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synced 2025-07-30 13:34:19 +08:00
Finally, some work on the beta video
This commit is contained in:
Grant Sanderson
@ -1,9 +1,10 @@
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from manimlib.imports import *
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from from_3b1b.active.bayes.beta_helpers import *
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OUTPUT_DIRECTORY = "bayes/beta"
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class BarChart(Axes):
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class Histogram(Axes):
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CONFIG = {
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"x_min": 0,
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"x_max": 10,
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@ -72,7 +73,6 @@ class BarChart(Axes):
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pass
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# Bar manipulations
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# Scenes
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@ -81,3 +81,239 @@ class BarChartTest(Scene):
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bar_chart = BarChart()
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bar_chart.to_edge(DOWN)
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self.add(bar_chart)
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class Thumbnail(Scene):
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def construct(self):
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t2c = {
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"95\\%": BLUE,
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"92\\%": YELLOW,
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"50": BLUE_C,
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"200": YELLOW,
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}
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kw = {"tex_to_color_map": t2c}
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text = VGroup(
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TextMobject("95\\% with 50 reviews", **kw),
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TextMobject("vs.", **kw),
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TextMobject("92\\% with 200 reviews", **kw),
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)
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text.scale(2)
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text.arrange(DOWN, buff=LARGE_BUFF)
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text.set_width(FRAME_WIDTH - 1)
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self.add(text)
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self.embed()
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class AskAboutUnknownProbabilities(Scene):
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def construct(self):
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# Setup
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unknown_title, prob_title = titles = self.get_titles()
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v_line = Line(UP, DOWN)
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v_line.set_height(FRAME_HEIGHT)
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v_line.set_stroke([WHITE, LIGHT_GREY], 3)
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h_line = Line(LEFT, RIGHT)
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h_line.set_width(FRAME_WIDTH)
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h_line.next_to(titles, DOWN)
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processes = VGroup(
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get_random_coin(shuffle_time=1),
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get_random_die(shuffle_time=1.20),
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get_random_card(shuffle_time=2),
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)
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processes.arrange(DOWN, buff=0.7)
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processes.next_to(unknown_title, DOWN, LARGE_BUFF)
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processes_rect = BackgroundRectangle(processes)
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processes_rect.set_fill(BLACK, 1)
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prob_labels = VGroup(
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TexMobject("P(", "00", ")", "=", "1 / 2"),
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TexMobject("P(", "00", ")", "=", "1 / 6}"),
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TexMobject("P(", "00", ")", "=", "1 / 52}"),
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)
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prob_labels.scale(1.5)
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prob_labels.arrange(DOWN, aligned_edge=LEFT)
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prob_labels.match_x(prob_title)
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for pl, pr in zip(prob_labels, processes):
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pl.match_y(pr)
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content = pr[1].copy()
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content.replace(pl[1], dim_to_match=0)
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pl.submobjects[1] = content
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# Putting numbers to the unknown
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number_rects = VGroup(*[
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SurroundingRectangle(pl[-1])
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for pl in prob_labels
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])
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number_rects.set_stroke(YELLOW, 2)
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for pl in prob_labels:
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pl.save_state()
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pl[:3].match_x(prob_title)
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pl[3:].match_x(prob_title)
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pl.set_opacity(0)
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self.add(processes)
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self.play(
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LaggedStartMap(FadeInFromDown, titles),
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LaggedStart(
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ShowCreation(v_line),
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ShowCreation(h_line),
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),
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run_time=1
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)
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self.wait(2)
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self.play(
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LaggedStartMap(Restore, prob_labels),
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run_time=3,
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lag_ratio=0.3,
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)
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self.play(
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LaggedStartMap(
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ShowCreationThenFadeOut,
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number_rects,
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run_time=3,
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)
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)
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self.wait(2)
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# Highlight coin flip
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fade_rect = BackgroundRectangle(
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VGroup(prob_labels[1:], processes[1:]),
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buff=MED_SMALL_BUFF,
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)
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fade_rect.set_width(FRAME_WIDTH, stretch=True)
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fade_rect.set_fill(BLACK, 0.8)
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prob_half = prob_labels[0]
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half = prob_half[-1]
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half_underline = Line(LEFT, RIGHT)
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half_underline.set_width(half.get_width() + MED_SMALL_BUFF)
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half_underline.next_to(half, DOWN, buff=SMALL_BUFF)
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half_underline.set_stroke(YELLOW, 3)
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self.add(fade_rect, v_line, prob_half)
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self.play(FadeIn(fade_rect))
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self.wait(2)
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self.play(
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ShowCreation(half_underline),
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half.set_color, YELLOW,
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)
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self.play(FadeOut(half_underline))
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self.wait(4)
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# Transition to question
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processes.suspend_updating()
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self.play(
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LaggedStart(
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FadeOutAndShift(unknown_title, UP),
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FadeOutAndShift(prob_title, UP),
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lag_ratio=0.2,
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),
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FadeOutAndShift(h_line, UP, lag_ratio=0.1),
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FadeOutAndShift(processes, LEFT, lag_ratio=0.1),
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FadeOut(prob_labels[1]),
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FadeOut(prob_labels[2]),
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ApplyMethod(fade_rect.set_fill, BLACK, 1, remover=True),
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v_line.rotate, 90 * DEGREES,
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v_line.shift, 0.6 * FRAME_HEIGHT * UP,
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prob_half.center,
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prob_half.to_edge, UP,
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run_time=2,
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)
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self.clear()
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self.add(prob_half)
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arrow = Vector(UP)
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arrow.next_to(half, DOWN)
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question = TextMobject("What exactly does\\\\this mean?")
