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Preliminary finish to zeta project
This commit is contained in:
Grant Sanderson
@ -28,12 +28,12 @@ class SVGMobject(VMobject):
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]
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for path in possible_paths:
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if os.path.exists(path):
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self.file_name = path
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self.file_path = path
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return
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raise IOError("No file matching %s in image directory"%self.file_name)
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def generate_points(self):
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doc = minidom.parse(self.file_name)
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doc = minidom.parse(self.file_path)
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self.ref_to_element = {}
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for svg in doc.getElementsByTagName("svg"):
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self.add(*self.get_mobjects_from(svg))
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@ -44,7 +44,7 @@ class Headphones(SVGMobject):
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}
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def __init__(self, **kwargs):
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digest_config(self, kwargs)
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SVGMobject.__init__(self, self.file_name, **kwargs)
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SVGMobject.__init__(self, file_name = self.file_name, **kwargs)
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self.stretch(self.y_stretch_factor, 1)
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self.scale_to_fit_height(self.height)
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self.set_stroke(width = 0)
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344
zeta.py
344
zeta.py
@ -17,6 +17,7 @@ from topics.number_line import *
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from topics.combinatorics import *
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from topics.numerals import *
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from topics.three_dimensions import *
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from topics.objects import *
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from scene import Scene
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from camera import Camera
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from mobject.svg_mobject import *
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@ -1003,13 +1004,12 @@ class FromRealToComplex(ComplexTransformationScene):
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bubble = randy.get_bubble(height = 4)
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bubble.set_fill(BLACK, opacity = 1)
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pre_frac = self.zeta[2][2].copy()
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frac = VGroup(
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VectorizedPoint(pre_frac.get_left()),
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VGroup(*pre_frac[:3]),
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VectorizedPoint(pre_frac.get_right()),
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VGroup(*pre_frac[3:])
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)
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VectorizedPoint(self.zeta[2][3].get_left()),
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self.zeta[2][3],
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VectorizedPoint(self.zeta[2][3].get_right()),
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self.zeta[2][4],
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).copy()
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frac.generate_target()
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frac.target.scale(frac_scale_factor)
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bubble.add_content(frac.target)
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@ -1057,7 +1057,7 @@ class FromRealToComplex(ComplexTransformationScene):
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self.input_label.save_state()
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zeta = self.get_zeta_definition("2", "\\frac{\\pi^2}{6}")
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lines, output_dot = self.get_sum_lines(2)
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sum_terms = self.zeta[2][:-1:2]
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sum_terms = self.zeta[2][:-1:3]
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dots_copy = zeta[2][-1].copy()
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pi_copy = zeta[3].copy()
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def transform_and_replace(m1, m2):
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@ -2548,9 +2548,6 @@ class ButWhatIsTheExensions(TeacherStudentsScene):
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self.random_blink(3)
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class DiscussZeros(ZetaTransformationScene):
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CONFIG = {
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# "anchor_density" : 5,
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}
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def construct(self):
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self.establish_plane()
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self.ask_about_zeros()
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@ -2631,6 +2628,11 @@ class DiscussZeros(ZetaTransformationScene):
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self.dots.restore,
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run_time = 2
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)
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self.remove(*self.get_mobjects_from_last_animation())
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self.plane.restore()
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self.dots.restore()
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self.add(self.plane, self.dots)
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self.play(Write(trivial_zero_words))
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self.dither()
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self.play(FadeIn(randy))
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@ -2666,8 +2668,8 @@ class DiscussZeros(ZetaTransformationScene):
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photo.scale_to_fit_width(5)
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photo.to_corner(UP+LEFT)
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new_dots = VGroup(*[
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Dot(0.5*RIGHT + (y*random.random())*UP)
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for y in np.linspace(-3, 3, 5)
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Dot(0.5*RIGHT + y*UP)
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for y in np.linspace(-2.5, 3.2, 5)
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])
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new_dots.highlight(YELLOW)
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critical_line = Line(
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@ -2692,7 +2694,7 @@ class DiscussZeros(ZetaTransformationScene):
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for x in range(7):
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self.play(*self.get_dot_wandering_anims())
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self.play(
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FadeIn(photo),
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GrowFromCenter(photo),
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FadeOut(name),
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FadeOut(arrow),
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*self.get_dot_wandering_anims()
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@ -2700,9 +2702,13 @@ class DiscussZeros(ZetaTransformationScene):
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self.play(Transform(self.dots, new_dots))
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self.play(ShowCreation(critical_line))
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self.dither(3)
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self.play(*map(FadeOut, [
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photo, primes, self.dots, strip
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]))
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self.play(
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photo.shift, 7*LEFT,
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*map(FadeOut, [
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primes, self.dots, strip
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])
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)
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self.remove(photo)
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self.critical_line = critical_line
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def give_dots_wandering_anims(self):
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@ -2714,19 +2720,18 @@ class DiscussZeros(ZetaTransformationScene):
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self.wandering_path = ParametricFunction(func)
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for i, dot in enumerate(self.dots):
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dot.target = dot.copy()
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dot.target.move_to(self.wandering_path.point_from_proportion(
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(2*i+2)/(4.*len(list(self.dots)))
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))
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q_mark = TexMobject("?")
