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https://github.com/3b1b/manim.git
synced 2025-09-01 00:48:45 +00:00
More filler animations for fractal project
This commit is contained in:
Grant Sanderson
parent
a2d62c08fd
commit
9676aef253
1 changed files with 261 additions and 21 deletions
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@ -450,6 +450,33 @@ class ConstrastSmoothAndFractal(Scene):
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run_time = 10,
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)
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self.dither(2)
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class InfiniteKochZoom(Scene):
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CONFIG = {
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"order" : 6,
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"left_point" : 3*LEFT,
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}
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def construct(self):
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small_curve = self.get_curve(self.order)
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larger_curve = self.get_curve(self.order + 1)
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larger_curve.scale(3, about_point = small_curve.points[0])
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self.play(Transform(small_curve, larger_curve, run_time = 2))
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self.repeat_frames(5)
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def get_curve(self, order):
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koch_curve = KochCurve(
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monochromatic = True,
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order = order,
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color = BLUE,
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stroke_width = 2,
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)
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koch_curve.scale_to_fit_width(18)
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koch_curve.shift(
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self.left_point - koch_curve.points[0]
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)
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return koch_curve
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class ShowIdealizations(Scene):
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def construct(self):
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@ -1834,21 +1861,30 @@ class BoxCountingWithDisk(BoxCountingScene):
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CONFIG = {
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"box_width" : 0.25,
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"num_boundary_check_points" : 200,
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"corner_rect_left_extension" : 2,
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"disk_opacity" : 0.5,
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"disk_stroke_width" : 0.5,
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"decimal_string" : "= %.2f",
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}
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def construct(self):
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disk = Circle(radius = 1)
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disk.set_fill(BLUE, opacity = 0.5)
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disk.set_stroke(BLUE, width = 1)
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disk.set_fill(BLUE, opacity = self.disk_opacity)
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disk.set_stroke(BLUE, width = self.disk_stroke_width)
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disk.shift(0.1*np.sqrt(2)*(UP+RIGHT))
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radius = Line(disk.get_center(), disk.get_right())
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disk.add(radius)
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one = TexMobject("1").next_to(radius, DOWN, SMALL_BUFF)
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boxes = self.get_highlighted_boxes(disk)
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small_box_num = len(boxes)
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grid = self.get_grid()
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corner_rect = self.get_corner_rect()
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counting_label = self.get_counting_label()
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prop_words = TextMobject("Proportional to", "$\\pi r^2$")
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prop_words[1].highlight(BLUE)
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prop_words.next_to(counting_label, DOWN, aligned_edge = LEFT)
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self.add(disk, one)
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self.play(
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@ -1861,7 +1897,11 @@ class BoxCountingWithDisk(BoxCountingScene):
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FadeIn(counting_label)
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)
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counting_mob = self.count_boxes(boxes)
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self.dither()
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self.play(Write(prop_words, run_time = 2))
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self.dither(2)
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self.play(FadeOut(prop_words))
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disk.generate_target()
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disk.target.scale(2, about_point = disk.get_top())
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@ -1873,6 +1913,7 @@ class BoxCountingWithDisk(BoxCountingScene):
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)
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self.play(counting_mob.next_to, counting_mob, DOWN)
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boxes = self.get_highlighted_boxes(disk)
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large_box_count = len(boxes)
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new_counting_mob = self.count_boxes(boxes)
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self.dither()
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@ -1880,15 +1921,31 @@ class BoxCountingWithDisk(BoxCountingScene):
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frac_line.highlight(YELLOW)
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frac_line.stretch_to_fit_width(new_counting_mob.get_width())
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frac_line.next_to(new_counting_mob, DOWN, buff = SMALL_BUFF)
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decimal = TexMobject(self.decimal_string%(float(large_box_count)/small_box_num))
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decimal.next_to(frac_line, RIGHT)
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approx = TexMobject("\\approx 2^2")
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approx.next_to(frac_line, RIGHT)
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approx.next_to(decimal, RIGHT, aligned_edge = DOWN)
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approx.shift_onto_screen()
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self.play(*map(Write, [frac_line, approx]))
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self.dither(2)
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self.play(*map(Write, [frac_line, decimal]))
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self.play(Write(approx))
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self.dither()
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randy = Randolph().shift(3*RIGHT).to_edge(DOWN)
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self.play(FadeIn(randy))
