from manim import * import numpy as np import math class GeneratedScene(Scene): def construct(self): self.camera.background_color = "#0E1116" TEXT_C = "#E6EAF0" ACCENT = "#E8A33D" CORAL = "#D96B5C" NEUTRAL = "#E6EAF0" def safe_text(text, max_width=6.0, font_size=28, color=TEXT_C, weight=NORMAL): t = Text(text, font_size=font_size, color=color, weight=weight) if t.width > max_width: t.scale(max_width / t.width) return t # ---- Build the 10x10 grid of dots (the single source of truth) ---- spacing = 0.5 dot_radius = 0.13 all_dots = [] dots = VGroup() for r in range(10): for c in range(10): pos = np.array([(c - 4.5) * spacing, (4.5 - r) * spacing, 0]) d = Circle(radius=dot_radius, color=NEUTRAL, fill_opacity=0.6, stroke_width=0) d.move_to(pos) all_dots.append(d) dots.add(d) sick_dot = all_dots[0] # row 0, col 0 fp_dots = [all_dots[i] for i in [1, 2, 3, 4, 5]] # ~5 false positives remaining_idx = [i for i in range(100) if i not in [0, 1, 2, 3, 4, 5]] remaining = VGroup(*[all_dots[i] for i in remaining_idx]) right_block = VGroup(*[all_dots[i] for i in range(1, 100)]) # =================== Scene 1 — Anchor the Population =================== self.play(FadeIn(dots), run_time=0.6) self.wait(0.3) sick_target = Circle(radius=dot_radius * 1.4, color=ACCENT, fill_opacity=1.0, stroke_width=0 ).move_to(sick_dot.get_center()) self.play(Transform(sick_dot, sick_target), run_time=0.8) glow = Circle(radius=dot_radius * 2.4, color=ACCENT, fill_opacity=0.22, stroke_width=0).move_to(sick_dot.get_center()) self.play(FadeIn(glow), run_time=0.4) self.play(FadeOut(glow), run_time=0.4) cap1 = safe_text("100 people", max_width=4.0, font_size=30) cap1.to_corner(UL, buff=0.35) cap2 = safe_text("1% have the disease", max_width=4.0, font_size=26, color=ACCENT) cap2.next_to(cap1, DOWN, aligned_edge=LEFT, buff=0.15) self.play(Write(cap1), run_time=0.5) self.play(FadeIn(cap2, shift=UP * 0.15), run_time=0.5) bracket = Brace(sick_dot, LEFT, color=ACCENT) blabel = safe_text("1 sick", max_width=1.6, font_size=22, color=ACCENT) blabel.next_to(bracket, LEFT, buff=0.15) self.play(GrowFromCenter(bracket), FadeIn(blabel, shift=RIGHT * 0.15), run_time=1.0) self.wait(1.2) divider = Line([-2.0, -2.6, 0], [-2.0, 2.6, 0], color=TEXT_C, stroke_width=1.5, stroke_opacity=0.5) self.play(FadeOut(bracket), FadeOut(blabel), Create(divider), run_time=0.8) self.play(FadeOut(cap1), FadeOut(cap2), run_time=0.4) # =================== Scene 2 — Sensitivity on the Sick =================== s2_l1 = safe_text("Test catches 90%", max_width=4.0, font_size=28, color=ACCENT) s2_l2 = safe_text("of the sick", max_width=4.0, font_size=24) s2_l1.to_corner(UL, buff=0.35) s2_l2.next_to(s2_l1, DOWN, aligned_edge=LEFT, buff=0.15) self.play(right_block.animate.set_fill(opacity=0.35), run_time=0.6) self.play(Write(s2_l1), run_time=0.5) self.play(FadeIn(s2_l2, shift=UP * 0.15), run_time=0.5) slabel = safe_text("Sick = 1", max_width=1.8, font_size=22, color=ACCENT) slabel.next_to(sick_dot, LEFT, buff=0.3) self.play(FadeIn(slabel), run_time=0.4) meter_w = 1.4 meter_bg = Rectangle(width=meter_w, height=0.12, color=TEXT_C, fill_opacity=0, stroke_width=1.2, stroke_opacity=0.4) meter_bg.next_to(sick_dot, DOWN, buff=0.25).align_to(sick_dot, LEFT) meter_fill = Rectangle(width=0.001, height=0.12, color=ACCENT, fill_opacity=0.9, stroke_width=0) meter_fill.align_to(meter_bg, LEFT).align_to(meter_bg, DOWN) meter_target = Rectangle(width=meter_w * 0.9, height=0.12, color=ACCENT, fill_opacity=0.9, stroke_width=0) meter_target.align_to(meter_bg, LEFT).align_to(meter_bg, DOWN) self.play(FadeIn(meter_bg), run_time=0.3) self.play(Transform(meter_fill, meter_target), run_time=1.2) tp_label = safe_text("True positive = 