import numpy as np import itertools as it import os from manimlib.imports import * from from_3b1b.old.brachistochrone.drawing_images import sort_by_color class Intro(Scene): def construct(self): logo = ImageMobject("LogoGeneration", invert = False) name_mob = TextMobject("3Blue1Brown").center() name_mob.set_color("grey") name_mob.shift(2*DOWN) self.add(name_mob, logo) new_text = TextMobject(["with ", "Steven Strogatz"]) new_text.next_to(name_mob, DOWN) self.play(*[ ShimmerIn(part) for part in new_text.split() ]) self.wait() with_word, steve = new_text.split() steve_copy = steve.copy().center().to_edge(UP) # logo.sort_points(lambda p : -get_norm(p)) sort_by_color(logo) self.play( Transform(steve, steve_copy), DelayByOrder(Transform(logo, Point())), FadeOut(with_word), FadeOut(name_mob), run_time = 3 ) class IntroduceSteve(Scene): 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.wait() class ShowTweets(Scene): def construct(self): tweets = [ ImageMobject("tweet%d"%x, invert = False) for x in range(1, 4) ] for tweet in tweets: tweet.scale(0.4) tweets[0].to_corner(UP+LEFT) tweets[1].next_to(tweets[0], RIGHT, aligned_edge = UP) tweets[2].next_to(tweets[1], DOWN) self.play(GrowFromCenter(tweets[0])) for x in 1, 2: self.play( Transform(Point(tweets[x-1].get_center()), tweets[x]), Animation(tweets[x-1]) ) self.wait() class LetsBeHonest(Scene): def construct(self): self.play(ShimmerIn(TextMobject(""" Let's be honest about who benefits from this collaboration... """))) self.wait() class WhatIsTheBrachistochrone(Scene): def construct(self): self.play(ShimmerIn(TextMobject(""" So \\dots what is the Brachistochrone? """))) self.wait() class DisectBrachistochroneWord(Scene): 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.set_color(YELLOW) time = TextMobject("Time") time.next_to(overbrace2, UP) time.set_color(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.set_color(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.set_color(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().set_color(BLACK) stars.scale(0.5).shift(question_mark.get_center()) self.play(Transform(original_word, word), ShowCreation(dots)) self.play(ShimmerIn(pronunciation)) self.wait() self.play( GrowFromCenter(overbrace1), GrowFromCenter(overbrace2) ) self.wait() self.play(ShimmerIn(latin)) self.play(FadeIn(question_mark)) self.play(Transform( latin, greek, path_func = counterclockwise_path() )) self.wait() self.play(Transform(question_mark, stars)) self.remove(stars) self.wait() 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.wait() class OneSolutionTwoInsights(Scene): def construct(self): one_solution = TextMobject(["One ", "solution"]) two_insights = TextMobject(["Two ", " insights"]) two, insights = two_insights.split() johann = ImageMobject("Johann_Bernoulli2", invert = False) mark = ImageMobject("Mark_Levi", invert = False) for mob in johann, mark: mob.scale(0.4) johann.next_to(insights, LEFT) mark.next_to(johann, RIGHT) name = TextMobject("Mark Levi").to_edge(UP) self.play(*list(map(ShimmerIn, one_solution.split()))) self.wait() for pair in zip(one_solution.split(), two_insights.split()): self.play(Transform(*pair, path_func = path_along_arc(np.pi))) self.wait() self.clear() self.add(two, insights) for word, man in [(two, johann), (insights, mark)]: self.play( Transform(word, Point(word.get_left())), GrowFromCenter(man) ) self.wait() self.clear() self.play(ApplyMethod(mark.center)) self.play(ShimmerIn(name)) self.wait() class CircleOfIdeas(Scene): def construct(self): words = list(map(TextMobject, [ "optics", "calculus", "mechanics", "geometry", "history" ])) words[0].set_color(YELLOW) words[1].set_color(BLUE_D) words[2].set_color(GREY) words[3].set_color(GREEN) words[4].set_color(MAROON) brachistochrone = TextMobject("Brachistochrone") displayed_words = [] for word in words: anims = self.get_spinning_anims(displayed_words) word.shift(3*RIGHT) point = Point() anims.append(Transform(point, word)) self.play(*anims) self.remove(point) self.add(word) displayed_words.append(word) self.play(*self.get_spinning_anims(displayed_words)) self.play(*[ Transform( word, word.copy().set_color(BLACK).center().scale(0.1), path_func = path_along_arc(np.pi), rate_func=linear, run_time = 2 ) for word in displayed_words ]+[ GrowFromCenter(brachistochrone) ]) self.wait() def get_spinning_anims(self, words, angle = np.pi/6): anims = [] for word in words: old_center = word.get_center() new_center = rotate_vector(old_center, angle) vect = new_center-old_center anims.append(ApplyMethod( word.shift, vect, path_func = path_along_arc(angle), rate_func=linear )) return anims class FermatsPrincipleStatement(Scene): def construct(self): words = TextMobject([ "Fermat's principle:", """ If a beam of light travels from point $A$ to $B$, it does so along the fastest path