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question.next_to(arrow, DOWN)
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self.play(
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GrowArrow(arrow),
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FadeInFrom(question, UP),
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)
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self.wait(2)
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self.play(
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FadeOutAndShift(question, RIGHT),
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Rotate(arrow, 90 * DEGREES),
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VFadeOut(arrow),
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)
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# Show long run averages
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self.show_many_coins(20, 50)
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self.show_many_coins(40, 100)
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# Make probability itself unknown
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q_marks = TexMobject("???")
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q_marks.set_color(YELLOW)
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q_marks.replace(half, dim_to_match=0)
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randy = Randolph(mode="confused")
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randy.center()
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randy.look_at(prob_half)
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self.play(
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FadeOutAndShift(half, UP),
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FadeInFrom(q_marks, DOWN),
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)
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self.play(FadeIn(randy))
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self.play(Blink(randy))
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self.wait()
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# self.embed()
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def get_titles(self):
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unknown_label = TextMobject("Unknown event")
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prob_label = TextMobject("Probability")
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titles = VGroup(unknown_label, prob_label)
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titles.scale(1.5)
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unknown_label.move_to(FRAME_WIDTH * LEFT / 4)
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prob_label.move_to(FRAME_WIDTH * RIGHT / 4)
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titles.to_edge(UP, buff=MED_SMALL_BUFF)
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titles.set_color(BLUE)
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return titles
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def show_many_coins(self, n_rows, n_cols):
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coin_choices = VGroup(
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get_coin(BLUE_E, "H"),
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get_coin(RED_E, "T"),
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)
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coin_choices.set_stroke(width=0)
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coins = VGroup(*[
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random.choice(coin_choices).copy()
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for x in range(n_rows * n_cols)
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])
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def organize_coins(coin_group):
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coin_group.scale(1 / coin_group[0].get_height())
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coin_group.arrange_in_grid(n_rows=n_rows)
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coin_group.set_width(FRAME_WIDTH - 1)
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coin_group.to_edge(DOWN, MED_LARGE_BUFF)
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organize_coins(coins)
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sorted_coins = VGroup()
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for coin in coins:
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coin.generate_target()
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sorted_coins.add(coin.target)
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sorted_coins.submobjects.sort(key=lambda m: m.symbol)
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organize_coins(sorted_coins)
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self.play(LaggedStartMap(
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FadeInFrom, coins,
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lambda m: (m, 0.2 * DOWN),
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run_time=3,
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rate_func=linear
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))
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self.wait()
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self.play(LaggedStartMap(
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MoveToTarget, coins,
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path_arc=30 * DEGREES,
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run_time=2,
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lag_ratio=1 / len(coins),
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))
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self.wait()
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self.play(FadeOut(coins))
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108
from_3b1b/active/bayes/beta_helpers.py
Normal file
108
from_3b1b/active/bayes/beta_helpers.py
Normal file
@ -0,0 +1,108 @@
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from manimlib.imports import *
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# Images of randomness
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def get_random_process(choices, shuffle_time=2, total_time=4, change_rate=0.05,
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h_buff=0.05, v_buff=0.05):
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content = choices[0]
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container = Square()
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container.set_opacity(0)
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container.set_width(content.get_width() + 2 * h_buff, stretch=True)
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container.set_height(content.get_height() + 2 * v_buff, stretch=True)
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container.move_to(content)
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container.add(content)
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container.time = 0
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container.last_change_time = 0
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def update(container, dt):
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container.time += dt
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time = container.time
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change = all([
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(time % total_time) < shuffle_time,
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(time - container.last_change_time) > change_rate,
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])
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if change:
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mob = container.submobjects[0]
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new_mob = random.choice(choices)
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new_mob.match_height(mob)
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new_mob.move_to(container, DL)
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new_mob.shift(2 * np.random.random() * h_buff * RIGHT)
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new_mob.shift(2 * np.random.random() * v_buff * UP)
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container.submobjects = [new_mob]
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container.last_change_time = time
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container.add_updater(update)
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return container
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def get_coin(color, symbol):
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coin = VGroup()
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circ = Circle()
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circ.set_fill(color, 1)
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circ.set_stroke(WHITE, 2)
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circ.set_height(1)
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label = TextMobject(symbol)
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label.set_height(0.5 * circ.get_height())
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label.move_to(circ)
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coin.add(circ, label)
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coin.symbol = symbol
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coin.lock_triangulation()
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return coin
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def get_random_coin(**kwargs):
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coins = VGroup(
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get_coin(BLUE_E, "H"),
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get_coin(RED_E, "T"),
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)
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return get_random_process(coins, **kwargs)
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def get_die_faces():
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dot = Dot()
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dot.set_width(0.15)
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dot.set_color(BLUE_B)
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square = Square()
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square.round_corners(0.25)
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square.set_stroke(WHITE, 2)
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square.set_fill(DARKER_GREY, 1)
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square.set_width(0.6)
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edge_groups = [
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(ORIGIN,),
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(UL, DR),
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(UL, ORIGIN, DR),
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(UL, UR, DL, DR),
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(UL, UR, ORIGIN, DL, DR),
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(UL, UR, LEFT, RIGHT, DL, DR),
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]
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arrangements = VGroup(*[
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VGroup(*[
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dot.copy().move_to(square.get_bounding_box_point(ec))
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for ec in edge_group
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])
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for edge_group in edge_groups
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])
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square.set_width(1)
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faces = VGroup(*[
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VGroup(square.copy(), arrangement)
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for arrangement in arrangements
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])
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faces.arrange(RIGHT)
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return faces
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def get_random_die(**kwargs):
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return get_random_process(get_die_faces(), **kwargs)
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def get_random_card(height=1, **kwargs):
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cards = DeckOfCards()
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cards.set_height(height)
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return get_random_process(cards, **kwargs)
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