def finite_analog(self, left_mob, arrow, right_mob): self.clear() self.add(left_mob, arrow, right_mob) ex = TextMobject("\\times") ex.highlight(RED) # ex.shift(arrow.get_center()) middle = TexMobject("\\sum_{n=0}^N 2^n \\equiv -1 \\mod 2^{N+1}") finite_analog = TextMobject("Finite analog") finite_analog.scale(0.8) brace = Brace(middle, UP) finite_analog.next_to(brace, UP) new_left = left_mob.copy().to_edge(LEFT) new_right = right_mob.copy().to_edge(RIGHT) left_arrow, right_arrow = [ Arrow(mob1.get_right()[0] * RIGHT, mob2.get_left()[0] * RIGHT, buff=0) for mob1, mob2 in [(new_left, middle), (middle, new_right)] ] for mob in ex, middle: mob.sort_points(np.linalg.norm) self.play(GrowFromCenter(ex)) self.wait() self.play(Transform(left_mob, new_left), Transform(arrow.copy(), left_arrow), DelayByOrder(Transform(ex, middle)), Transform(arrow, right_arrow), Transform(right_mob, new_right)) self.play(GrowFromCenter(brace), ShimmerIn(finite_analog)) self.wait() self.equivalence(left_mob, left_arrow, Mobject(middle, brace, finite_analog))
def construct(self): definition = TexMobject([ "\\text{HC}(", "x", ")", "=\\lim_{n \\to \\infty}\\text{PHC}_n(", "x", ")" ]) definition.to_edge(UP) definition.split()[1].highlight(BLUE) definition.split()[-2].highlight(BLUE) intro = TextMobject("Three things need to be proven") prove_that = TextMobject("Prove that HC is $\\dots$") prove_that.scale(0.7) prove_that.to_edge(LEFT) items = TextMobject([ "\\begin{enumerate}", "\\item Well-defined: ", "Points on Pseudo-Hilbert-curves really do converge", "\\item A Curve: ", "HC is continuous", "\\item Space-filling: ", "Each point in the unit square is an output of HC", "\\end{enumerate}", ]).split() items[1].highlight(GREEN) items[3].highlight(YELLOW_C) items[5].highlight(MAROON) Mobject(*items).to_edge(RIGHT) self.add(definition) self.play(ShimmerIn(intro)) self.wait() self.play(Transform(intro, prove_that)) for item in items[1:-1]: self.play(ShimmerIn(item)) self.wait()
def construct(self): scale_factor = 0.9 grid = Grid(4, 4, point_thickness = 1) curve = HilbertCurve(order = 2) for mob in grid, curve: mob.scale(scale_factor) words = TextMobject(""" Sequence of curves is stable $\\leftrightarrow$ existence of limit curve """, size = "\\normal") words.scale(1.25) words.to_edge(UP) self.add(curve, grid) self.dither() for n in range(3, 7): if n == 5: self.play(ShimmerIn(words)) new_grid = Grid(2**n, 2**n, point_thickness = 1) new_curve = HilbertCurve(order = n) for mob in new_grid, new_curve: mob.scale(scale_factor) self.play( ShowCreation(new_grid), Animation(curve) ) self.remove(grid) grid = new_grid self.play(Transform(curve, new_curve)) self.dither()
def construct(self): definition = TexMobject([ "\\text{HC}(", "x", ")", "=\\lim_{n \\to \\infty}\\text{PHC}_n(", "x", ")" ]) definition.to_edge(UP) definition.split()[1].highlight(BLUE) definition.split()[-2].highlight(BLUE) intro = TextMobject("Three things need to be proven") prove_that = TextMobject("Prove that HC is $\\dots$") prove_that.scale(0.7) prove_that.to_edge(LEFT) items = TextMobject([ "\\begin{enumerate}", "\\item Well-defined: ", "Points on Pseudo-Hilbert-curves really do converge", "\\item A Curve: ", "HC is continuous", "\\item Space-filling: ", "Each point in the unit square is an output of HC", "\\end{enumerate}", ]).split() items[1].highlight(GREEN) items[3].highlight(YELLOW_C) items[5].highlight(MAROON) Mobject(*items).to_edge(RIGHT) self.add(definition) self.play(ShimmerIn(intro)) self.dither() self.play(Transform(intro, prove_that)) for item in items[1:-1]: self.play(ShimmerIn(item)) self.dither()
def construct(self): scale_factor = 0.9 grid = Grid(4, 4, stroke_width=1) curve = HilbertCurve(order=2) for mob in grid, curve: mob.scale(scale_factor) words = TextMobject(""" Sequence of curves is stable $\\leftrightarrow$ existence of limit curve """, size="\\normal") words.scale(1.25) words.to_edge(UP) self.add(curve, grid) self.wait() for n in range(3, 7): if n == 5: self.play(ShimmerIn(words)) new_grid = Grid(2**n, 2**n, stroke_width=1) new_curve = HilbertCurve(order=n) for mob in new_grid, new_curve: mob.scale(scale_factor) self.play(ShowCreation(new_grid), Animation(curve)) self.remove(grid) grid = new_grid self.play(Transform(curve, new_curve)) self.wait()
