from big_ol_pile_of_manim_imports import * from old_projects.eoc.chapter8 import * from active_projects.eop.histograms import * import scipy.special COIN_RADIUS = 0.18 COIN_THICKNESS = 0.4 * COIN_RADIUS COIN_FORESHORTENING = 0.5 COIN_NB_RIDGES = 20 COIN_STROKE_WIDTH = 2 COIN_SEQUENCE_SPACING = 0.1 GRADE_COLOR_1 = COLOR_HEADS = RED GRADE_COLOR_2 = COLOR_TAILS = BLUE TALLY_BACKGROUND_WIDTH = 1.0 def binary(i): # returns an array of 0s and 1s if i == 0: return [] j = i binary_array = [] while j > 0: jj = j/2 if jj > 0: binary_array.append(j % 2) else: binary_array.append(1) j = jj return binary_array[::-1] def nb_of_ones(i): return binary(i).count(1) def rainbow_color(alpha): nb_colors = 100 rainbow = color_gradient([RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE], nb_colors) rainbow = np.append(rainbow,PURPLE) index = int(alpha * nb_colors) return rainbow[index] def graded_color(n,k): if n != 0: alpha = float(k)/n else: alpha = 0.5 color = interpolate_color(GRADE_COLOR_1, GRADE_COLOR_2, alpha) return color class PiCreatureCoin(VMobject): CONFIG = { "diameter": 0.8, "thickness": 0.2, "nb_ridges" : 7, "stroke_color": YELLOW, "stroke_width": 3, "fill_color": YELLOW, "fill_opacity": 0.7, } def generate_points(self): outer_rect = Rectangle( width = self.diameter, height = self.thickness, fill_color = self.fill_color, fill_opacity = self.fill_opacity, stroke_color = self.stroke_color, stroke_width = 0, #self.stroke_width ) self.add(outer_rect) PI = TAU/2 ridge_angles = np.arange(PI/self.nb_ridges,PI,PI/self.nb_ridges) ridge_positions = 0.5 * self.diameter * np.array([ np.cos(theta) for theta in ridge_angles ]) ridge_color = interpolate_color(BLACK,self.stroke_color,0.5) for x in ridge_positions: ridge = Line( x * RIGHT + 0.5 * self.thickness * DOWN, x * RIGHT + 0.5 * self.thickness * UP, stroke_color = ridge_color, stroke_width = self.stroke_width ) self.add(ridge) class CoinFlippingPiCreature(PiCreature): def __init__(self, **kwargs): coin = PiCreatureCoin() PiCreature.__init__(self,**kwargs) self.coin = coin self.add(coin) right_arm = self.get_arm_copies()[1] coin.next_to(right_arm, RIGHT+UP, buff = 0) coin.shift(0.15 * self.get_width() * LEFT) def flip_coin_up(self): self.change("raise_right_hand") class FlipUpAndDown(Animation): CONFIG = { "vector" : UP, "nb_turns" : 1 } def update(self,t): self.mobject.shift(4 * t * (1 - t) * self.vector) self.mobject.rotate(t * self.nb_turns * TAU) class FlipCoin(AnimationGroup): CONFIG = { "rate_func" : there_and_back } def __init__(self, pi_creature, **kwargs): digest_config(self, kwargs) pi_creature_motion = ApplyMethod( pi_creature.flip_coin_up, rate_func = self.rate_func, **kwargs ) coin_motion = Succession( EmptyAnimation(run_time = 1.0), FlipUpAndDown( pi_creature.coin, vector = UP, nb_turns = 5, rate_func = self.rate_func, **kwargs ) ) AnimationGroup.__init__(self,pi_creature_motion, coin_motion) class CoinFlippingPiCreatureScene(Scene): def construct(self): randy = CoinFlippingPiCreature() self.add(randy) self.play(FlipCoin(randy, run_time = 3)) class UprightCoin(Circle): # For use in coin sequences CONFIG = { "radius": COIN_RADIUS, "stroke_width": COIN_STROKE_WIDTH, "stroke_color": WHITE, "fill_opacity": 1, "symbol": "\euro" } def __init__(self, **kwargs): Circle.__init__(self,**kwargs) self.symbol_mob = TextMobject(self.symbol, stroke_color = self.stroke_color) self.symbol_mob.scale_to_fit_height(0.5*self.get_height()).move_to(self) self.add(self.symbol_mob) class UprightHeads(UprightCoin): CONFIG = { "fill_color": COLOR_HEADS, "symbol": "H", } class UprightTails(UprightCoin): CONFIG = { "fill_color": COLOR_TAILS, "symbol": "T", } class CoinSequence(VGroup): CONFIG = { "sequence": [], "spacing": COIN_SEQUENCE_SPACING, "direction": RIGHT } def __init__(self, sequence, **kwargs): VGroup.__init__(self, **kwargs) self.sequence = sequence offset = 0 for symbol in self.sequence: if symbol == "H": new_coin = UprightHeads() elif symbol == "T": new_coin = UprightTails() else: new_coin = UprightCoin(symbol = symbol) new_coin.shift(offset * self.direction) self.add(new_coin) offset += self.spacing class FlatCoin(UprightCoin): # For use in coin stacks CONFIG = { "thickness": COIN_THICKNESS, "foreshortening": COIN_FORESHORTENING, "nb_ridges": COIN_NB_RIDGES } def __init__(self, **kwargs): UprightCoin.__init__(self, **kwargs) self.symbol_mob.rotate(TAU/8) self.stretch_in_place(self.foreshortening, 1) # draw the edge control_points1 = self.points[12:25].tolist() control_points2 = self.copy().shift(self.thickness * DOWN).points[12:25].tolist() edge_anchors_and_handles = control_points1 edge_anchors_and_handles.append(edge_anchors_and_handles[-1] + self.thickness * DOWN) edge_anchors_and_handles.append(edge_anchors_and_handles[-1] + self.thickness * UP) edge_anchors_and_handles += control_points2[::-1] # list concatenation edge_anchors_and_handles.append(edge_anchors_and_handles[-1] + self.thickness * UP) edge_anchors_and_handles.append(edge_anchors_and_handles[-1] + self.thickness * DOWN) edge_anchors_and_handles.append(control_points1[0]) #edge_anchors_and_handles = edge_anchors_and_handles[::-1] edge = VMobject() edge.set_points(edge_anchors_and_handles) edge.set_fill( color = self.fill_color, opacity = self.fill_opacity ) edge.set_stroke(width = self.stroke_width) self.add(edge) # draw the ridges PI = TAU/2 dtheta = PI/self.nb_ridges ridge_angles = np.arange(dtheta,PI,dtheta) # add a twist onto each coin ridge_angles += np.random.rand(1) * dtheta # crop the angles that