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https://github.com/3b1b/manim.git
synced 2025-08-01 08:54:38 +08:00
Up to description of Sierpinski dimension
This commit is contained in:
Grant Sanderson
@ -352,8 +352,9 @@ class SelfSimilarFractalsAsSubset(Scene):
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)
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self.play(ShowCreation(britain), run_time = 5)
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self.play(
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britain.set_stroke, BLACK, 0,
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britain.set_fill, BLUE, 1,
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britain.set_stroke, None, 0,
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run_time = 2
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)
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self.play(FadeIn(randy))
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self.play(MoveToTarget(randy, run_time = 2))
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@ -361,8 +362,10 @@ class SelfSimilarFractalsAsSubset(Scene):
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class ConstrastSmoothAndFractal(Scene):
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CONFIG = {
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"britain_zoom_point_proportion" : 0.4,
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"scale_factor" : 15,
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"britain_zoom_point_proportion" : 0.45,
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"scale_factor" : 50,
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"fractalification_order" : 2,
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"fractal_dimension" : 1.21,
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}
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def construct(self):
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v_line = Line(UP, DOWN).scale(SPACE_HEIGHT)
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@ -398,7 +401,11 @@ class ConstrastSmoothAndFractal(Scene):
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britain.zoom_point = britain.point_from_proportion(
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self.britain_zoom_point_proportion
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)
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fractalify(britain, order = 2, dimension = 1.21)
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fractalify(
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britain,
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order = self.fractalification_order,
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dimension = self.fractal_dimension,
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)
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britains = VGroup(britain, smooth_britain)
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self.play(*[
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@ -425,7 +432,7 @@ class ConstrastSmoothAndFractal(Scene):
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),
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Animation(smooth),
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Animation(fractal),
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run_time = 5
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run_time = 10,
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)
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self.dither(2)
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@ -895,7 +902,9 @@ class DefineTwoDimensional(PiCreatureScene):
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"length_color" : GREEN,
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"dimension_color" : YELLOW,
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"shape_width" : 2,
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"scale_factor" : 1.5,
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"scale_factor" : 0.5,
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"bottom_shape_buff" : MED_BUFF,
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"scalar" : "s",
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}
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def construct(self):
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self.add_title()
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@ -937,11 +946,13 @@ class DefineTwoDimensional(PiCreatureScene):
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top_length = TextMobject("Length:", "$L$")
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top_mass = TextMobject("Mass:", "$M$")
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bottom_length = TextMobject(
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"Length: ", "$s$", "$L$",
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"Length: ", "$%s$"%self.scalar, "$L$",
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arg_separator = ""
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)
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bottom_mass = TextMobject(
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"Mass: ", "$s^%s$"%self.dimension, "$M$",
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"Mass: ",
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"$%s^%s$"%(self.scalar, self.dimension),
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"$M$",
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arg_separator = ""
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)
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self.dimension_in_exp = VGroup(
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@ -969,6 +980,7 @@ class DefineTwoDimensional(PiCreatureScene):
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self.top_L = top_length[-1]
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self.bottom_L = VGroup(*bottom_length[-2:])
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self.bottom_mass = bottom_mass
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def show_top_length(self):
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brace = Brace(self.shape, LEFT)
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@ -982,14 +994,16 @@ class DefineTwoDimensional(PiCreatureScene):
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def perform_scaling(self):
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group = VGroup(self.shape, self.brace).copy()
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self.play(group.shift, (group.get_top()[1]+MED_BUFF)*DOWN)
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self.play(
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group.shift,
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(group.get_top()[1]+self.bottom_shape_buff)*DOWN
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)
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shape, brace = group
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bottom_L = self.bottom_L.copy()
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shape.generate_target()
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shape.target.scale(
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shape.target.scale_in_place(
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self.scale_factor,
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about_point = shape.get_corner(UP+LEFT)
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)
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brace.target = Brace(shape.target, LEFT)
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self.play(*map(MoveToTarget, group))
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@ -999,11 +1013,11 @@ class DefineTwoDimensional(PiCreatureScene):
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def show_dimension(self):
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top_dimension = self.dimension_in_title.copy()
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self.play(self.pi_creature.look_at, top_dimension)
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self.play(
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top_dimension.replace,
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self.play(Transform(
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top_dimension,
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self.dimension_in_exp,
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run_time = 2,
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)
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))
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self.dither(3)
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def get_shape(self):
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@ -1013,7 +1027,210 @@ class DefineTwoDimensional(PiCreatureScene):
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fill_opacity = 0.7,
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)
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class DefineThreeDimensional(DefineTwoDimensional):
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CONFIG = {
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"dimension" : "3",
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}
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def get_shape(self):
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return Square(
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stroke_width = 0,
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fill_opacity = 0
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)
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class DefineSierpinskiDimension(DefineTwoDimensional):
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CONFIG = {
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"dimension" : "D",
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"scalar" : "\\left( \\frac{1}{2} \\right)",
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"sierpinski_order" : 6,
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"equation_scale_factor" : 1.3,
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}
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def construct(self):
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DefineTwoDimensional.construct(self)
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self.change_mode("confused")
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self.dither()
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self.add_one_third()
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self.isolate_equation()
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def add_one_third(self):
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equation = TextMobject(
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"$= \\left(\\frac{1}{3}\\right)$", "$M$",
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arg_separator = ""
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)
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equation.highlight_by_tex("$M$", self.mass_color)
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equation.next_to(self.bottom_mass)
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self.play(Write(equation))
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self.change_mode("pondering")
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self.dither()
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self.equation = VGroup(self.bottom_mass, equation)
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self.distilled_equation = VGroup(
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self.bottom_mass[1],