def construct(self): names = [ "Johann_Bernoulli2", "Jacob_Bernoulli", "Gottfried_Wilhelm_von_Leibniz", "Newton" ] guys = [ImageMobject(name, invert=False) for name in names] johann = guys[0] johann.scale(0.8) pensive_johann = johann.copy() pensive_johann.scale(0.25) pensive_johann.to_corner(DOWN + LEFT) comparitive_johann = johann.copy() template = Square(side_length=2) comparitive_johann.replace(template) comparitive_johann.shift(UP + LEFT) greater_than = TexMobject(">") greater_than.next_to(comparitive_johann) for guy, name in zip(guys, names)[1:]: guy.replace(template) guy.next_to(greater_than) name_mob = TextMobject(name.replace("_", " ")) name_mob.scale(0.5) name_mob.next_to(guy, DOWN) guy.name_mob = name_mob guy.sort_points(lambda p: np.dot(p, DOWN + RIGHT)) bubble = ThoughtBubble(initial_width=12) bubble.stretch_to_fit_height(6) bubble.ingest_submobjects() bubble.pin_to(pensive_johann) bubble.shift(DOWN) point = Point(johann.get_corner(UP + RIGHT)) upper_point = Point(comparitive_johann.get_corner(UP + RIGHT)) lightbulb = ImageMobject("Lightbulb", invert=False) lightbulb.scale(0.1) lightbulb.sort_points(np.linalg.norm) lightbulb.next_to(upper_point, RIGHT) self.add(johann) self.wait() self.play(Transform(johann, pensive_johann), Transform(point, bubble), run_time=2) self.remove(point) self.add(bubble) weakling = guys[1] self.play(FadeIn(comparitive_johann), ShowCreation(greater_than), FadeIn(weakling)) self.wait(2) for guy in guys[2:]: self.play(DelayByOrder(Transform(weakling, upper_point))) self.play(FadeIn(guy), ShimmerIn(guy.name_mob)) self.wait(3) self.remove(guy.name_mob) weakling = guy self.play(FadeOut(weakling), FadeOut(greater_than)) self.play(ShowCreation(lightbulb)) self.wait() self.play(FadeOut(comparitive_johann), FadeOut(lightbulb)) self.play(ApplyMethod(Mobject(johann, bubble).scale, 10, run_time=3))
def discontinuous_point(self): point_description = TextMobject("Point where the function jumps") point_description.shift(3 * RIGHT) discontinuous_at_A = TextMobject("``Discontinuous at A''", size="\\Large") discontinuous_at_A.shift(2 * UP).to_edge(LEFT) text = TextMobject(""" Circle around ouput \\\\ points can never \\\\ be smaller than \\\\ the jump """) text.scale(0.75) text.shift(3.5 * RIGHT) input_value = 0.5 input_radius = 0.04 vary_circles = VaryCircles( self, input_value, input_radius, run_time=5, ) for dot in self.input_dot, self.output_dot: dot.center() kwargs = { "rate_func": lambda t: interpolate(0.45, input_value, smooth(t)) } self.play(Homotopy(self.input_homotopy, self.input_dot, **kwargs), Homotopy(self.output_homotopy, self.output_dot, **kwargs)) discontinuous_arrow = Arrow(discontinuous_at_A, self.input_dot) arrow = Arrow(point_description, self.output_dot, buff=0.05, color=self.output_color) self.play(ShimmerIn(point_description), ShowCreation(arrow)) self.dither() self.remove(point_description, arrow) tup = self.get_circles_and_points(input_value - input_radius, input_value + input_radius) input_circle, input_points, output_circle, output_points = tup input_points_copy = input_points.copy() self.play(ShowCreation(input_circle)) self.play(ShowCreation(input_points)) self.play(Transform(input_points_copy, output_points), run_time=2) self.play(ShowCreation(output_circle)) self.dither() self.play(ShimmerIn(text)) self.remove(input_circle, input_points, output_circle, input_points_copy) self.play(vary_circles) self.dither() self.play(ShimmerIn(discontinuous_at_A), ShowCreation(discontinuous_arrow)) self.dither(3) self.remove(vary_circles.mobject, discontinuous_at_A, discontinuous_arrow)