possible. """ ]) words.split()[0].set_color(BLUE) everything = MobjectFromRegion(Region()) everything.scale(0.9) angles = np.apply_along_axis( angle_of_vector, 1, everything.points ) norms = np.apply_along_axis( get_norm, 1, everything.points ) norms -= np.min(norms) norms /= np.max(norms) alphas = 0.25 + 0.75 * norms * (1 + np.sin(12*angles))/2 everything.rgbas = alphas.repeat(3).reshape((len(alphas), 3)) Mobject(everything, words).show() everything.sort_points(get_norm) self.add(words) self.play( DelayByOrder(FadeIn(everything, run_time = 3)), Animation(words) ) self.play( ApplyMethod(everything.set_color, WHITE), ) self.wait() class VideoProgression(Scene): def construct(self): spacing = 2*UP brachy, optics, light_in_two, snells, multi = words = [ TextMobject(text) for text in [ "Brachistochrone", "Optics", "Light in two media", "Snell's Law", "Multilayered glass", ] ] for mob in light_in_two, snells: mob.shift(-spacing) arrow1 = Arrow(brachy, optics) arrow2 = Arrow(optics, snells) point = Point(DOWN) self.play(ShimmerIn(brachy)) self.wait() self.play( ApplyMethod(brachy.shift, spacing), Transform(point, optics) ) optics = point arrow1 = Arrow(optics, brachy) self.play(ShowCreation(arrow1)) self.wait() arrow2 = Arrow(light_in_two, optics) self.play( ShowCreation(arrow2), ShimmerIn(light_in_two) ) self.wait() self.play( FadeOut(light_in_two), GrowFromCenter(snells), DelayByOrder( ApplyMethod(arrow2.set_color, BLUE_D) ) ) self.wait() self.play( FadeOut(optics), GrowFromCenter(multi), DelayByOrder( ApplyMethod(arrow1.set_color, BLUE_D) ) ) self.wait() class BalanceCompetingFactors(Scene): args_list = [ ("Short", "Steep"), ("Minimal time \\\\ in water", "Short path") ] @staticmethod def args_to_string(*words): return "".join([word.split(" ")[0] for word in words]) def construct(self, *words): factor1, factor2 = [ TextMobject("Factor %d"%x).set_color(c) for x, c in [ (1, RED_D), (2, BLUE_D) ] ] real_factor1, real_factor2 = list(map(TextMobject, words)) for word in factor1, factor2, real_factor1, real_factor2: word.shift(0.2*UP-word.get_bottom()) for f1 in factor1, real_factor1: f1.set_color(RED_D) f1.shift(2*LEFT) for f2 in factor2, real_factor2: f2.set_color(BLUE_D) f2.shift(2*RIGHT) line = Line( factor1.get_left(), factor2.get_right() ) line.center() self.balancers = Mobject(factor1, factor2, line) self.hidden_balancers = Mobject(real_factor1, real_factor2) triangle = Polygon(RIGHT, np.sqrt(3)*UP, LEFT) triangle.next_to(line, DOWN, buff = 0) self.add(triangle, self.balancers) self.rotate(1) self.rotate(-2) self.wait() self.play(Transform( factor1, real_factor1, path_func = path_along_arc(np.pi/4) )) self.rotate(2) self.wait() self.play(Transform( factor2, real_factor2, path_func = path_along_arc(np.pi/4) )) self.rotate(-2) self.wait() self.rotate(1) def rotate(self, factor): angle = np.pi/11 self.play(Rotate( self.balancers, factor*angle, run_time = abs(factor) )) self.hidden_balancers.rotate(factor*angle) class Challenge(Scene): def construct(self): self.add(TextMobject(""" Can you find a new solution to the Brachistochrone problem by finding an intuitive reason that time-minimizing curves look like straight lines in $t$-$\\theta$ space? """)) self.wait() class Section1(Scene): def construct(self): self.add(TextMobject("Section 1: Johann Bernoulli's insight")) self.wait() class Section2(Scene): def construct(self): self.add(TextMobject( "Section 2: Mark Levi's insight, and a challenge", size = "\\large" )) self.wait() class NarratorInterjection(Scene): def construct(self): words1 = TexMobject("<\\text{Narrator interjection}>") words2 = TexMobject("<\\!/\\text{Narrator interjection}>") self.add(words1) self.wait() self.clear() self.add(words2) self.wait() class ThisCouldBeTheEnd(Scene): def construct(self): words = TextMobject([ "This could be the end\\dots", "but\\dots" ]) for part in words.split(): self.play(ShimmerIn(part)) self.wait() class MyOwnChallenge(Scene): def construct(self): self.add(TextMobject("My own challenge:")) self.wait() class WarmupChallenge(Scene): def construct(self): self.add(TextMobject("\\large Warm-up challenge: Confirm this for yourself")) self.wait() class FindAnotherSolution(Scene): def construct(self): self.add(TextMobject("Find another brachistochrone solution\\dots")) self.wait() class ProofOfSnellsLaw(Scene): def construct(self): self.add(TextMobject("Proof of Snell's law:")) self.wait() class CondensedVersion(Scene): def construct(self): snells = TextMobject("Snell's") snells.shift(-snells.get_left()) snells.to_edge(UP) for vect in [RIGHT, RIGHT, LEFT, DOWN, DOWN, DOWN]: snells.add(snells.copy().next_to(snells, vect)) snells.ingest_submobjects() snells.show() condensed = TextMobject("condensed") self.add(snells) self.wait() self.play(DelayByOrder( Transform(snells, condensed, run_time = 2) )) self.wait()