0.9", max_width=3.2, font_size=22, color=ACCENT) tp_label.next_to(meter_bg, DOWN, buff=0.18) self.play(FadeIn(tp_label, shift=UP * 0.15), run_time=0.6) self.wait(1.2) self.play(right_block.animate.set_fill(opacity=0.6), run_time=0.6) self.play(FadeOut(slabel), FadeOut(meter_bg), FadeOut(meter_fill), FadeOut(tp_label), FadeOut(divider), FadeOut(s2_l1), FadeOut(s2_l2), run_time=0.5) # =================== Scene 3 — The Base-Rate Trap =================== s3_l1 = safe_text("5% of healthy test positive", max_width=5.0, font_size=26, color=CORAL) s3_l2 = safe_text("≈ 4.95 people", max_width=3.5, font_size=24, color=CORAL) s3_l1.to_corner(UL, buff=0.35) s3_l2.next_to(s3_l1, DOWN, aligned_edge=LEFT, buff=0.15) self.play(Write(s3_l1), run_time=0.5) self.play(FadeIn(s3_l2, shift=UP * 0.15), run_time=0.5) h_meter_w = 4.0 h_meter_bg = Rectangle(width=h_meter_w, height=0.12, color=TEXT_C, fill_opacity=0, stroke_width=1.2, stroke_opacity=0.4) h_meter_bg.next_to(dots, DOWN, buff=0.35) h_meter_fill = Rectangle(width=0.001, height=0.12, color=CORAL, fill_opacity=0.9, stroke_width=0) h_meter_fill.align_to(h_meter_bg, LEFT).align_to(h_meter_bg, DOWN) h_meter_target = Rectangle(width=h_meter_w * 0.05, height=0.12, color=CORAL, fill_opacity=0.9, stroke_width=0) h_meter_target.align_to(h_meter_bg, LEFT).align_to(h_meter_bg, DOWN) self.play(FadeIn(h_meter_bg), run_time=0.3) self.play(Transform(h_meter_fill, h_meter_target), run_time=1.0) for d in fp_dots: dt = Circle(radius=dot_radius, color=CORAL, fill_opacity=0.9, stroke_width=0).move_to(d.get_center()) self.play(Transform(d, dt), run_time=0.3) fp_label = safe_text("False positives ≈ 4.95", max_width=4.0, font_size=22, color=CORAL) fp_label.next_to(h_meter_bg, DOWN, buff=0.18) self.play(FadeIn(fp_label, shift=UP * 0.15), run_time=0.6) self.wait(1.5) self.play(FadeOut(h_meter_bg), FadeOut(h_meter_fill), FadeOut(fp_label), FadeOut(s3_l1), FadeOut(s3_l2), run_time=0.5) # =================== Scene 4 — Side-by-Side Comparison =================== s4_l1 = safe_text("Everyone who tested positive", max_width=5.5, font_size=26) s4_l2 = safe_text("≈ 5.85 people", max_width=3.5, font_size=24) s4_l1.to_corner(UL, buff=0.35) s4_l2.next_to(s4_l1, DOWN, aligned_edge=LEFT, buff=0.15) self.play(Write(s4_l1), run_time=0.5) self.play(FadeIn(s4_l2, shift=UP * 0.15), run_time=0.5) row_y = 0.0 row_spacing = 0.42 n = 6 total_w = (n - 1) * row_spacing start_x = -total_w / 2 row_positions = [np.array([start_x + i * row_spacing, row_y, 0]) for i in range(n)] accent_row = Circle(radius=dot_radius * 0.7, color=ACCENT, fill_opacity=1.0, stroke_width=0).move_to(row_positions[0]) coral_targets = [] for i, d in enumerate(fp_dots): t = Circle(radius=dot_radius, color=CORAL, fill_opacity=0.9, stroke_width=0).move_to(row_positions[i + 1]) coral_targets.append(t) self.play( Transform(sick_dot, accent_row), *[Transform(d, t) for d, t in zip(fp_dots, coral_targets)], run_time=1.2 ) self.play(remaining.animate.set_fill(opacity=0.15), run_time=0.6) row_grp = VGroup(sick_dot, *fp_dots) total_label = safe_text("Positive = 5.85", max_width=3.0, font_size=22, color=TEXT_C) total_label.next_to(row_grp, RIGHT, buff=0.4) self.play(FadeIn(total_label, shift=LEFT * 0.15), run_time=0.5) brace = Brace(row_grp, DOWN, color=TEXT_C) brace_label = safe_text("all positives", max_width=2.2, font_size=20, color=TEXT_C) brace_label.next_to(brace, DOWN, buff=0.1) self.play(GrowFromCenter(brace), FadeIn(brace_label), run_time=0.6) self.wait(1.2) vdiv_x = (row_positions[0][0] + row_positions[1][0]) / 2 vdiv = Line([vdiv_x, -0.45, 0], [vdiv_x, 0.45, 