def construct(self): logo = MirekOlsakLogo(self.camera) series_title = TextMobject(self.series_str).to_edge(UP) self.add(series_title) chapter_title = TextMobject(self.chapter_str) chapter_title.scale(1.4) self.play(Write(chapter_title)) self.play(ShowCreation(logo)) self.dither(self.dither_time) self.play(FadeOut(VGroup(series_title, chapter_title, logo)))
def add_title(self): title = TextMobject("Clicky Stuffs") title.scale(1.5) title.to_edge(UP, buff = MED_SMALL_BUFF) randy, morty = Randolph(), Mortimer() for pi, vect in (randy, LEFT), (morty, RIGHT): pi.scale_to_fit_height(title.get_height()) pi.change_mode("thinking") pi.look(DOWN) pi.next_to(title, vect, buff = MED_LARGE_BUFF) self.add_foreground_mobjects(title, randy, morty)
def construct(self): name = TextMobject("Steven Strogatz") name.to_edge(UP) contributions = TextMobject("Frequent Contributions") contributions.scale(0.5).to_edge(RIGHT).shift(2 * UP) books_word = TextMobject("Books") books_word.scale(0.5).to_edge(LEFT).shift(2 * UP) radio_lab, sci_fri, cornell, book2, book3, book4 = [ ImageMobject(filename, invert=False, filter_color=WHITE) for filename in [ "radio_lab", "science_friday", "cornell", "strogatz_book2", "strogatz_book3", "strogatz_book4", ] ] book1 = ImageMobject("strogatz_book1", invert=False) nyt = ImageMobject("new_york_times") logos = [radio_lab, nyt, sci_fri] books = [book1, book2, book3, book4] sample_size = Square(side_length=2) last = contributions for image in logos: image.replace(sample_size) image.next_to(last, DOWN) last = image sci_fri.scale_in_place(0.9) shift_val = 0 sample_size.scale(0.75) for book in books: book.replace(sample_size) book.next_to(books_word, DOWN) book.shift(shift_val * (RIGHT + DOWN)) shift_val += 0.5 sample_size.scale(2) cornell.replace(sample_size) cornell.next_to(name, DOWN) self.add(name) self.play(FadeIn(cornell)) self.play(ShimmerIn(books_word)) for book in books: book.shift(5 * LEFT) self.play(ApplyMethod(book.shift, 5 * RIGHT)) self.play(ShimmerIn(contributions)) for logo in logos: self.play(FadeIn(logo)) self.dither()
def construct(self): name = TextMobject("Steven Strogatz") name.to_edge(UP) contributions = TextMobject("Frequent Contributions") contributions.scale(0.5).to_edge(RIGHT).shift(2*UP) books_word = TextMobject("Books") books_word.scale(0.5).to_edge(LEFT).shift(2*UP) radio_lab, sci_fri, cornell, book2, book3, book4 = [ ImageMobject(filename, invert = False, filter_color = WHITE) for filename in [ "radio_lab", "science_friday", "cornell", "strogatz_book2", "strogatz_book3", "strogatz_book4", ] ] book1 = ImageMobject("strogatz_book1", invert = False) nyt = ImageMobject("new_york_times") logos = [radio_lab, nyt, sci_fri] books = [book1, book2, book3, book4] sample_size = Square(side_length = 2) last = contributions for image in logos: image.replace(sample_size) image.next_to(last, DOWN) last = image sci_fri.scale_in_place(0.9) shift_val = 0 sample_size.scale(0.75) for book in books: book.replace(sample_size) book.next_to(books_word, DOWN) book.shift(shift_val*(RIGHT+DOWN)) shift_val += 0.5 sample_size.scale(2) cornell.replace(sample_size) cornell.next_to(name, DOWN) self.add(name) self.play(FadeIn(cornell)) self.play(ShimmerIn(books_word)) for book in books: book.shift(5*LEFT) self.play(ApplyMethod(book.shift, 5*RIGHT)) self.play(ShimmerIn(contributions)) for logo in logos: self.play(FadeIn(logo)) self.dither()
def construct(self): horiz_radius = 5 vert_radius = 3 vert_axis = NumberLine(numerical_radius=vert_radius) vert_axis.rotate(np.pi / 2) vert_axis.shift(horiz_radius * LEFT) horiz_axis = NumberLine(numerical_radius=5, numbers_with_elongated_ticks=[]) axes = Mobject(horiz_axis, vert_axis) graph = FunctionGraph(lambda x: 0.4 * (x - 2) * (x + 2) + 3, x_min=-2, x_max=2, density=3 * DEFAULT_POINT_DENSITY_1D) graph.stretch_to_fit_width(2 * horiz_radius) graph.highlight(YELLOW) min_point = Dot(graph.get_bottom()) nature_finds = TextMobject("Nature finds this point") nature_finds.scale(0.5) nature_finds.highlight(GREEN) nature_finds.shift(2 * RIGHT + 3 * UP) arrow = Arrow(nature_finds.get_bottom(), min_point, color=GREEN) side_words_start = TextMobject("Parameter describing") top_words, last_side_words = [ map(TextMobject, pair) for pair in [("Light's travel time", "Potential energy"), ("path", "mechanical state")] ] for word in top_words + last_side_words + [side_words_start]: word.scale(0.7) side_words_start.next_to(horiz_axis, DOWN) side_words_start.to_edge(RIGHT) for words in top_words: words.next_to(vert_axis, UP) words.to_edge(LEFT) for words in last_side_words: words.next_to(side_words_start, DOWN) for words in top_words[1], last_side_words[1]: words.highlight(RED) self.add(axes, top_words[0], side_words_start, last_side_words[0]) self.play(ShowCreation(graph)) self.play(ShimmerIn(nature_finds), ShowCreation(arrow), ShowCreation(min_point)) self.dither() self.play(FadeOut(top_words[0]), FadeOut(last_side_words[0]), GrowFromCenter(top_words[1]), GrowFromCenter(last_side_words[1])) self.dither(3)
def finite_analog(self, left_mob, arrow, right_mob): self.clear() self.add(left_mob, arrow, right_mob) ex = TextMobject("\\times") ex.highlight(RED) # ex.shift(arrow.get_center()) middle = TexMobject( "\\sum_{n=0}^N 2^n \\equiv -1 \\mod 2^{N+1}" ) finite_analog = TextMobject("Finite analog") finite_analog.scale(0.8) brace = Brace(middle, UP) finite_analog.next_to(brace, UP) new_left = left_mob.copy().to_edge(LEFT) new_right = right_mob.copy().to_edge(RIGHT) left_arrow, right_arrow = [ Arrow( mob1.get_right()[0]*RIGHT, mob2.get_left()[0]*RIGHT, buff = 0 ) for mob1, mob2 in [ (new_left, middle), (middle, new_right) ] ] for mob in ex, middle: mob.sort_points(np.linalg.norm) self.play(GrowFromCenter(ex)) self.dither() self.play( Transform(left_mob, new_left), Transform(arrow.copy(), left_arrow), DelayByOrder(Transform(ex, middle)), Transform(arrow, right_arrow), Transform(right_mob, new_right) ) self.play( GrowFromCenter(brace), ShimmerIn(finite_analog) ) self.dither() self.equivalence( left_mob, left_arrow, Mobject(middle, brace, finite_analog) )
def label(self, text, time = 5): mob = TextMobject(text) mob.scale(1.5) mob.to_edge(UP) rectangle = region_from_polygon_vertices(*[ mob.get_corner(vect) + 0.3*vect for vect in [ UP+RIGHT, UP+LEFT, DOWN+LEFT, DOWN+RIGHT ] ]) mob.highlight(self.text_color) rectangle = MobjectFromRegion(rectangle, "#111111") rectangle.point_thickness = 3 self.add(rectangle, mob) self.dither(time) self.remove(mob, rectangle)
def construct(self): words1 = TextMobject( "If you watched my video about Hilbert's space-filling curve\\dots" ) words2 = TextMobject( "\\dots you might be curious to see what a few other space-filling curves look like." ) words2.scale(0.8) for words in words1, words2: words.to_edge(UP, buff=0.2) self.setup(HilbertCurve) self.play(ShimmerIn(words1)) for x in range(4): self.increase_order() self.remove(words1) self.increase_order(ShimmerIn(words2)) for x in range(4): self.increase_order()
def construct(self): words1 = TextMobject(""" But of course, there's no reason we should limit ourselves to filling in squares. """) words2 = TextMobject(""" Here's a simple triangle-filling curve I defined in a style reflective of a Hilbert curve. """) words1.to_edge(UP) words2.scale(0.8).to_edge(UP, buff=0.2) self.setup(TriangleFillingCurve) self.play(ShimmerIn(words1)) for x in range(3): self.increase_order() self.remove(words1) self.add(words2) for x in range(5): self.increase_order()
def construct(self): words1 = TextMobject(""" But of course, there's no reason we should limit ourselves to filling in squares. """) words2 = TextMobject(""" Here's a simple triangle-filling curve I defined in a style reflective of a Hilbert curve. """) words1.to_edge(UP) words2.scale(0.8).to_edge(UP, buff = 0.2) self.setup(TriangleFillingCurve) self.play(ShimmerIn(words1)) for x in range(3): self.increase_order() self.remove(words1) self.add(words2) for x in range(5): self.increase_order()