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q_mark.next_to(dot.target, UP)
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dot.target.add(q_mark)
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dot.target.move_to(self.wandering_path.point_from_proportion(
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(float(2+2*i)/(4*len(list(self.dots))))%1
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))
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self.dot_anim_count = 0
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def get_dot_wandering_anims(self):
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self.dot_anim_count += 1
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if self.dot_anim_count == 1:
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return map(MoveToTarget, self.dots)
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result = []
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denom = 4*(len(list(self.dots)))
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def get_rate_func(index):
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return lambda t : (float(self.dot_anim_count + 2*index + t)/denom)%1
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@ -2739,9 +2744,9 @@ class DiscussZeros(ZetaTransformationScene):
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]
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def transform_bit_of_critical_line(self):
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group = VGroup(self.plane, self.critical_line)
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self.play(
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group.scale, 0.8,
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self.plane.scale, 0.8,
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self.critical_line.scale, 0.8,
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rate_func = there_and_back,
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run_time = 2
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)
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@ -2751,8 +2756,12 @@ class DiscussZeros(ZetaTransformationScene):
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Animation(self.critical_line)
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)
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self.plane.add(self.critical_line)
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self.apply_zeta()
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self.apply_zeta_function()
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self.dither(2)
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self.play(
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self.plane.fade,
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Animation(self.critical_line)
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)
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def extend_transformed_critical_line(self):
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def func(t):
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@ -2768,10 +2777,291 @@ class DiscussZeros(ZetaTransformationScene):
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self.play(ShowCreation(full_line, run_time = 20, rate_func = None))
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self.dither()
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class HighlightCriticalLineAgain(DiscussZeros):
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def construct(self):
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self.establish_plane()
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title = TexMobject("\\zeta(", "s", ") = 0")
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title.highlight_by_tex("s", YELLOW)
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title.add_background_rectangle()
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title.to_corner(UP+LEFT)
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self.add(title)
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strip = Rectangle(
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height = 2*SPACE_HEIGHT,
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width = 1
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)
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strip.next_to(ORIGIN, RIGHT, buff = 0)
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strip.set_stroke(width = 0)
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strip.set_fill(YELLOW, opacity = 0.3)
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line = Line(
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0.5*RIGHT+SPACE_HEIGHT*UP,
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0.5*RIGHT+SPACE_HEIGHT*DOWN,
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color = YELLOW
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)
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randy = Randolph().to_corner(DOWN+LEFT)
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million = TexMobject("\\$1{,}000{,}000")
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million.highlight(GREEN_B)
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million.next_to(ORIGIN, UP+LEFT)
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million.shift(2*LEFT)
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arrow1 = Arrow(million.get_right(), line.get_top())
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arrow2 = Arrow(million.get_right(), line.get_bottom())
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self.add(randy, strip)
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self.play(Write(million))
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self.play(
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randy.change_mode, "pondering",
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randy.look_at, line.get_top(),
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ShowCreation(arrow1),
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run_time = 3
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)
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self.play(
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randy.look_at, line.get_bottom(),
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ShowCreation(line),
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Transform(arrow1, arrow2)
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)
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self.play(FadeOut(arrow1))
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self.play(Blink(randy))
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self.dither()
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self.play(randy.look_at, line.get_center())
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self.play(randy.change_mode, "confused")
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self.play(Blink(randy))
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self.dither()
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self.play(randy.change_mode, "pondering")
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self.dither()