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equation[0]
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).copy()
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def isolate_equation(self):
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# everything = VGroup(*self.get_mobjects())
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keepers = [self.pi_creature, self.equation]
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for mob in keepers:
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mob.save_state()
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keepers_copies = [mob.copy() for mob in keepers]
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self.play(
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*[
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ApplyMethod(mob.fade, 0.5)
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for mob in self.get_mobjects()
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] + [
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Animation(mob)
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for mob in keepers_copies
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]
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)
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self.remove(*keepers_copies)
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for mob in keepers:
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ApplyMethod(mob.restore).update(1)
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self.add(*keepers)
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self.play(
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self.pi_creature.change_mode, "confused",
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self.pi_creature.look_at, self.equation
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)
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self.dither()
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equation = self.distilled_equation
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self.play(
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equation.arrange_submobjects, RIGHT,
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equation.scale, self.equation_scale_factor,
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equation.to_corner, UP+RIGHT,
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run_time = 2
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)
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self.dither(2)
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simpler_equation = TexMobject("2^D = 3")
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simpler_equation[1].highlight(self.dimension_color)
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simpler_equation.scale(self.equation_scale_factor)
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simpler_equation.next_to(equation, DOWN, buff = 2*MED_BUFF)
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log_expression = TexMobject("\\log_2(3) \\approx", "1.585")
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log_expression[-1].highlight(self.dimension_color)
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log_expression.scale(self.equation_scale_factor)
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log_expression.next_to(simpler_equation, DOWN, buff = 2*MED_BUFF)
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log_expression.shift_onto_screen()
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self.play(Write(simpler_equation))
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self.change_mode("pondering")
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self.dither(2)
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self.play(Write(log_expression))
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self.play(
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self.pi_creature.change_mode, "hooray",
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self.pi_creature.look_at, log_expression
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)
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self.dither(2)
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def get_shape(self):
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return Sierpinski(
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order = self.sierpinski_order,
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color = RED,
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)
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class ShowSierpinskiCurve(Scene):
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CONFIG = {
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"max_order" : 8,
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}
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def construct(self):
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curve = self.get_curve(2)
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self.play(ShowCreation(curve, run_time = 2))
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for order in range(3, self.max_order + 1):
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self.play(Transform(
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curve, self.get_curve(order),
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run_time = 2
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))
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self.dither()
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def get_curve(self, order):
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curve = SierpinskiCurve(order = order, monochromatic = True)
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curve.highlight(RED)
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return curve
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class LengthAndAreaOfSierpinski(ShowSierpinskiCurve):
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CONFIG = {
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"curve_start_order" : 5,
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"sierpinski_start_order" : 4,
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"n_iterations" : 3,
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}
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def construct(self):
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length = TextMobject("Length = $\\infty$")
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length.shift(SPACE_WIDTH*LEFT/2).to_edge(UP)
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area = TextMobject("Area = $0$")
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area.shift(SPACE_WIDTH*RIGHT/2).to_edge(UP)
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v_line = Line(UP, DOWN).scale(SPACE_HEIGHT)
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self.add(length, area, v_line)
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curve = self.get_curve(order = self.curve_start_order)
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sierp = self.get_sierpinski(order = self.sierpinski_start_order)
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self.add(curve, sierp)
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self.dither()
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for x in range(self.n_iterations):
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new_curve = self.get_curve(order = self.curve_start_order+x+1)
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new_sierp = self.get_sierpinski(
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order = self.sierpinski_start_order+x+1
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)
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self.play(
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Transform(curve, new_curve),
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Transform(sierp, new_sierp),
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run_time = 2
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)
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self.dither()
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def get_curve(self, order):
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# curve = ShowSierpinskiCurve.get_curve(self, order)
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curve = SierpinskiCurve(order = order)
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curve.scale_to_fit_height(4).center()
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curve.shift(SPACE_WIDTH*LEFT/2)
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return curve
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def get_sierpinski(self, order):
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result = Sierpinski(order = order)
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result.shift(SPACE_WIDTH*RIGHT/2)
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return result
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class MortyLookingAtRectangle(Scene):
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def construct(self):
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morty = Mortimer()
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morty.to_corner(DOWN+RIGHT)
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url = TextMobject("affirmjobs.3b1b.co")
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url.to_corner(UP+LEFT)
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rect = Rectangle(height = 9, width = 16)
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rect.scale_to_fit_height(5)
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rect.next_to(url, DOWN)
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rect.shift_onto_screen()
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url.save_state()
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url.next_to(morty.get_corner(UP+LEFT), UP)
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self.play(morty.change_mode, "raise_right_hand")
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self.play(Write(url))
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self.play(Blink(morty))
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self.dither()
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self.play(
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url.restore,
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morty.change_mode, "happy"
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)
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self.play(ShowCreation(rect))
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self.dither()
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self.play(Blink(morty))
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for mode in ["wave_2", "hooray", "happy", "pondering", "happy"]:
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self.play(morty.change_mode, mode)
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self.dither(2)
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self.play(Blink(morty))
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self.dither(2)
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@ -169,6 +169,7 @@ class FractalCurve(VMobject):
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self.add(corner)
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def init_colors(self):
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VMobject.init_colors(self)
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self.gradient_highlight(*self.colors)
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def get_anchor_points(self):
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