def construct(self): words1 = TextMobject( "If you watched my video about Hilbert's space-filling curve\\dots" ) words2 = TextMobject( "\\dots you might be curious to see what a few other space-filling curves look like." ) words2.scale(0.8) for words in words1, words2: words.to_edge(UP, buff = 0.2) self.setup(HilbertCurve) self.play(ShimmerIn(words1)) for x in range(4): self.increase_order() self.remove(words1) self.increase_order( ShimmerIn(words2) ) for x in range(4): self.increase_order()
def construct(self): horiz_radius = 5 vert_radius = 3 vert_axis = NumberLine(numerical_radius = vert_radius) vert_axis.rotate(np.pi/2) vert_axis.shift(horiz_radius*LEFT) horiz_axis = NumberLine( numerical_radius = 5, numbers_with_elongated_ticks = [] ) axes = Mobject(horiz_axis, vert_axis) graph = FunctionGraph( lambda x : 0.4*(x-2)*(x+2)+3, x_min = -2, x_max = 2, density = 3*DEFAULT_POINT_DENSITY_1D ) graph.stretch_to_fit_width(2*horiz_radius) graph.highlight(YELLOW) min_point = Dot(graph.get_bottom()) nature_finds = TextMobject("Nature finds this point") nature_finds.scale(0.5) nature_finds.highlight(GREEN) nature_finds.shift(2*RIGHT+3*UP) arrow = Arrow( nature_finds.get_bottom(), min_point, color = GREEN ) side_words_start = TextMobject("Parameter describing") top_words, last_side_words = [ map(TextMobject, pair) for pair in [ ("Light's travel time", "Potential energy"), ("path", "mechanical state") ] ] for word in top_words + last_side_words + [side_words_start]: word.scale(0.7) side_words_start.next_to(horiz_axis, DOWN) side_words_start.to_edge(RIGHT) for words in top_words: words.next_to(vert_axis, UP) words.to_edge(LEFT) for words in last_side_words: words.next_to(side_words_start, DOWN) for words in top_words[1], last_side_words[1]: words.highlight(RED) self.add( axes, top_words[0], side_words_start, last_side_words[0] ) self.play(ShowCreation(graph)) self.play( ShimmerIn(nature_finds), ShowCreation(arrow), ShowCreation(min_point) ) self.dither() self.play( FadeOut(top_words[0]), FadeOut(last_side_words[0]), GrowFromCenter(top_words[1]), GrowFromCenter(last_side_words[1]) ) self.dither(3)
def construct(self): clock = Circle(radius=2, color=WHITE) clock.add(Dot(ORIGIN)) ticks = Mobject(*[ Line(1.8 * vect, 2 * vect, color=GREY) for vect in compass_directions(12) ]) clock.add(ticks) hour_hand = Line(ORIGIN, UP) minute_hand = Line(ORIGIN, 1.5 * UP) clock.add(hour_hand, minute_hand) clock.to_corner(UP + RIGHT) hour_hand.get_center = lambda: clock.get_center() minute_hand.get_center = lambda: clock.get_center() solution = ImageMobject("Newton_brachistochrone_solution2", use_cache=False) solution.stroke_width = 3 solution.highlight(GREY) solution.scale_to_fit_width(5) solution.to_corner(UP + RIGHT) newton = ImageMobject("Old_Newton", invert=False) newton.scale(0.8) phil_trans = TextMobject("Philosophical Transactions") rect = Rectangle(height=6, width=4.5, color=WHITE) rect.to_corner(UP + RIGHT) rect.shift(DOWN) phil_trans.scale_to_fit_width(0.8 * rect.get_width()) phil_trans.next_to(Point(rect.get_top()), DOWN) new_solution = solution.copy() new_solution.scale_to_fit_width(phil_trans.get_width()) new_solution.next_to(phil_trans, DOWN, buff=1) not_newton = TextMobject("-Totally not by Newton") not_newton.scale_to_fit_width(2.5) not_newton.next_to(new_solution, DOWN, aligned_edge=RIGHT) phil_trans.add(rect) newton_complaint = TextMobject([ "``I do not love to be", " \\emph{dunned} ", "and teased by foreigners''" ], size="\\small") newton_complaint.to_edge(UP, buff=0.2) dunned = newton_complaint.split()[1] dunned.highlight() dunned_def = TextMobject( "(old timey term for making \\\\ demands on someone)") dunned_def.scale(0.7) dunned_def.next_to(phil_trans, LEFT) dunned_def.shift(2 * UP) dunned_arrow = Arrow(dunned_def, dunned) johann = ImageMobject("Johann_Bernoulli2", invert=False) johann.scale(0.4) johann.to_edge(LEFT) johann.shift(DOWN) johann_quote = TextMobject("``I recognize the lion by his