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class DiscussSumOfNaturals(Scene):
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def construct(self):
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title = TexMobject(
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"\\zeta(s) = \\sum_{n=1}^\\infty \\frac{1}{n^s}"
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)
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VGroup(title[2], title[-1]).highlight(YELLOW)
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title.to_corner(UP+LEFT)
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neg_twelfth, eq, zeta_neg_1, sum_naturals = equation = TexMobject(
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"-\\frac{1}{12}",
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"=",
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"\\zeta(-1)",
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"= 1 + 2 + 3 + 4 + \\cdots"
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)
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neg_twelfth.highlight(GREEN_B)
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VGroup(*zeta_neg_1[2:4]).highlight(YELLOW)
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q_mark = TexMobject("?").next_to(sum_naturals[0], UP)
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q_mark.highlight(RED)
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randy = Randolph()
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randy.to_corner(DOWN+LEFT)
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analytic_continuation = TextMobject("Analytic continuation")
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analytic_continuation.next_to(title, RIGHT, 3*LARGE_BUFF)
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sum_to_zeta = Arrow(title.get_corner(DOWN+RIGHT), zeta_neg_1)
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sum_to_ac = Arrow(title.get_right(), analytic_continuation)
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ac_to_zeta = Arrow(analytic_continuation.get_bottom(), zeta_neg_1.get_top())
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cross = TexMobject("\\times")
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cross.scale(2)
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cross.highlight(RED)
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cross.rotate(np.pi/6)
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cross.move_to(sum_to_zeta.get_center())
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brace = Brace(VGroup(zeta_neg_1, sum_naturals))
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words = TextMobject(
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"If not equal, at least connected",
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"\\\\(see links in description)"
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)
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words.next_to(brace, DOWN)
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self.add(neg_twelfth, eq, zeta_neg_1, randy, title)
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self.dither()
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self.play(
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Write(sum_naturals),
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Write(q_mark),
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randy.change_mode, "confused"
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)
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self.play(Blink(randy))
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self.dither()
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self.play(randy.change_mode, "angry")
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self.play(
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ShowCreation(sum_to_zeta),
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Write(cross)
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)
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self.play(Blink(randy))
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self.dither()
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self.play(
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Transform(sum_to_zeta, sum_to_ac),
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FadeOut(cross),
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Write(analytic_continuation),
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randy.change_mode, "pondering",
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randy.look_at, analytic_continuation,
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)
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self.play(ShowCreation(ac_to_zeta))
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self.play(Blink(randy))
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self.dither()
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self.play(
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GrowFromCenter(brace),
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Write(words[0]),
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randy.look_at, words[0],
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)
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self.dither()
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self.play(FadeIn(words[1]))
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self.play(Blink(randy))
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self.dither()
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class InventingMathPreview(Scene):
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def construct(self):
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rect = Rectangle(height = 9, width = 16)
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rect.scale_to_fit_height(4)
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title = TextMobject("What does it feel like to invent math?")
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title.next_to(rect, UP)
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sum_tex = TexMobject("1+2+4+8+\\cdots = -1")
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sum_tex.scale_to_fit_width(rect.get_width()-1)
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self.play(
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ShowCreation(rect),
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Write(title)
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)
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self.play(Write(sum_tex))
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self.dither()
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class FinalAnimationTease(Scene):
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def construct(self):
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morty = Mortimer().shift(2*(DOWN+RIGHT))
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bubble = morty.get_bubble("speech")
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bubble.write("""
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Want to know what
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$\\zeta'(s)$ looks like?