overshoot on either side ridge_angles = ridge_angles[(ridge_angles > 0) * (ridge_angles < PI)] ridge_positions = 0.5 * 2 * self.radius * np.array([ np.cos(theta) for theta in ridge_angles ]) ridge_color = interpolate_color(self.stroke_color, self.fill_color, 0.7) for x in ridge_positions: y = -(1 - (x/self.radius)**2)**0.5 * self.foreshortening * self.radius ridge = Line( x * RIGHT + y * UP, x * RIGHT + y * UP + self.thickness * DOWN, stroke_color = ridge_color, stroke_width = self.stroke_width ) self.add(ridge) # redraw the unfilled edge to cover the ridge ends empty_edge = edge.copy() empty_edge.set_fill(opacity = 0) self.add(empty_edge) class FlatHeads(FlatCoin): CONFIG = { "fill_color": COLOR_HEADS, "symbol": "H", } class FlatTails(FlatCoin): CONFIG = { "fill_color": COLOR_TAILS, "symbol": "T", } class CoinStack(VGroup): CONFIG = { "coin_thickness": COIN_THICKNESS, "size": 5, "face": FlatCoin, } def generate_points(self): for n in range(self.size): coin = self.face(thickness = self.coin_thickness) coin.shift(n * self.coin_thickness * UP) self.add(coin) class HeadsStack(CoinStack): CONFIG = { "face": FlatHeads } class TailsStack(CoinStack): CONFIG = { "face": FlatTails } class TallyStack(VGroup): CONFIG = { "coin_thickness": COIN_THICKNESS } def __init__(self,h,t,anchor = ORIGIN, **kwargs): self.nb_heads = h self.nb_tails = t self.anchor = anchor VGroup.__init__(self,**kwargs) def generate_points(self): stack1 = HeadsStack(size = self.nb_heads, coin_thickness = self.coin_thickness) stack2 = TailsStack(size = self.nb_tails, coin_thickness = self.coin_thickness) stack1.next_to(self.anchor, LEFT, buff = 0.5 * SMALL_BUFF) stack2.next_to(self.anchor, RIGHT, buff = 0.5 * SMALL_BUFF) stack1.align_to(self.anchor, DOWN) stack2.align_to(self.anchor, DOWN) self.heads_stack = stack1 self.tails_stack = stack2 self.add(stack1, stack2) background_rect = RoundedRectangle( width = TALLY_BACKGROUND_WIDTH, height = TALLY_BACKGROUND_WIDTH, corner_radius = 0.1, fill_color = DARK_GREY, fill_opacity = 1.0, stroke_width = 3 ).align_to(self.anchor, DOWN).shift(0.1 * DOWN) self.add_to_back(background_rect) def move_anchor_to(self, new_anchor): for submob in self.submobjects: submob.shift(new_anchor - self.anchor) self.anchor = new_anchor return self class CoinFlipTree(VGroup): CONFIG = { "total_width": 12, "level_height": 0.8, "nb_levels": 4, "sort_until_level": 3 } def __init__(self, **kwargs): VGroup.__init__(self, **kwargs) self.rows = [] for n in range(self.nb_levels + 1): if n <= self.sort_until_level: self.create_row(n, sorted = True) else: self.create_row(n, sorted = False) for row in self.rows: for leaf in row: dot = Dot() dot.move_to(leaf[0]) line = Line(leaf[2], leaf[0]) if leaf[2][0] > leaf[0][0]: line_color = COLOR_HEADS else: line_color = COLOR_TAILS line.set_stroke(color = line_color) group = VGroup() group.add(dot) group.add_to_back(line) self.add(group) def create_row(self, level, sorted = True): if level == 0: new_row = [[ORIGIN,0,ORIGIN]] # is its own parent self.rows.append(new_row) return previous_row = self.rows[level - 1] new_row = [] dx = float(self.total_width) / (2 ** level) x = - 0.5 * self.total_width + 0.5 * dx y = - self.level_height * level for root in previous_row: root_point = root[0] root_tally = root[1] for i in range(2): # 0 = heads = left, 1 = tails = right leaf = x * RIGHT + y * UP new_row.append([leaf, root_tally + i, root_point]) # leaf and its parent x += dx if sorted: # sort the new_row by its tallies sorted_row = [] x = - 0.5 * self.total_width + 0.5 * dx for i in range(level + 1): for leaf in new_row: if leaf[1] == i: sorted_leaf = leaf sorted_leaf[0][0] = x x += dx sorted_row.append(leaf) self.rows.append(sorted_row) else: self.rows.append(new_row) class Chapter1OpeningQuote(OpeningQuote): CONFIG = { "fade_in_kwargs": { "submobject_mode": "lagged_start", "rate_func": None, "lag_factor": 9, "run_time": 10, }, "text_size" : "\\normalsize", "use_quotation_marks": False, "quote" : [ "To see a world in a grain of sand\\\\", "And a heaven in a wild flower,\\\\", "Hold infinity in the palm of your hand\\\\", "\phantom{r}And eternity in an hour.\\\\" ], "quote_arg_separator" : " ", "highlighted_quote_terms" : {}, "author" : "William Blake: \\\\ \emph{Auguries of Innocence}", } class Introduction(TeacherStudentsScene): CONFIG = { "default_pi_creature_kwargs": { "color": MAROON_E, "flip_at_start": True, }, } def construct(self): self.show_series() self.show_examples() def show_series(self): series = VideoSeries(num_videos = 11) series.to_edge(UP) this_video = series[0] this_video.set_color(YELLOW) this_video.save_state() this_video.set_fill(opacity = 0) this_video.center() this_video.scale_to_fit_height(FRAME_HEIGHT) self.this_video = this_video words = TextMobject( "Welcome to \\\\", "Essence of Probability" ) words.set_color_by_tex("Essence of Probability", YELLOW) self.teacher.change_mode("happy") self.play( FadeIn( series, submobject_mode = "lagged_start", run_time = 2 ), Blink(self.get_teacher()) ) self.teacher_says(words, target_mode = "hooray") self.change_student_modes( *["hooray"]*3, look_at_arg = series[1].get_left(), added_anims = [ ApplyMethod(this_video.restore, run_time = 3), ] ) self.play(*[ ApplyMethod( video.shift, 0.5*video.get_height()*DOWN, run_time = 3, rate_func = squish_rate_func( there_and_back, alpha, alpha+0.3 ) ) for video, alpha in zip(series, np.linspace(0, 0.7, len(series))) ]+[ Animation(self.teacher.bubble), Animation(self.teacher.bubble.content), ]) self.play( FadeOut(self.teacher.bubble), FadeOut(self.teacher.bubble.content), self.get_teacher().change_mode, "raise_right_hand", *[ ApplyMethod(pi.change_mode, "pondering") for pi in self.get_students() ] ) self.wait() self.series = series def show_examples(self): self.wait(10) # put examples here in video editor # # # # # # # # # # # # # # # # # # # show examples of the area model # # # # # # # # # # # # # # # # # # # class IllustrateAreaModel1(Scene): def construct(self): color_A = YELLOW color_not_A = YELLOW_E color_B = MAROON color_not_B = MAROON_E opacity_B = 0.7 # show independent events sample_space_width = sample_space_height = 3 p_of_A = 0.7 p_of_not_A = 1 - p_of_A p_of_B = 0.8 p_of_not_B = 1 - p_of_B rect_A = Rectangle( width = p_of_A * sample_space_width, height = 1 * sample_space_height, stroke_width = 0, fill_color = color_A, fill_opacity = 1.0 ).move_to(3 * RIGHT + 1.5 * UP) rect_not_A = Rectangle( width = p_of_not_A * sample_space_width, height = 1 * sample_space_height, stroke_width = 0, fill_color = color_not_A, fill_opacity = 1.0 ).next_to(rect_A, RIGHT, buff = 0) brace_A = Brace(rect_A, DOWN) label_A = TexMobject("P(A)").next_to(brace_A, DOWN).scale(0.7) brace_not_A = Brace(rect_not_A, DOWN) label_not_A = TexMobject("P(\\text{not }A)").next_to(brace_not_A, DOWN).scale(0.7) # self.play( # LaggedStart(FadeIn, VGroup(rect_A, rect_not_A), lag_factor = 0.5) # ) # self.play( # ShowCreation(brace_A), # Write(label_A), # ) rect_B = Rectangle( width = 1 * sample_space_width, height = p_of_B * sample_space_height, stroke_width = 0, fill_color = color_B, fill_opacity = opacity_B ) rect_not_B = Rectangle( width = 1 * sample_space_width, height = p_of_not_B * sample_space_height, stroke_width = 0, fill_color = color_not_B, fill_opacity = opacity_B ).next_to(rect_B, UP, buff = 0) VGroup(rect_B, rect_not_B).move_to(VGroup(rect_A, rect_not_A)) brace_B = Brace(rect_B, LEFT) label_B = TexMobject("P(B)").next_to(brace_B, LEFT).scale(0.7) brace_not_B = Brace(rect_not_B, LEFT) label_not_B = TexMobject("P(\\text{not }B)").next_to(brace_not_B, LEFT).scale(0.7) # self.play( # LaggedStart(FadeIn, VGroup(rect_B, rect_not_B), lag_factor = 0.5) # ) # self.play( # ShowCreation(brace_B), # Write(label_B), # ) rect_A_and_B = Rectangle( width = p_of_A * sample_space_width, height = p_of_B * sample_space_height, stroke_width = 3, fill_opacity = 0.0 ).align_to(rect_A, DOWN).align_to(rect_A,LEFT) label_A_and_B = TexMobject("P(A\\text{ and }B)").scale(0.7) label_A_and_B.move_to(rect_A_and_B) # self.play( # ShowCreation(rect_A_and_B) # ) indep_formula = TexMobject("P(A\\text{ and }B)", "=", "P(A)", "\cdot", "P(B)") indep_formula = indep_formula.scale(0.7) label_p_of_b = indep_formula.get_part_by_tex("P(B)") label_A_and_B_copy = label_A_and_B.copy() label_A_copy = label_A.copy() label_B_copy = label_B.copy() # self.add(label_A_and_B_copy, label_A_copy, label_B_copy) # self.play(Transform(label_A_and_B_copy, indep_formula[0])) # self.play(FadeIn(indep_formula[1])) # self.play(Transform(label_A_copy, indep_formula[2])) # self.play(FadeIn(indep_formula[3])) # self.play(Transform(label_B_copy, indep_formula[4])) #self.wait() label_A_and_B_copy = indep_formula[0] label_A_copy = indep_formula[2] label_B_copy = indep_formula[4] # show conditional prob rect_A_and_B.set_fill(color = RED, opacity = 0.5) rect_A_and_not_B = Rectangle( width = p_of_A * sample_space_width, height = p_of_not_B * sample_space_height, stroke_width = 0, fill_color = color_not_B, fill_opacity = opacity_B ).next_to(rect_A_and_B, UP, buff = 0) rect_not_A_and_B = Rectangle( width = p_of_not_A * sample_space_width, height = p_of_B * sample_space_height, stroke_width = 0, fill_color = color_B, fill_opacity = opacity_B ).next_to(rect_A_and_B, RIGHT, buff = 0) rect_not_A_and_not_B = Rectangle( width = p_of_not_A * sample_space_width, height = p_of_not_B * sample_space_height, stroke_width = 0, fill_color = color_not_B, fill_opacity = opacity_B ).next_to(rect_not_A_and_B, UP, buff = 0) indep_formula.next_to(rect_not_A, LEFT, buff = 5) #indep_formula.shift(UP) self.play(Write(indep_formula)) self.play( FadeIn(VGroup( rect_A, rect_not_A, brace_A, label_A, brace_B, label_B, rect_A_and_not_B, rect_not_A_and_B, rect_not_A_and_not_B, rect_A_and_B, label_A_and_B, )) ) self.wait() p_of_B_knowing_A = 0.6 rect_A_and_B.target = Rectangle( width = p_of_A * sample_space_width, height = p_of_B_knowing_A * sample_space_height, stroke_width = 3, fill_color = color_B, fill_opacity = opacity_B ).align_to(rect_A_and_B, DOWN).align_to(rect_A_and_B, LEFT) rect_A_and_not_B.target = Rectangle( width = p_of_A * sample_space_width, height = (1 - p_of_B_knowing_A) * sample_space_height, stroke_width = 0, fill_color = color_not_B, fill_opacity = opacity_B ).next_to(rect_A_and_B.target, UP, buff = 0) brace_B.target = Brace(rect_A_and_B.target, LEFT) label_B.target = TexMobject("P(B\mid A)").scale(0.7).next_to(brace_B.target, LEFT) self.play( MoveToTarget(rect_A_and_B), MoveToTarget(rect_A_and_not_B), MoveToTarget(brace_B), MoveToTarget(label_B), label_A_and_B.move_to,rect_A_and_B.target ) label_B_knowing_A = label_B #self.play(FadeOut(label_B_copy)) self.remove(indep_formula.get_part_by_tex("P(B)")) indep_formula.remove(indep_formula.get_part_by_tex("P(B)")) label_B_knowing_A_copy = label_B_knowing_A.copy() self.add(label_B_knowing_A_copy) self.play( label_B_knowing_A_copy.next_to, indep_formula.get_part_by_tex("\cdot"), RIGHT, ) # solve formula for P(B|A) rearranged_formula = TexMobject(["P(B\mid A)", "=", "{P(A\\text{ and }B) \over P(A)}"]) rearranged_formula.move_to(indep_formula) self.wait() self.play( # in some places get_part_by_tex does not find the correct part # so I picked out fitting indices label_B_knowing_A_copy.move_to, rearranged_formula.get_part_by_tex("P(B\mid A)"), label_A_copy.move_to, rearranged_formula[-1][10], label_A_and_B_copy.move_to, rearranged_formula[-1][3], indep_formula.get_part_by_tex("=").move_to, rearranged_formula.get_part_by_tex("="), Transform(indep_formula.get_part_by_tex("\cdot"), rearranged_formula[2][8]), ) rect = SurroundingRectangle(rearranged_formula, buff = 0.5 * MED_LARGE_BUFF) self.play(ShowCreation(rect)) self.wait() class IllustrateAreaModel2(GraphScene): CONFIG = { "x_min" : -3.0, "x_max" : 3.0, "y_min" : 0, "y_max" : 1.0, "num_rects": 400, "y_axis_label" : "", "x_axis_label" : "", "variable_point_label" : "a", "graph_origin": 2.5 * DOWN + 4 * RIGHT, "x_axis_width": 5, "y_axis_height": 5 } def construct(self): # integral bounds x_min_1 = -0.0001 x_max_1 = 0.0001 x_min_2 = self.x_min x_max_2 = self.x_max self.setup_axes() self.remove(self.x_axis, self.y_axis) graph = self.get_graph(lambda x: np.exp(-x**2) * 2.0 / TAU ** 0.5) area = self.area = self.get_area(graph, x_min_1, x_max_1) pdf_formula = TexMobject("p(x) = {1\over \sigma\sqrt{2\pi}}e^{-{1\over 2}({x\over\sigma})^2}") pdf_formula.set_color(graph.color) cdf_formula = TexMobject("P(|X| < ", "a", ") = \int", "_{-a}", "^a", "p(x) dx") cdf_formula.set_color_by_tex("a", YELLOW) cdf_formula.next_to(graph, LEFT, buff = 2) pdf_formula.next_to(cdf_formula, UP) formulas = VGroup(pdf_formula, cdf_formula) self.play(Write(pdf_formula)) self.play(Write(cdf_formula)) self.wait() self.play(ShowCreation(self.x_axis)) self.play(ShowCreation(graph)) self.play(FadeIn(area)) self.v_graph = graph self.add_T_label( x_min_1, label = "-a", side = LEFT, color = YELLOW, animated = False ) self.add_T_label( x_max_1, label = "a", side = RIGHT, color = YELLOW, animated = False ) # don't show the labels just yet self.remove( self.left_T_label_group[0], self.right_T_label_group[0], ) def integral_update_func(t): return scipy.special.erf( self.point_to_coords(self.right_v_line.get_center())[0] ) def integral_update_func_percent(t): return 100 * integral_update_func(t) equals_sign = TexMobject("=").next_to(cdf_formula, buff = MED_LARGE_BUFF) cdf_value = DecimalNumber(0, color = graph.color, num_decimal_points = 3) cdf_value.next_to(equals_sign) self.play( FadeIn(equals_sign), FadeIn(cdf_value) ) self.add_foreground_mobject(cdf_value) cdf_percentage = DecimalNumber(0, unit = "\%") cdf_percentage.move_to(self.coords_to_point(0,0.2)) self.add_foreground_mobject(cdf_percentage) self.add(ContinualChangingDecimal( decimal_number_mobject = cdf_value, number_update_func = integral_update_func, num_decimal_points = 3 )) self.add(ContinualChangingDecimal( decimal_number_mobject = cdf_percentage, number_update_func = integral_update_func_percent, num_decimal_points = 1 )) anim = self.get_animation_integral_bounds_change( graph, x_min_2, x_max_2, run_time = 3) self.play( anim ) rect = SurroundingRectangle(formulas, buff = 0.5 * MED_LARGE_BUFF) self.play(ShowCreation(rect)) class IllustrateAreaModel3(Scene): def construct(self): formula = TexMobject("E[X] = \sum_{i=1}^N p_i x_i").move_to(3 * LEFT + UP) self.play(Write(formula)) x_scale = 5.0 y_scale = 1.0 probabilities = np.array([1./8, 3./8, 3./8, 1./8]) prob_strings = ["{1\over 8}","{3\over 8}","{3\over 8}","{1\over 8}"] cumulative_probabilities = np.cumsum(probabilities) cumulative_probabilities = np.insert(cumulative_probabilities, 0, 0) y_values = np.array([0, 1, 2, 3]) hist = Histogram(probabilities, y_values, mode = "widths", x_scale = x_scale, y_scale = y_scale, x_labels = "none" ) flat_hist = Histogram(probabilities, 0 * y_values, mode = "widths", x_scale = x_scale, y_scale = y_scale, x_labels = "none" ) self.play(FadeIn(flat_hist)) self.play( ReplacementTransform(flat_hist, hist) ) braces = VGroup() p_labels = VGroup() # add x labels (braces) for (p,string,bar) in zip(probabilities, prob_strings,hist.bars): brace = Brace(bar, DOWN, buff = 0.1) p_label = TexMobject(string).next_to(brace, DOWN, buff = SMALL_BUFF).scale(0.7) group = VGroup(brace, p_label) braces.add(brace) p_labels.add(p_label) self.play( LaggedStart(FadeIn,braces), LaggedStart(FadeIn, p_labels) ) y_average = np.mean(y_values) averaged_y_values = y_average * np.ones(np.shape(y_values)) averaged_hist = flat_hist = Histogram(probabilities, averaged_y_values, mode = "widths", x_scale = x_scale, y_scale = y_scale, x_labels = "none", y_labels = "none" ).fade(0.2) ghost_hist = hist.copy().fade(0.8) self.bring_to_back(ghost_hist) self.play(Transform(hist, averaged_hist, run_time = 3)) self.wait() average_brace = Brace(averaged_hist, RIGHT, buff = 0.1) average_label = TexMobject(str(y_average)).scale(0.7) average_label.next_to(average_brace, RIGHT, SMALL_BUFF) average_group = VGroup(average_brace, average_label) one_brace = Brace(averaged_hist, DOWN, buff = 0.1) one_p_label = TexMobject(str(1)).next_to(one_brace, DOWN, buff = SMALL_BUFF).scale(0.7) one_group = VGroup(one_brace, one_p_label) self.play( FadeIn(average_group), Transform(braces, one_brace), Transform(p_labels, one_p_label), ) rect = SurroundingRectangle(formula, buff = 0.5 * MED_LARGE_BUFF) self.play(ShowCreation(rect)) class DieFace(SVGMobject): def __init__(self, value, **kwargs): self.value = value self.file_name = "Dice-" + str(value) self.ensure_valid_file() SVGMobject.