mode, "plain"
)
self.wait()
self.play(RemovePiCreatureBubble(self.students[1]))
self.wait()
self.teacher_says("Don't worry -- philosophy can come later!")
self.wait()
class EmptyTSScene(TeacherStudentsScene):
CONFIG = {
"default_pi_creature_kwargs": {
"color": MAROON_E,
"flip_at_start": True,
},
}
def construct(self):
self.wait()
self.play(*[
ApplyMethod(pi.look_at,ORIGIN) for pi in self.get_pi_creatures()
])
self.wait(8)

View file

@ -2,11 +2,14 @@ from mobject.types.vectorized_mobject import *
from mobject.svg.tex_mobject import *
class BinaryOption(VMobject):
CONFIG = {
"text_scale" : 0.5
}
def __init__(self, mob1, mob2, **kwargs):
VMobject.__init__(self, **kwargs)
text = TextMobject("or").scale(0.5)
text = TextMobject("or").scale(self.text_scale)
mob1.next_to(text, LEFT)
mob2.next_to(text, RIGHT)
self.add(mob1, text, mob2)

View file

@ -6,8 +6,8 @@ from active_projects.eop.reusables.upright_coins import *
class BrickRow(VMobject):
CONFIG = {
"left_color" : RED,
"right_color" : BLUE,
"left_color" : COLOR_HEADS,
"right_color" : COLOR_TAILS,
"height" : 1.0,
"width" : 8.0,
"outcome_shrinkage_factor_x" : 0.95,
@ -104,14 +104,14 @@ class BrickRow(VMobject):
outcome_width = float(self.width) / (2 ** r)
outcome_height = self.height
corner_radius = min(0.1, 0.3 * min(outcome_width, outcome_height))
corner_radius = 0.1 # max(0.1, 0.3 * min(outcome_width, outcome_height))
# this scales down the corner radius for very narrow rects
rect = RoundedRectangle(
width = outcome_width,
height = outcome_height,
corner_radius = corner_radius,
fill_color = WHITE,
fill_opacity = 0.2,
fill_color = OUTCOME_COLOR,
fill_opacity = OUTCOME_OPACITY,
stroke_width = 0
)
rects = VGroup()
@ -179,11 +179,11 @@ class BrickRow(VMobject):
class SplitRectsInBrickWall(AnimationGroup):
def __init__(self, mobject, **kwargs):
#print mobject.height, mobject.get_height()
r = self.subdiv_level = mobject.subdiv_level + 1
subdivs = VGroup()
@ -196,6 +196,7 @@ class SplitRectsInBrickWall(AnimationGroup):
subdiv = DashedLine(
mobject.get_top() + x * RIGHT,
mobject.get_bottom() + x * RIGHT,
dashed_segment_length = 0.05
)
subdivs.add(subdiv)
anims.append(ShowCreation(subdiv))

View file

@ -9,10 +9,16 @@ COIN_STROKE_WIDTH = 2
COIN_SEQUENCE_SPACING = 0.1
GRADE_COLOR_1 = COLOR_HEADS = RED
GRADE_COLOR_2 = COLOR_TAILS = BLUE_E
GRADE_COLOR_1 = COLOR_HEADS = RED_E
GRADE_COLOR_2 = COLOR_TAILS = BLUE_C
COLOR_HEADS_COIN = RED
COLOR_TAILS_COIN = BLUE_E
TALLY_BACKGROUND_WIDTH = 1.0
TALLY_BACKGROUND_COLOR = BLACK
SICKLY_GREEN = "#9BBD37"
SICKLY_GREEN = "#9BBD37"
OUTCOME_COLOR = WHITE
OUTCOME_OPACITY = 0.5

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@ -24,13 +24,13 @@ class UprightCoin(Circle):
class UprightHeads(UprightCoin):
CONFIG = {
"fill_color": COLOR_HEADS,
"fill_color": COLOR_HEADS_COIN,
"symbol": "H",
}
class UprightTails(UprightCoin):
CONFIG = {
"fill_color": COLOR_TAILS,
"fill_color": COLOR_TAILS_COIN,
"symbol": "T",
}
@ -120,13 +120,13 @@ class FlatCoin(UprightCoin):
class FlatHeads(FlatCoin):
CONFIG = {
"fill_color": COLOR_HEADS,
"fill_color": COLOR_HEADS_COIN,
"symbol": "H",
}
class FlatTails(FlatCoin):
CONFIG = {
"fill_color": COLOR_TAILS,
"fill_color": COLOR_TAILS_COIN,
"symbol": "T",
}

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@ -16,6 +16,15 @@ class WhatDoesItReallyMean(TeacherStudentsScene):
student_q.set_color_by_tex("probability", YELLOW)
self.student_says(student_q, target_mode = "sassy")
self.wait()
question_bubble = VGroup(student_q, students[1].bubble)
scaled_qb = question_bubble.copy()
scaled_qb.scale(0.4).to_corner(UL)
self.play(Transform(question_bubble, scaled_qb))
self.wait()
self.teacher_says("Don't worry -- philosophy can come later!")
self.wait()

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@ -458,9 +458,9 @@ class Bubble(SVGMobject):
def pin_to(self, mobject):
mob_center = mobject.get_center()
want_to_filp = np.sign(mob_center[0]) != np.sign(self.direction[0])
want_to_flip = np.sign(mob_center[0]) != np.sign(self.direction[0])
can_flip = not self.direction_was_specified
if want_to_filp and can_flip:
if want_to_flip and can_flip:
self.flip()
boundary_point = mobject.get_critical_point(UP - self.direction)
vector_from_center = 1.0 * (boundary_point - mob_center)

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@ -82,3 +82,24 @@ def squish_rate_func(func, a=0.4, b=0.6):
def lingering(t):
return squish_rate_func(lambda t: t, 0, 0.8)(t)
def exponential_decay(t, half_life = 0.1):
# The half-life should be rather small to minimize the cut-off error at the end
return 1 - np.exp(-t/half_life)