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""")
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self.add(morty)
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self.play(
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morty.change_mode, "hooray",
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morty.look_at, bubble.content,
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ShowCreation(bubble),
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Write(bubble.content)
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)
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self.play(Blink(morty))
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self.dither()
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class PatreonThanks(Scene):
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CONFIG = {
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"specific_patrons" : [
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"CrypticSwarm",
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"Ali Yahya",
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"Damion Kistler",
|
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"Juan Batiz-Benet",
|
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"Yu Jun",
|
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"Othman Alikhan",
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"Markus Persson",
|
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"Joseph John Cox",
|
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"Luc Ritchie",
|
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"Shimin Kuang",
|
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"Einar Johansen",
|
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"Rish Kundalia",
|
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"Achille Brighton",
|
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"Kirk Werklund",
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"Ripta Pasay",
|
||||
"Felipe Diniz",
|
||||
]
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}
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def construct(self):
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morty = Mortimer()
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morty.next_to(ORIGIN, DOWN)
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n_patrons = len(self.specific_patrons)
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special_thanks = TextMobject("Special thanks to:")
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special_thanks.highlight(YELLOW)
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special_thanks.shift(3*UP)
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patreon_logo = ImageMobject("patreon", invert = False)
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patreon_logo.scale_to_fit_height(1.5)
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patreon_logo.next_to(special_thanks, DOWN)
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left_patrons = VGroup(*map(TextMobject,
|
||||
self.specific_patrons[:n_patrons/2]
|
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))
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right_patrons = VGroup(*map(TextMobject,
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||||
self.specific_patrons[n_patrons/2:]
|
||||
))
|
||||
for patrons, vect in (left_patrons, LEFT), (right_patrons, RIGHT):
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||||
patrons.arrange_submobjects(DOWN, aligned_edge = LEFT)
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||||
patrons.next_to(special_thanks, DOWN)
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||||
patrons.to_edge(vect, buff = LARGE_BUFF)
|
||||
|
||||
self.add(patreon_logo)
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||||
self.play(morty.change_mode, "gracious")
|
||||
self.play(Write(special_thanks, run_time = 1))
|
||||
self.play(
|
||||
Write(left_patrons),
|
||||
morty.look_at, left_patrons
|
||||
)
|
||||
self.play(
|
||||
Write(right_patrons),
|
||||
morty.look_at, right_patrons
|
||||
)
|
||||
self.play(Blink(morty))
|
||||
for patrons in left_patrons, right_patrons:
|
||||
for index in 0, -1:
|
||||
self.play(morty.look_at, patrons[index])
|
||||
self.dither()
|
||||
|
||||
class CreditTwo(Scene):
|
||||
def construct(self):
|
||||
morty = Mortimer()
|
||||
morty.next_to(ORIGIN, DOWN)
|
||||
morty.to_edge(RIGHT)
|
||||
|
||||
brother = PiCreature(color = GOLD_E)
|
||||
brother.next_to(morty, LEFT)
|
||||
brother.look_at(morty.eyes)
|
||||
|
||||
headphones = Headphones(height = 1)
|
||||
headphones.move_to(morty.eyes, aligned_edge = DOWN)
|
||||
headphones.shift(0.1*DOWN)
|
||||
|
||||
url = TextMobject("www.audible.com/3blue1brown")
|
||||
url.to_corner(UP+RIGHT, buff = LARGE_BUFF)
|
||||
|
||||
self.add(morty)
|
||||
self.play(Blink(morty))
|
||||
self.play(
|
||||
FadeIn(headphones),
|
||||
Write(url),
|
||||
Animation(morty)
|
||||
)
|
||||
self.play(morty.change_mode, "happy")
|
||||
self.dither()
|
||||
self.play(Blink(morty))
|
||||
self.dither()
|
||||
self.play(
|
||||
FadeIn(brother),
|
||||
morty.look_at, brother.eyes
|
||||
)
|
||||
self.play(brother.change_mode, "surprised")
|
||||
self.play(Blink(brother))
|
||||
self.dither()
|
||||
self.play(
|
||||
morty.look, LEFT,
|
||||
brother.change_mode, "happy",
|
||||
brother.look, LEFT
|
||||
)
|
||||
self.play(Blink(morty))
|
||||
self.dither()
|
||||
|
||||
class FinalAnimation(ZetaTransformationScene):
|
||||
CONFIG = {
|
||||
"min_added_anchors" : 100,
|
||||
}
|
||||
def construct(self):
|
||||
self.add_transformable_plane()
|
||||
self.add_extra_plane_lines_for_zeta()
|
||||
self.add_reflected_plane()
|
||||
title = TexMobject("s", "\\to \\frac{d\\zeta}{ds}(", "s", ")")
|
||||
title.highlight_by_tex("s", YELLOW)
|
||||
title.add_background_rectangle()
|
||||
title.scale(1.5)
|
||||
title.to_corner(UP+LEFT)
|
||||
|
||||
self.play(Write(title))
|
||||
self.add_foreground_mobjects(title)
|
||||
self.dither()
|
||||
self.apply_complex_function(d_zeta, run_time = 8)
|
||||
self.dither()
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user