__init__(self, file_name = self.file_name) class RowOfDice(VGroup): CONFIG = { "values" : range(1,7), "direction": RIGHT, } def generate_points(self): for value in self.values: new_die = DieFace(value) new_die.submobjects[0].set_fill(opacity = 0) new_die.submobjects[0].set_stroke(width = 7) new_die.next_to(self, self.direction) self.add(new_die) self.move_to(ORIGIN) class ShowUncertainty1(Scene): def throw_a_die(self): eye = np.random.randint(1,7) face = self.row_of_dice.submobjects[eye - 1] self.play( ApplyMethod(face.submobjects[0].set_fill, {"opacity": 1}, rate_func = there_and_back, run_time = 0.3, ), ) def construct(self): self.row_of_dice = RowOfDice(direction = DOWN).scale(0.5) self.add(self.row_of_dice) for i in range(5): self.throw_a_die() self.wait(1) for i in range(10): self.throw_a_die() self.wait(0.3) for i in range(10): self.throw_a_die() self.wait(0.1) class IdealizedDieHistogram(Scene): def construct(self): self.probs = 1.0/6 * np.ones(6) x_scale = 1.3 y_labels = ["${1\over 6}$"] * 6 hist = Histogram(np.ones(6), self.probs, mode = "widths", x_labels = "none", y_labels = y_labels, y_label_position = "center", y_scale = 20, x_scale = x_scale, ) hist.rotate(-TAU/4) for label in hist.y_labels_group: label.rotate(TAU/4) hist.remove(hist.y_labels_group) self.play(FadeIn(hist)) self.play(LaggedStart(FadeIn, hist.y_labels_group)) class ShowUncertainty2(Scene): def throw_darts(self, n, run_time = 1): points = np.random.normal( loc = self.dartboard.get_center(), scale = 0.6 * np.ones(3), size = (n,3) ) points[:,2] = 0 dots = VGroup() for point in points: dot = Dot(point, radius = 0.04, fill_opacity = 0.7) dots.add(dot) self.add(dot) self.play( LaggedStart(FadeIn, dots, lag_ratio = 0.01, run_time = run_time) ) def construct(self): self.dartboard = ImageMobject("dartboard").scale(2) dartboard_circle = Circle( radius = self.dartboard.get_width() / 2, fill_color = BLACK, fill_opacity = 0.5, stroke_color = WHITE, stroke_width = 5 ) self.dartboard.add(dartboard_circle) self.add(self.dartboard) self.throw_darts(5,5) self.throw_darts(20,5) self.throw_darts(100,5) self.throw_darts(1000,5) class ShowUncertainty3(Scene): def construct(self): randy = CoinFlippingPiCreature(color = MAROON_E) randy.scale(0.5).to_edge(LEFT + DOWN) heads = tails = 0 tally = TallyStack(heads, tails, anchor = ORIGIN) nb_flips = 10 flips = np.random.randint(2, size = nb_flips) for i in range(nb_flips): self.play(FlipCoin(randy)) self.wait(0.5) flip = flips[i] if flip == 0: heads += 1 elif flip == 1: tails += 1 else: raise Exception("That side does not exist on this coin") new_tally = TallyStack(heads, tails, anchor = ORIGIN) if tally.nb_heads == 0 and new_tally.nb_heads == 1: self.play(FadeIn(new_tally.heads_stack)) elif tally.nb_tails == 0 and new_tally.nb_tails == 1: self.play(FadeIn(new_tally.tails_stack)) else: self.play(Transform(tally, new_tally)) tally = new_tally SICKLY_GREEN = "#9BBD37" class OneIn200HasDisease(Scene): def construct(self): title = TextMobject("1 in 200") title.to_edge(UP) creature = PiCreature() all_creatures = VGroup(*[ VGroup(*[ creature.copy() for y in range(20) ]).arrange_submobjects(DOWN, SMALL_BUFF) for x in range(10) ]).arrange_submobjects(RIGHT, SMALL_BUFF) all_creatures.scale_to_fit_height(FRAME_HEIGHT * 0.8) all_creatures.next_to(title, DOWN) randy = all_creatures[0][0] all_creatures[0].remove(randy) randy.change_mode("sick") randy.set_color(SICKLY_GREEN) randy.save_state() randy.scale_to_fit_height(3) randy.center() randy.change_mode("plain") randy.set_color(BLUE) self.add(randy) p_sick = TexMobject("p(","\\text{sick}",") = 0.5\%") p_sick.set_color_by_tex("sick", SICKLY_GREEN) p_sick.next_to(randy, RIGHT+UP) self.add(p_sick) self.wait() self.play( randy.change_mode, "sick", randy.set_color, SICKLY_GREEN ) self.play(Blink(randy)) self.play(randy.restore) self.play( FadeOut(p_sick), Write(title), LaggedStart(FadeIn, all_creatures, run_time = 3) ) self.wait() class PascalBrickWall(VMobject): CONFIG = { "left_color" : YELLOW, "right_color" : BLUE, "height" : 1.0, "width" : 8.0, "outcome_shrinkage_factor_x" : 0.85, "outcome_shrinkage_factor_y" : 0.95 } def __init__(self, n, **kwargs): self.subdiv_level = n self.coloring_level = n VMobject.__init__(self, **kwargs) def generate_points(self): self.submobjects = [] self.rects = self.get_rects_for_level(self.coloring_level) self.add(self.rects) self.subdivs = self.get_subdivs_for_level(self.subdiv_level) self.add(self.subdivs) self.border = SurroundingRectangle(self, buff = 0, color = WHITE) self.add(self.border) def get_rects_for_level(self,r): rects = VGroup() for k in range(r + 1): proportion = float(choose(r,k)) / 2**r new_rect = Rectangle( width = proportion * self.width, height = self.height, fill_color = graded_color(r,k), fill_opacity = 1, stroke_width = 0 ) if len(rects.submobjects) > 0: new_rect.next_to(rects,RIGHT,buff = 0) else: new_rect.next_to(self.get_center() + 0.5 * self.width * LEFT, RIGHT, buff = 0) rects.add(new_rect) return rects def get_subdivs_for_level(self,r): subdivs = VGroup() x = - 0.5 * self.width for k in range(0, r): proportion = float(choose(r,k)) / 2**r x += proportion * self.width subdiv = Line( x * RIGHT + 0.5 * self.height * UP, x * RIGHT + 0.5 * self.height * DOWN, ) subdivs.add(subdiv) subdivs.move_to(self.get_center()) return subdivs def get_outcome_centers_for_level(self,r): dpos = float(self.width) / (2 ** r) * RIGHT pos = 0.5 * self.width * LEFT + 0.5 * dpos centers = [] for k in range(0, 2 ** r): centers.append(self.get_center() + pos + k * dpos) return centers def get_outcome_rects_for_level(self,r, with_labels = False): centers = self.get_outcome_centers_for_level(r) outcome_width = self.outcome_shrinkage_factor_x * float(self.width) / (2 ** r) outcome_height = self.outcome_shrinkage_factor_y * self.height corner_radius = min(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 = BLACK, fill_opacity = 0.2, stroke_width = 0 ) rects = VGroup() for center in centers: rects.add(rect.copy().move_to(center)) rects.move_to(self.get_center()) if with_labels == False: return rects # else sequences = self.get_coin_sequences_for_level(r) labels = VGroup() for (seq, rect) in zip(sequences, rects): coin_seq = CoinSequence(seq, direction = DOWN) coin_seq.shift(rect.get_center() - coin_seq.get_center()) # not simply move_to bc coin_seq is not centered rect.add(coin_seq) return rects def get_coin_sequences_for_level(self,r): # array of arrays of characters if r < 0 or int(r) != r: raise Exception("Level must be a positive integer") if r == 0: return [] if r == 1: return [["H"], ["T"]] previous_seq_array = self.get_coin_sequences_for_level(r - 1) subdiv_lengths = [choose(r - 1, k) for k in range(r)] seq_array = [] index = 0 for length in subdiv_lengths: for seq in previous_seq_array[index:index + length]: seq_copy = copy.copy(seq) seq_copy.append("H") seq_array.append(seq_copy) for seq in previous_seq_array[index:index + length]: seq_copy = copy.copy(seq) seq_copy.append("T") seq_array.append(seq_copy) index += length return seq_array def get_outcome_width_for_level(self,r): return self.width / (2**r) def get_rect_widths_for_level(self, r): ret_arr = [] for k in range(0, r): proportion = float(choose(r,k)) / 2**r ret_arr.append(proportion * self.width) return ret_arr class SplitRectsInBrickWall(Animation): def __init__(self, mobject, **kwargs): r = self.subdiv_level = mobject.subdiv_level + 1 self.subdivs = VGroup() x = - 0.5 * mobject.width for k in range(0, r): proportion = float(choose(r,k)) / 2**r x += proportion * mobject.width subdiv = DashedLine( mobject.get_center() + x * RIGHT + 0.5 * mobject.height * UP, mobject.get_center() + x * RIGHT + 0.5 * mobject.height * UP, ) self.subdivs.add(subdiv) mobject.add(self.subdivs) Animation.__init__(self, mobject, **kwargs) def update_mobject(self, alpha): for subdiv in self.subdivs: x = subdiv.get_start()[0] start = self.mobject.get_center() start += x * RIGHT + 0.5 * self.mobject.height * UP end = start + alpha * self.mobject.height * DOWN subdiv.put_start_and_end_on(start,end) class PascalBrickWallScene(Scene): def split_tallies(self, direction = DOWN): self.tallies_copy = self.tallies.copy() self.add_foreground_mobject(self.tallies_copy) tally_targets_left = [ rect.get_center() + 0.25 * rect.get_width() * LEFT for rect in self.row.rects ] tally_targets_right = [ rect.get_center() + 0.25 * rect.get_width() * RIGHT for rect in self.row.rects ] if np.all(direction == LEFT) or np.all(direction == RIGHT): tally_y_pos = self.tallies[0].anchor[1] for target in tally_targets_left: target[1] = tally_y_pos for target in tally_targets_right: target[1] = tally_y_pos for (i, tally) in enumerate(self.tallies): if len(self.decimals) > 0: decimal = self.decimals[i] else: decimal = VMobject() target_left = tally_targets_left[i] new_tally_left = TallyStack(tally.nb_heads + 1, tally.nb_tails) new_tally_left.move_anchor_to(target_left) v = target_left - tally.anchor self.play( tally.move_anchor_to, target_left, decimal.shift,v ) tally.anchor = target_left self.play(Transform(tally, new_tally_left)) tally_copy = self.tallies_copy[i] decimal_copy = decimal.copy() target_right = tally_targets_right[i] new_tally_right = TallyStack(tally.nb_heads, tally.nb_tails + 1) new_tally_right.move_anchor_to(target_right) v = target_right - tally_copy.anchor self.play(tally_copy.move_anchor_to, target_right) tally_copy.anchor = target_right self.play(Transform(tally_copy, new_tally_right)) tally_copy.nb_heads = new_tally_right.nb_heads tally_copy.nb_tails = new_tally_right.nb_tails tally.nb_heads = new_tally_left.nb_heads tally.nb_tails = new_tally_left.nb_tails def tally_split_animations(self, direction = DOWN): self.tallies_copy = self.tallies.copy() self.add_foreground_mobject(self.tallies_copy) tally_targets_left = [ rect.get_center() + 0.25 * rect.get_width() * LEFT for rect in self.row.rects ] tally_targets_right = [ rect.get_center() + 0.25 * rect.get_width() * RIGHT for rect in self.row.rects ] if np.all(direction == LEFT) or np.all(direction == RIGHT): tally_y_pos = self.tallies[0].anchor[1] for target in tally_targets_left: target[1] = tally_y_pos for target in tally_targets_right: target[1] = tally_y_pos anims1 = [] if len(self.decimals) > 0: self.decimal_copies = VGroup() for (i, tally) in enumerate(self.tallies): if len(self.decimals) > 0: decimal = self.decimals[i] else: decimal = VMobject() target_left = tally_targets_left[i] v = target_left - tally.anchor anims1.append(tally.move_anchor_to) anims1.append(target_left) anims1.append(decimal.shift) anims1.append(v) tally.anchor = target_left tally_copy = self.tallies_copy[i] decimal_copy = decimal.copy() target_right = tally_targets_right[i] v = target_right - tally_copy.anchor anims1.append(tally_copy.move_anchor_to) anims1.append(target_right) anims1.append(decimal_copy.shift) anims1.append(v) if len(self.decimals) > 0: self.decimal_copies.add(decimal_copy) tally_copy.anchor = target_right anims2 = [] for (i, tally) in enumerate(self.tallies): new_tally_left = TallyStack(tally.nb_heads + 1, tally.nb_tails) new_tally_left.move_anchor_to(tally.anchor) anims2.append(Transform(tally, new_tally_left)) tally_copy = self.tallies_copy[i] new_tally_right = TallyStack(tally.nb_heads, tally.nb_tails + 1) new_tally_right.move_anchor_to(tally_copy.anchor) anims2.append(Transform(tally_copy, new_tally_right)) tally_copy.nb_heads = new_tally_right.nb_heads tally_copy.nb_tails = new_tally_right.nb_tails tally.nb_heads = new_tally_left.nb_heads tally.nb_tails = new_tally_left.nb_tails if len(self.decimals) > 0: self.add_foreground_mobject(self.decimal_copies) return anims1, anims2 def split_tallies_at_once(self, direction = DOWN): anims1, anims2 = self.tally_split_animations(direction = direction) self.play(*(anims1 + anims2)) def split_tallies_in_two_steps(self, direction = DOWN): anims1, anims2 = self.tally_split_animations(direction = direction) self.play(*anims1) self.wait(0.3) self.play(*anims2) def split_decimals_alone(self): r = self.row.coloring_level targets_left = [] targets_right = [] for rect in self.row.get_rects_for_level(r): target = rect.get_center() + 0.25 * rect.get_width() * LEFT targets_left.append(target) target = rect.get_center() + 0.25 * rect.get_width() * RIGHT targets_right.append(target) anims = [] self.decimal_copies = VGroup() for (i, decimal) in enumerate(self.decimals): anims.append(decimal.move_to) anims.append(targets_left[i]) decimal_copy = decimal.copy() anims.append(decimal_copy.move_to) anims.append(targets_right[i]) self.decimal_copies.add(decimal_copy) self.play(*anims) self.add_foreground_mobject(self.decimal_copies) def merge_rects_by_subdiv(self): half_merged_row = self.row.copy() half_merged_row.subdiv_level += 1 half_merged_row.generate_points() half_merged_row.move_to(self.row.get_center()) self.play(FadeIn(half_merged_row)) self.row = half_merged_row def merge_tallies(self, direction = UP): r = self.row.subdiv_level tally_targets = [ rect.get_center() for rect in self.row.get_rects_for_level(r) ] if np.all(direction == LEFT) or np.all(direction == RIGHT): y_pos = self.row.get_center()[1] + 1.2 * 0.5 * self.row.get_height() for target in tally_targets: target[1] = y_pos anims = [] for (tally, target) in zip(self.tallies[1:], tally_targets[1:-1]): anims.append(tally.move_anchor_to) anims.append(target) for (tally, target) in zip(self.tallies_copy[:-1], tally_targets[1:-1]): anims.append(tally.move_anchor_to) anims.append(target) self.play(*anims) # update anchors for (tally, target) in zip(self.tallies[1:], tally_targets[1:-1]): tally.anchor = target for (tally, target) in zip(self.tallies_copy[:-1], tally_targets[1:-1]): tally.anchor = target self.remove(self.tallies_copy) self.tallies.add(self.tallies_copy[-1]) def merge_rects_by_coloring(self): merged_row = self.row.copy() merged_row.coloring_level += 1 merged_row.generate_points() self.play(FadeIn(merged_row)) self.row = merged_row def merge_decimals(self): anims = [] if self.decimals in self.mobjects: anims.append(FadeOut(self.decimals)) if self.decimal_copies in self.mobjects: anims.append(FadeOut(self.decimal_copies)) self.new_decimals = VGroup() self.decimal_copies = VGroup() r = self.row.coloring_level for (i, rect) in enumerate(self.row.rects): k = choose(r,i) decimal = Integer(k) decimal.move_to(rect) if rect.get_width() < 0.2: # then the rect is too narrow, # let the decimal go in dignity decimal.set_stroke(width = 0) decimal.set_fill(opacity = 0) self.new_decimals.add(decimal) anims.append(FadeIn(self.new_decimals)) self.play(*anims) self.remove(self.decimal_copies) self.decimals = self.new_decimals.copy() #self.remove(self.new_decimals) self.add_foreground_mobject(self.decimals) def move_tallies_on_top(self): self.play( self.tallies.shift, 1.2 * 0.5 * self.row.height * UP ) for tally in self.tallies: tally.anchor += 1.2 * 0.5 * self.row.height * UP def construct(self): #self.force_skipping() randy = CoinFlippingPiCreature() randy = randy.scale(0.5).move_to(3*DOWN + 6*LEFT) self.add(randy) self.row = PascalBrickWall(1, height = 2, width = 10) self.decimals = VGroup() self.play(FlipCoin(randy), FadeIn(self.row)) self.wait() # put tallies on top self.tallies = VGroup(*[ TallyStack(1 - i, i) for i in range(2) ]) for (tally, rect) in zip(self.tallies, self.row.rects): new_anchor = rect.get_center() + 1.2 * 0.5 * rect.get_height() * UP tally.move_anchor_to(new_anchor) self.play(FadeIn(tally)) self.add_foreground_mobject(self.tallies) self.wait() # # # # # # # # # SECOND FLIP # # # # # # # # # self.play(FlipCoin(randy)) self.wait() self.play( SplitRectsInBrickWall(self.row) ) self.wait() self.split_tallies_in_two_steps() self.wait() self.merge_rects_by_subdiv() self.wait() self.merge_tallies() self.merge_rects_by_coloring() self.wait() self.move_tallies_on_top() # show individual outcomes outcomes = self.row.get_outcome_rects_for_level(2, with_labels = True) self.play( LaggedStart(FadeIn, outcomes) ) self.wait() self.play( LaggedStart(FadeOut, outcomes) ) # show their numbers nb_outcomes = [1,2,1] self.decimals = VGroup() for (n,rect) in zip(nb_outcomes, self.row.rects): decimal = Integer(n).move_to(rect) self.decimals.add(decimal) self.play( LaggedStart(FadeIn, self.decimals) ) self.wait() self.play( LaggedStart(FadeOut, self.decimals) ) self.decimals = VGroup() # # # # # # # # # THIRD FLIP # # # # # # # # # self.play(FlipCoin(randy)) self.wait() self.play( SplitRectsInBrickWall(self.row) ) self.wait() self.split_tallies_in_two_steps() self.wait() self.merge_rects_by_subdiv() self.wait() self.merge_tallies() self.merge_rects_by_coloring() self.wait() self.move_tallies_on_top() # show