from big_ol_pile_of_manim_imports import * from old_projects.eoc.chapter8 import * COIN_RADIUS = 0.3 COIN_THICKNESS = 0.4 * COIN_RADIUS COIN_FORESHORTENING = 0.3 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 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) 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() # Line(ORIGIN, 0.4 * RIGHT, stroke_width = 15, color = YELLOW) 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 = 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 } 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 * RIGHT) 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): def __init__(self,h,t,**kwargs): self.nb_heads = h self.nb_tails = t 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) stack2.next_to(stack1, RIGHT, buff = SMALL_BUFF) stack2.align_to(stack1, DOWN) self.add(stack1, stack2) 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 #print "tallies for row", level, ":", [new_row[i][1] for i in range(2**level)] 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) print "sorted roots:", [sorted_row[i][2][0] for i in range(2**level)] self.rows.append(sorted_row) else: self.rows.append(new_row) class TestScene(Scene): def construct(self): #seq = CoinSequence(["H", "T", "T", "H"]).move_to(2 * LEFT) #self.add(seq) #stack = TallyStack(4,7, coin_thickness = COIN_THICKNESS) #self.add(stack) tree = CoinFlipTree(nb_levels = 7, sort_until_level = 0) tree.move_to(ORIGIN) self.add(tree) for i in range(1, 8): new_tree = CoinFlipTree(nb_levels = 7, sort_until_level = i) new_tree.move_to(ORIGIN) self.play(Transform(tree, new_tree)) self.wait() self.wait() class CoinFlipBranchToAreaScene(Scene): def construct(self): pass 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() def show_series(self): series = VideoSeries() 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), ]) essence_words = words.get_part_by_tex("Essence").copy() self.play( FadeOut(self.teacher.bubble), FadeOut(self.teacher.bubble.content), essence_words.next_to, series, DOWN, *[ ApplyMethod(pi.change_mode, "pondering") for pi in self.get_pi_creatures() ] ) self.wait(3) self.series = series self.essence_words = essence_words class IllustrateAreaModel1(Scene): def construct(self): # show independent events sample_space_width = sample_space_height = 3.0 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 = BLUE, fill_opacity = 1.0 ) rect_not_A = Rectangle( width = p_of_not_A * sample_space_width, height = 1 * sample_space_height, stroke_width = 0, fill_color = BLUE_E, 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), ) # self.play( # ShowCreation(brace_not_A), # Write(label_not_A), # ) rect_B = Rectangle( width = 1 * sample_space_width, height = p_of_B * sample_space_height, stroke_width = 0, fill_color = GREEN, fill_opacity = 0.5 ) rect_not_B = Rectangle( width = 1 * sample_space_width, height = p_of_not_B * sample_space_height, stroke_width = 0, fill_color = GREEN_E, fill_opacity = 0.5 ).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), ) # self.play( # ShowCreation(brace_not_B), # Write(label_not_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) ) self.play(FadeIn(label_A_and_B)) self.add_foreground_mobject(label_A_and_B) indep_formula = TexMobject("P(A\\text{ and }B)", "=", "P(A)", "\cdot", "P(B)") indep_formula = indep_formula.scale(0.7).next_to(rect_not_B, UP, buff = MED_LARGE_BUFF) 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() # show conditional prob rect_A_and_B.set_fill(color = GREEN, 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 = GREEN_E, fill_opacity = 0.5 ).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 = GREEN, fill_opacity = 0.5 ).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 = GREEN_E, fill_opacity = 0.5 ).next_to(rect_not_A_and_B, UP, buff = 0) self.remove(rect_B, rect_not_B) self.add(rect_A_and_not_B, rect_not_A_and_B, rect_not_A_and_not_B) 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 = GREEN, fill_opacity = 0.5 ).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 = GREEN_E, fill_opacity = 0.5 ).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)) 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[-2], RIGHT ) self.wait() # def show_independent_events(self): # sample_space = SampleSpace( # full_space_config = { # "height" : 3, # "width" : 3, # "fill_opacity" : 0 # } # ) # sample_space.divide_horizontally(0.4) # sample_space.horizontal_parts.set_fill(opacity = 0) # h_labels = [ # TexMobject("P(", "A", ")"), # TexMobject("P(\\text{not }", "A", ")"), # ] # for label in h_labels: # label.scale(0.7) # #self.color_label(label) # sample_space.get_side_braces_and_labels(h_labels) # sample_space.add_braces_and_labels() # h_parts = sample_space.horizontal_parts # for (label, part) in zip(h_labels, h_parts): # label.next_to(part, 2 * LEFT) # sample_space.add(label) # values = [0.2, 0.2] # color_pairs = [(GREEN, BLUE), (GREEN_E, BLUE_E)] # v_parts = VGroup() # for tup in zip(h_parts, values, color_pairs): # part, value, colors = tup # part.divide_vertically(value, colors = colors) # part.vertical_parts.set_fill(opacity = 0.8) # #label = TexMobject( # # "P(", "B", "|", given_str, "A", ")" # #) # #label.scale(0.7) # #self.color_label(label) # if part == h_parts[0]: # part.get_subdivision_braces_and_labels( # part.vertical_parts, [label], DOWN # ) # sample_space.add( # part.vertical_parts.braces, # # part.vertical_parts.labels, # ) # v_parts.add(part.vertical_parts.submobjects) # v_labels = [ # TexMobject("P(", "B", ")"), # TexMobject("P(\\text{not }", "B", ")"), # ] # for (label, part) in zip(v_labels, v_parts[1::2]): # label.scale(0.7) # label.next_to(part, DOWN) # sample_space.add(label) # sample_space.to_edge(LEFT) # self.add(sample_space) # self.sample_space = sample_space # self.wait() def color_label(self, label): label.set_color_by_tex("B", RED) label.set_color_by_tex("I", GREEN) class IllustrateAreaModel2(AreaIsDerivative): CONFIG = { "y_max" : 4, "y_min" : -4, "num_iterations" : 7, "y_axis_label" : "", "num_rects" : 400, "dT" : 0.25, "variable_point_label" : "T", "area_opacity" : 0.8, } def construct(self): self.setup_axes() self.introduce_variable_area() graph, label = self.get_v_graph_and_label() rect_list = self.get_riemann_rectangles_list( graph, self.num_iterations ) VGroup(*rect_list).set_fill(opacity = 0.8) rects = rect_list[0] self.play(ShowCreation(graph)) self.play(Write(rects)) for new_rects in rect_list[1:]: rects.align_submobjects(new_rects) for every_other_rect in rects[::2]: every_other_rect.set_fill(opacity = 0) self.play(Transform( rects, new_rects, run_time = 2, submobject_mode = "lagged_start" )) self.wait() # self.play(FadeOut(self.x_axis.numbers)) self.add_T_label(6) self.change_area_bounds( new_t_max = 4, rate_func = there_and_back, run_time = 2 ) def func(self, x): return np.exp(-x**2/2) class AreaSplitting(Scene): def create_rect_row(self,n): rects_group = VGroup() for k in range(n+1): proportion = float(choose(n,k)) / 2**n new_rect = Rectangle( width = proportion * WIDTH, height = HEIGHT, fill_color = graded_color(n,k), fill_opacity = 1 ) new_rect.next_to(rects_group,RIGHT,buff = 0) rects_group.add(new_rect) return rects_group def split_rect_row(self,rect_row): split_row = VGroup() for rect in rect_row.submobjects: half = rect.copy().stretch_in_place(0.5,0) left_half = half.next_to(rect.get_center(),LEFT,buff = 0) right_half = half.copy().next_to(rect.get_center(),RIGHT,buff = 0) split_row.add(left_half, right_half) return split_row def rect_center(self,n,i,j): if n < 0: raise Exception("wrong indices " + str(n) + ", " + str(i) + ", " + str(j)) if i < 0 or i > n: raise Exception("wrong indices " + str(n) + ", " + str(i) + ", " + str(j)) if j > choose(n,i) or j < 0: raise Exception("wrong indices " + str(n) + ", " + str(i) + ", " + str(j)) rect = self.brick_array[n][i] width = rect.get_width() left_x = rect.get_center()[0] - width/2 spacing = width / choose(n,i) x = left_x + (j+0.5) * spacing return np.array([x,rect.get_center()[1], rect.get_center()[2]]) def construct(self): # Draw the bricks brick_wall = VGroup() rect_row = self.create_rect_row(0) rect_row.move_to(3.5*UP + 0*HEIGHT*DOWN) self.add(rect_row) brick_wall.add(rect_row) self.brick_array = [[rect_row.submobjects[0]]] for n in range(NB_ROWS): # copy and shift new_rect_row = rect_row.copy() self.add(new_rect_row) self.play(new_rect_row.shift,HEIGHT * DOWN) self.wait() #split split_row = self.split_rect_row(new_rect_row) self.play(FadeIn(split_row)) self.remove(new_rect_row) self.wait() # merge rect_row = self.create_rect_row(n+1) rect_row.move_to(3.5*UP + (n+1)*HEIGHT*DOWN) self.play(FadeIn(rect_row)) brick_wall.add(rect_row) self.remove(split_row) self.wait() # add to brick dict rect_array = [] for rect in rect_row.submobjects: rect_array.append(rect) self.brick_array.append(rect_array) self.play( brick_wall.set_fill, {"opacity" : 0.2} ) # Draw the branches for (n, rect_row_array) in enumerate(self.brick_array): for (i, rect) in enumerate(rect_row_array): pos = rect.get_center() tally = TallyStack(n - i, i) tally.move_to(pos) # from the left lines = VGroup() if i > 0: for j in range(choose(n-1,i-1)): start_pos = self.rect_center(n-1,i-1,j) end_pos = self.rect_center(n,i,j) lines.add(Line(start_pos,end_pos, stroke_color = GRADE_COLOR_2)) self.play( LaggedStart(ShowCreation, lines)) # from the right lines = VGroup() if i < n: for j in range(choose(n-1,i)): start_pos = self.rect_center(n-1,i,j) if i != 0: end_pos = self.rect_center(n,i,choose(n-1,i-1) + j) else: end_pos = self.rect_center(n,i,j) lines.add(Line(start_pos,end_pos, stroke_color = GRADE_COLOR_1)) self.play( LaggedStart(ShowCreation, lines)) #self.play(FadeIn(tally))