claw''") johann_quote.next_to(johann, UP, aligned_edge=LEFT) self.play(ApplyMethod(newton.to_edge, LEFT)) self.play(ShowCreation(clock)) kwargs = {"axis": OUT, "rate_func": smooth} self.play(Rotating(hour_hand, radians=-2 * np.pi, **kwargs), Rotating(minute_hand, radians=-12 * 2 * np.pi, **kwargs), run_time=5) self.wait() self.clear() self.add(newton) clock.ingest_submobjects() self.play(Transform(clock, solution)) self.remove(clock) self.add(solution) self.wait() self.play(FadeIn(phil_trans), Transform(solution, new_solution)) self.wait() self.play(ShimmerIn(not_newton)) phil_trans.add(solution, not_newton) self.wait() self.play(*map(ShimmerIn, newton_complaint.split())) self.wait() self.play(ShimmerIn(dunned_def), ShowCreation(dunned_arrow)) self.wait() self.remove(dunned_def, dunned_arrow) self.play(FadeOut(newton_complaint)) self.remove(newton_complaint) self.play(FadeOut(newton), GrowFromCenter(johann)) self.remove(newton) self.wait() self.play(ShimmerIn(johann_quote)) self.wait()
def construct(self): names = [ "Johann_Bernoulli2", "Jacob_Bernoulli", "Gottfried_Wilhelm_von_Leibniz", "Newton" ] guys = [ ImageMobject(name, invert = False) for name in names ] johann = guys[0] johann.scale(0.8) pensive_johann = johann.copy() pensive_johann.scale(0.25) pensive_johann.to_corner(DOWN+LEFT) comparitive_johann = johann.copy() template = Square(side_length = 2) comparitive_johann.replace(template) comparitive_johann.shift(UP+LEFT) greater_than = TexMobject(">") greater_than.next_to(comparitive_johann) for guy, name in zip(guys, names)[1:]: guy.replace(template) guy.next_to(greater_than) name_mob = TextMobject(name.replace("_", " ")) name_mob.scale(0.5) name_mob.next_to(guy, DOWN) guy.name_mob = name_mob guy.sort_points(lambda p : np.dot(p, DOWN+RIGHT)) bubble = ThoughtBubble(initial_width = 12) bubble.stretch_to_fit_height(6) bubble.ingest_submobjects() bubble.pin_to(pensive_johann) bubble.shift(DOWN) point = Point(johann.get_corner(UP+RIGHT)) upper_point = Point(comparitive_johann.get_corner(UP+RIGHT)) lightbulb = ImageMobject("Lightbulb", invert = False) lightbulb.scale(0.1) lightbulb.sort_points(np.linalg.norm) lightbulb.next_to(upper_point, RIGHT) self.add(johann) self.dither() self.play( Transform(johann, pensive_johann), Transform(point, bubble), run_time = 2 ) self.remove(point) self.add(bubble) weakling = guys[1] self.play( FadeIn(comparitive_johann), ShowCreation(greater_than), FadeIn(weakling) ) self.dither(2) for guy in guys[2:]: self.play(DelayByOrder(Transform( weakling, upper_point ))) self.play( FadeIn(guy), ShimmerIn(guy.name_mob) ) self.dither(3) self.remove(guy.name_mob) weakling = guy self.play(FadeOut(weakling), FadeOut(greater_than)) self.play(ShowCreation(lightbulb)) self.dither() self.play(FadeOut(comparitive_johann), FadeOut(lightbulb)) self.play(ApplyMethod( Mobject(johann, bubble).scale, 10, run_time = 3 ))
def construct(self): word = TextMobject(["Bra", "chis", "to", "chrone"]) original_word = word.copy() dots = [] for part in word.split(): if dots: part.next_to(dots[-1], buff = 0.06) dot = TexMobject("\\cdot") dot.next_to(part, buff = 0.06) dots.append(dot) dots = Mobject(*dots[:-1]) dots.shift(0.1*DOWN) Mobject(word, dots).center() overbrace1 = Brace(Mobject(*word.split()[:-1]), UP) overbrace2 = Brace(word.split()[-1], UP) shortest = TextMobject("Shortest") shortest.next_to(overbrace1, UP) shortest.highlight(YELLOW) time = TextMobject("Time") time.next_to(overbrace2, UP) time.highlight(YELLOW) chrono_example = TextMobject(""" As in ``Chronological'' \\\\ or ``Synchronize'' """) chrono_example.scale(0.5) chrono_example.to_edge(RIGHT) chrono_example.shift(2*UP) chrono_example.highlight(BLUE_D) chrono_arrow = Arrow( word.get_right(), chrono_example.get_bottom(), color = BLUE_D ) brachy_example = TextMobject("As in . . . brachydactyly?") brachy_example.scale(0.5) brachy_example.to_edge(LEFT) brachy_example.shift(2*DOWN) brachy_example.highlight(GREEN) brachy_arrow = Arrow( word.get_left(), brachy_example.get_top(), color = GREEN ) pronunciation = TextMobject(["/br", "e", "kist","e","kr$\\bar{o}$n/"]) pronunciation.split()[1].rotate_in_place(np.pi) pronunciation.split()[3].rotate_in_place(np.pi) pronunciation.scale(0.7) pronunciation.shift(DOWN) latin = TextMobject(list("Latin")) greek = TextMobject(list("Greek")) for mob in latin, greek: mob.to_edge(LEFT) question_mark = TextMobject("?").next_to(greek, buff = 0.1) stars = Stars().highlight(BLACK) stars.scale(0.5).shift(question_mark.get_center()) self.play(Transform(original_word, word), ShowCreation(dots)) self.play(ShimmerIn(pronunciation)) self.dither() self.play( GrowFromCenter(overbrace1), GrowFromCenter(overbrace2) ) self.dither() self.play(ShimmerIn(latin)) self.play(FadeIn(question_mark)) self.play(Transform( latin, greek, path_func = counterclockwise_path() )) self.dither() self.play(Transform(question_mark, stars)) self.remove(stars) self.dither() self.play(ShimmerIn(shortest)) self.play(ShimmerIn(time)) for ex, ar in [(chrono_example, chrono_arrow), (brachy_example, brachy_arrow)]: self.play( ShowCreation(ar), ShimmerIn(ex) ) self.dither()
def construct(self): word = TextMobject(["Bra", "chis", "to", "chrone"]) original_word = word.copy() dots = [] for part in word.split(): if dots: part.next_to(dots[-1], buff=0.06) dot = TexMobject("\\cdot") dot.next_to(part, buff=0.06) dots.append(dot) dots = Mobject(*dots[:-1]) dots.shift(0.1 * DOWN) Mobject(word, dots).center() overbrace1 = Brace(Mobject(*word.split()[:-1]), UP) overbrace2 = Brace(word.split()[-1], UP) shortest = TextMobject("Shortest") shortest.next_to(overbrace1, UP) shortest.highlight(YELLOW) time = TextMobject("Time") time.next_to(overbrace2, UP) time.highlight(YELLOW) chrono_example = TextMobject(""" As in ``Chronological'' \\\\ or ``Synchronize'' """) chrono_example.scale(0.5) chrono_example.to_edge(RIGHT) chrono_example.shift(2 * UP) chrono_example.highlight(BLUE_D) chrono_arrow = Arrow(word.get_right(), chrono_example.get_bottom(), color=BLUE_D) brachy_example = TextMobject("As in . . . brachydactyly?") brachy_example.scale(0.5) brachy_example.to_edge(LEFT) brachy_example.shift(2 * DOWN) brachy_example.highlight(GREEN) brachy_arrow = Arrow(word.get_left(), brachy_example.get_top(), color=GREEN) pronunciation = TextMobject( ["/br", "e", "kist", "e", "kr$\\bar{o}$n/"]) pronunciation.split()[1].rotate_in_place(np.pi) pronunciation.split()[3].rotate_in_place(np.pi) pronunciation.scale(0.7) pronunciation.shift(DOWN) latin = TextMobject(list("Latin")) greek = TextMobject(list("Greek")) for mob in latin, greek: mob.to_edge(LEFT) question_mark = TextMobject("?").next_to(greek, buff=0.1) stars = Stars().highlight(BLACK) stars.scale(0.5).shift(question_mark.get_center()) self.play(Transform(original_word, word), ShowCreation(dots)) self.play(ShimmerIn(pronunciation)) self.dither() self.play(GrowFromCenter(overbrace1), GrowFromCenter(overbrace2)) self.dither() self.play(ShimmerIn(latin)) self.play(FadeIn(question_mark)) self.play(Transform(latin, greek, path_func=counterclockwise_path())) self.dither() self.play(Transform(question_mark, stars)) self.remove(stars) self.dither() self.play(ShimmerIn(shortest)) self.play(ShimmerIn(time)) for ex, ar in [(chrono_example, chrono_arrow), (brachy_example, brachy_arrow)]: self.play(ShowCreation(ar), ShimmerIn(ex)) self.dither()
def construct(self): clock = Circle(radius = 2, color = WHITE) clock.add(Dot(ORIGIN)) ticks = Mobject(*[ Line(1.8*vect, 2*vect, color = GREY) for vect in compass_directions(12) ]) clock.add(ticks) hour_hand = Line(ORIGIN, UP) minute_hand = Line(ORIGIN, 1.5*UP) clock.add(hour_hand, minute_hand) clock.to_corner(UP+RIGHT) hour_hand.get_center = lambda : clock.get_center() minute_hand.get_center = lambda : clock.get_center() solution = ImageMobject( "Newton_brachistochrone_solution2", use_cache = False ) solution.stroke_width = 3 solution.highlight(GREY) solution.scale_to_fit_width(5) solution.to_corner(UP+RIGHT) newton = ImageMobject("Old_Newton", invert = False) newton.scale(0.8) phil_trans = TextMobject("Philosophical Transactions") rect = Rectangle(height = 6, width = 4.5, color = WHITE) rect.to_corner(UP+RIGHT) rect.shift(DOWN) phil_trans.scale_to_fit_width(0.8*rect.get_width()) phil_trans.next_to(Point(rect.get_top()), DOWN) new_solution = solution.copy() new_solution.scale_to_fit_width(phil_trans.get_width()) new_solution.next_to(phil_trans, DOWN, buff = 1) not_newton = TextMobject("-Totally not by Newton") not_newton.scale_to_fit_width(2.5) not_newton.next_to(new_solution, DOWN, aligned_edge = RIGHT) phil_trans.add(rect) newton_complaint = TextMobject([ "``I do not love to be", " \\emph{dunned} ", "and teased by foreigners''" ], size = "\\small") newton_complaint.to_edge(UP, buff = 0.2) dunned = newton_complaint.split()[1] dunned.highlight() dunned_def = TextMobject("(old timey term for making \\\\ demands on someone)") dunned_def.scale(0.7) dunned_def.next_to(phil_trans, LEFT) dunned_def.shift(2*UP) dunned_arrow = Arrow(dunned_def, dunned) johann = ImageMobject("Johann_Bernoulli2", invert = False) johann.scale(0.4) johann.to_edge(LEFT) johann.shift(DOWN) johann_quote = TextMobject("``I recognize the lion by his claw''") johann_quote.next_to(johann, UP, aligned_edge = LEFT) self.play(ApplyMethod(newton.to_edge, LEFT)) self.play(ShowCreation(clock)) kwargs = { "axis" : OUT, "rate_func" : smooth } self.play( Rotating(hour_hand, radians = -2*np.pi, **kwargs), Rotating(minute_hand, radians = -12*2*np.pi, **kwargs), run_time = 5 ) self.dither() self.clear() self.add(newton) clock.ingest_submobjects() self.play(Transform(clock, solution)) self.remove(clock) self.add(solution) self.dither() self.play( FadeIn(phil_trans), Transform(solution, new_solution) ) self.dither() self.play(ShimmerIn(not_newton)) phil_trans.add(solution, not_newton) self.dither() self.play(*map(ShimmerIn, newton_complaint.split())) self.dither() self.play( ShimmerIn(dunned_def), ShowCreation(dunned_arrow) ) self.dither() self.remove(dunned_def, dunned_arrow) self.play(FadeOut(newton_complaint)) self.remove(newton_complaint) self.play( FadeOut(newton), GrowFromCenter(johann) ) self.remove(newton) self.dither() self.play(ShimmerIn(johann_quote)) self.dither()
def discontinuous_point(self): point_description = TextMobject( "Point where the function jumps" ) point_description.shift(3*RIGHT) discontinuous_at_A = TextMobject( "``Discontinuous at A''", size = "\\Large" ) discontinuous_at_A.shift(2*UP).to_edge(LEFT) text = TextMobject(""" Circle around ouput \\\\ points can never \\\\ be smaller than \\\\ the jump """) text.scale(0.75) text.shift(3.5*RIGHT) input_value = 0.5 input_radius = 0.04 vary_circles = VaryCircles( self, input_value, input_radius, run_time = 5, ) for dot in self.input_dot, self.output_dot: dot.center() kwargs = { "rate_func" : lambda t : interpolate(0.45, input_value, smooth(t)) } self.play( Homotopy(self.input_homotopy, self.input_dot, **kwargs), Homotopy(self.output_homotopy, self.output_dot, **kwargs) ) discontinuous_arrow = Arrow(discontinuous_at_A, self.input_dot) arrow = Arrow( point_description, self.output_dot, buff = 0.05, color = self.output_color ) self.play( ShimmerIn(point_description), ShowCreation(arrow) ) self.dither() self.remove(point_description, arrow) tup = self.get_circles_and_points( input_value-input_radius, input_value+input_radius ) input_circle, input_points, output_circle, output_points = tup input_points_copy = input_points.copy() self.play(ShowCreation(input_circle)) self.play(ShowCreation(input_points)) self.play( Transform(input_points_copy, output_points), run_time = 2 ) self.play(ShowCreation(output_circle)) self.dither() self.play(ShimmerIn(text)) self.remove(input_circle, input_points, output_circle, input_points_copy) self.play(vary_circles) self.dither() self.play( ShimmerIn(discontinuous_at_A), ShowCreation(discontinuous_arrow) ) self.dither(3) self.remove(vary_circles.mobject, discontinuous_at_A, discontinuous_arrow)