0], color=TEXT_C, stroke_width=1.5, stroke_opacity=0.6) self.play(Create(vdiv), run_time=0.4) self.wait(0.6) self.play(FadeOut(brace), FadeOut(brace_label), FadeOut(total_label), FadeOut(vdiv), FadeOut(s4_l1), FadeOut(s4_l2), run_time=0.5) # =================== Scene 5 — Convert to Probability =================== eq_lhs = MathTex("P(\\text{disease} \\mid \\text{positive}) =", font_size=34, color=TEXT_C) # Build fraction manually to color numerator/denominator independently num_tex = MathTex("0.9", font_size=34, color=ACCENT) den_tex = MathTex("5.85", font_size=34, color=CORAL) frac_line = Line(LEFT * 0.35, RIGHT * 0.35, color=TEXT_C, stroke_width=1.5) frac = VGroup(num_tex, frac_line, den_tex).arrange(DOWN, buff=0.06) eq = VGroup(eq_lhs, frac).arrange(RIGHT, buff=0.25) eq.move_to([0, 2.7, 0]) self.play(Write(eq_lhs), run_time=0.8) self.play(FadeIn(frac, shift=LEFT * 0.2), run_time=0.6) self.play(sick_dot.animate.scale(1.4), run_time=0.3) self.play(sick_dot.animate.scale(1 / 1.4), run_time=0.3) self.play(VGroup(*fp_dots).animate.scale(1.15), run_time=0.3) self.play(VGroup(*fp_dots).animate.scale(1 / 1.15), run_time=0.3) decimal = MathTex("0.154", font_size=40, color=TEXT_C).move_to(frac.get_center()) self.play(Transform(frac, decimal), run_time=0.6) result = MathTex("\\approx 15\\%", font_size=40, color=ACCENT).move_to(frac.get_center()) self.play(Transform(frac, result), run_time=0.5) self.play(frac.animate.scale(1.15), run_time=0.2) self.play(frac.animate.scale(1 / 1.15), run_time=0.2) self.wait(1.2) eq_grp = VGroup(eq_lhs, frac) self.play(eq_grp.animate.scale(0.6).to_edge(UR, buff=0.4), run_time=0.6) # =================== Scene 6 — The Insight =================== line1 = safe_text("Most positives are healthy", max_width=5.5, font_size=30, color=TEXT_C) line2 = safe_text("because healthy people outnumber the sick", max_width=6.2, font_size=24, color=TEXT_C) line1.move_to([0, -1.7, 0]) line2.move_to([0, -2.4, 0]) self.play(VGroup(*fp_dots).animate.set_fill(opacity=0.55), run_time=1.0) self.play(Write(line1), run_time=0.5) self.wait(1.2) self.play(Write(line2), run_time=0.5) self.wait(1.3) self.play(FadeOut(line1), FadeOut(line2), FadeOut(eq_grp), run_time=0.5) # =================== Scene 7 — Recombine Through Bayes' Eyes =================== self.play(remaining.animate.set_fill(opacity=0.6), run_time=0.6) sick_home = np.array([(0 - 4.5) * spacing, (4.5 - 0) * spacing, 0]) sick_back = Circle(radius=dot_radius * 1.4, color=ACCENT, fill_opacity=1.0, stroke_width=0).move_to(sick_home) coral_back = [] for i, d in enumerate(fp_dots): idx = i + 1 r, c = idx // 10, idx % 10 pos = np.array([(c - 4.5) * spacing, (4.5 - r) * spacing, 0]) t = Circle(radius=dot_radius, color=CORAL, fill_opacity=0.9, stroke_width=0).move_to(pos) coral_back.append(t) self.play( Transform(sick_dot, sick_back), *[Transform(d, t) for d, t in zip(fp_dots, coral_back)], run_time=0.8 ) sick_bracket = Brace(sick_dot, LEFT, color=ACCENT) sick_blabel = safe_text("true positive", max_width=2.2, font_size=18, color=ACCENT) sick_blabel.next_to(sick_bracket, LEFT, buff=0.12) coral_grp = VGroup(*fp_dots) coral_bracket = Brace(coral_grp, UP, color=CORAL) coral_blabel = safe_text("false positives", max_width=2.4, font_size=18, color=CORAL) coral_blabel.next_to(coral_bracket, UP, buff=0.1) self.play(GrowFromCenter(sick_bracket), FadeIn(sick_blabel), GrowFromCenter(coral_bracket), FadeIn(coral_blabel), run_time=0.8) final_cap = safe_text("Base rates matter most", max_width=5.0, font_size=32, color=TEXT_C) final_cap.to_edge(DOWN, buff=0.5) self.play(Write(final_cap), run_time=0.6) self.wait(1.5) self.play(FadeOut(dots), FadeOut(sick_bracket), FadeOut(sick_blabel), FadeOut(coral_bracket), FadeOut(coral_blabel), run_time=0.8) self.play(FadeOut(final_cap), run_time=0.6) self.wait(0.3)