individual outcomes outcomes = self.row.get_outcome_rects_for_level(3, with_labels = True) self.play( LaggedStart(FadeIn, outcomes) ) self.wait() self.play( LaggedStart(FadeOut, outcomes) ) # show their numbers nb_outcomes = [1,3,3,1] self.decimals = VGroup() for (n,rect) in zip(nb_outcomes, self.row.rects): decimal = Integer(n).move_to(rect) self.decimals.add(decimal) self.play( LaggedStart(FadeIn, self.decimals) ) self.wait() self.add_foreground_mobject(self.decimals) # # # # # # # # # FOURTH FLIP # # # # # # # # # self.play(FlipCoin(randy)) self.wait() self.play( SplitRectsInBrickWall(self.row) ) self.wait() self.add_foreground_mobject(self.tallies[-1]) # this tweaks an undesirable overlap in the next animation self.split_tallies_at_once(direction = LEFT) self.wait() self.merge_rects_by_subdiv() self.wait() self.merge_tallies(direction = LEFT) self.merge_rects_by_coloring() self.merge_decimals() self.wait() # # # # # # # # # FIFTH FLIP # # # # # # # # # self.play(FlipCoin(randy)) self.wait() self.play( SplitRectsInBrickWall(self.row) ) self.wait() self.split_tallies_at_once(direction = LEFT) self.wait() self.merge_rects_by_subdiv() self.wait() self.merge_tallies(direction = LEFT) self.merge_rects_by_coloring() self.merge_decimals() self.wait() # # # # # # # # # SIXTH FLIP # # # # # # # # # self.revert_to_original_skipping_status() # removing the tallies (boy are they sticky) self.play(FadeOut(self.tallies)) self.remove(self.tallies, self.tallies_copy) for tally in self.tallies: self.remove_foreground_mobject(tally) self.remove(tally) for tally in self.tallies_copy: self.remove_foreground_mobject(tally) self.remove(tally) # delete all the old crap hidden behind the row # before we can move it self.remove(*self.mobjects) self.add(randy,self.decimals,self.decimal_copies) previous_row = self.row.copy() self.add(previous_row) v = 1.25 * self.row.height * UP self.play( previous_row.shift, v, self.decimals.shift, v, self.decimal_copies.shift, v ) self.add(self.row) self.bring_to_back(self.row) self.row.shift(v) w = 1.5 * self.row.height * DOWN self.play( self.row.shift, w ) self.play( SplitRectsInBrickWall(self.row) ) self.wait() self.merge_rects_by_subdiv() self.wait() # show individual outcomes outcomes = previous_row.get_outcome_rects_for_level(5, with_labels = False) grouped_outcomes = VGroup() index = 0 for i in range(6): size = choose(5,i) grouped_outcomes.add(VGroup(outcomes[index:index + size])) index += size grouped_outcomes_copy = grouped_outcomes.copy() original_grouped_outcomes = grouped_outcomes.copy() # for later reference self.play( LaggedStart(FadeIn, grouped_outcomes), LaggedStart(FadeIn, grouped_outcomes_copy), ) self.wait() # show how the outcomes in one tally split into two copies # going into the neighboring tallies n = 5 # level to split k = 2 # tally to split target_outcomes = self.row.get_outcome_rects_for_level(n + 1, with_labels = False) grouped_target_outcomes = VGroup() 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],grouped_target_outcomes[k][0][old_tally_sizes[k - 1]:]) ) self.play( Transform(grouped_outcomes_copy[k],grouped_target_outcomes[k + 1][0][:old_tally_sizes[k]]) ) old_tally_sizes.append(0) # makes the ege cases work properly # split the other for i in range(k) + range(k + 1, n + 1): self.play( Transform(grouped_outcomes[i][0], grouped_target_outcomes[i][0][old_tally_sizes[i - 1]:] ), Transform(grouped_outcomes_copy[i][0], grouped_target_outcomes[i + 1][0][:old_tally_sizes[i]] ) ) self.wait() # remove outcomes and sizes except for one tally anims = [] for i in range(n + 1): if i != k - 1: anims.append(FadeOut(grouped_outcomes_copy[i])) if i != k: anims.append(FadeOut(grouped_outcomes[i])) self.play(*anims) self.wait() self.play( Transform(grouped_outcomes_copy[k - 1], original_grouped_outcomes[k - 1]) ) self.play( Transform(grouped_outcomes[k], original_grouped_outcomes[k]) ) new_rects = self.row.get_rects_for_level(n + 1) decimals_copy = self.decimals.copy() decimals_copy2 = self.decimals.copy() self.play( Transform(grouped_outcomes[k],grouped_target_outcomes[k][0][old_tally_sizes[k - 1]:]), Transform(grouped_outcomes_copy[k - 1],grouped_target_outcomes[k][0][:old_tally_sizes[k]]), decimals_copy[k - 1].move_to, new_rects[k], decimals_copy2[k].move_to, new_rects[k], ) # show new outcome sizes new_decimals = VGroup() for (i,rect) in zip(new_tally_sizes, new_rects): decimal = Integer(i).move_to(rect) new_decimals.add(decimal) self.play( FadeOut(decimals_copy[k - 1]), FadeOut(decimals_copy2[k]), FadeIn(new_decimals[k]) ) # move the old decimals into the new row anims = [] anims.append(decimals_copy2[0].move_to) anims.append(new_rects[0]) for i in range(1,k) + range(k + 1, n): anims.append(decimals_copy[i - 1].move_to) anims.append(new_rects[i]) anims.append(decimals_copy2[i].move_to) anims.append(new_rects[i]) anims.append(decimals_copy[n].move_to) anims.append(new_rects[n + 1]) self.play(*anims) # fade them out and fade in their sums anims = [] for i in range(1,k) + range(k + 1, n): anims.append(FadeOut(decimals_copy[i - 1])) anims.append(FadeOut(decimals_copy2[i])) anims.append(FadeIn(new_decimals[i])) self.play(*anims) self.add_foreground_mobject(new_decimals) class IRecognizeThis(TeacherStudentsScene): def construct(self): self.student_says("I have seen this before!") self.change_student_modes("pondering", "raise_right_hand", "pondering") self.teacher_says("This is Pascal's Triangle")