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self.play(PiCreatureSays(
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randy, "Is it?",
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target_mode = "sassy",
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bubble_kwargs = {"direction" : LEFT}
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))
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self.play(Blink(randy))
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self.dither()
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class FinerBoxCountingWithDisk(BoxCountingWithDisk):
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CONFIG = {
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"box_width" : 0.1
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"box_width" : 0.03,
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"num_boundary_check_points" : 1000,
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"disk_stroke_width" : 0.5,
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"decimal_string" : "= %.2f",
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}
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class PlotDiskBoxCounting(GraphScene):
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@ -2141,6 +2198,28 @@ class BoxCountingWithBritain(BoxCountingScene):
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simpler_eq, rewired_log_expression1
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)
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class GiveShapeAndPonder(Scene):
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def construct(self):
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morty = Mortimer()
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randy = Randolph()
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morty.next_to(ORIGIN, DOWN).shift(3*RIGHT)
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randy.next_to(ORIGIN, DOWN).shift(3*LEFT)
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norway = Norway(fill_opacity = 0, stroke_width = 1)
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norway.scale_to_fit_width(2)
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norway.next_to(morty, UP+LEFT, buff = -MED_BUFF)
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self.play(
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morty.change_mode, "raise_right_hand",
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morty.look_at, norway,
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randy.look_at, norway,
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ShowCreation(norway)
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)
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self.play(Blink(morty))
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self.play(randy.change_mode, "pondering")
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self.play(Blink(randy))
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self.dither()
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class CheapBoxCountingWithBritain(BoxCountingWithBritain):
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CONFIG = {
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"skip_animations" : True,
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@ -2210,6 +2289,17 @@ class IntroduceLogLogPlot(GraphScene):
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slope.next_to(slope_lines, RIGHT)
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self.dither()
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data_points = [
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self.input_to_graph_point(x) + ((random.random()-0.5)/x)*UP
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for x in np.arange(1, 8, 0.7)
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]
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data_dots = VGroup(*[
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Dot(point, radius = 0.05, color = YELLOW)
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for point in data_points
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])
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self.play(ShowCreation(data_dots, run_time = 3))
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self.dither()
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self.play(
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ShowCreation(graph),
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Animation(expression)
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@ -2219,17 +2309,124 @@ class IntroduceLogLogPlot(GraphScene):
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self.play(Write(slope))
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self.dither()
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class ManyBritainCounts(BoxCountingWithBritain):
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CONFIG = {
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"box_width" : 0.1,
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"num_boundary_check_points" : 5000,
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"corner_rect_left_extension" : 1,
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}
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def construct(self):
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britain = Britain(
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stroke_width = 2,
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fill_opacity = 0
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)
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britain = fractalify(britain, order = 1, dimension = 1.21)
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britain.next_to(ORIGIN, LEFT)
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self.add(self.get_grid())
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self.add(britain)
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for width in range(1, 6):
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self.play(britain.scale_to_fit_width, width)
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boxes = self.get_highlighted_boxes(britain)
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self.play(ShowCreation(boxes))
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self.dither()
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self.play(FadeOut(boxes))
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class ReadyForRealDefinition(TeacherStudentsScene):
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def construct(self):
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self.teacher_says("""
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Now for what
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fractals really are.
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""")
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self.change_student_modes(*["hooray"]*3)
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self.dither(2)
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class DefineFractal(TeacherStudentsScene):
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def construct(self):
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self.teacher_says("""
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Fractals are shapes
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with a non-integer dimension.
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""")
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self.change_student_modes("thinking", "happy", "erm")
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self.dither(3)
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self.teacher_says(
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"Kind of...",
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target_mode = "sassy"
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)
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self.change_student_modes(*["pondering"]*3)
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self.play(*[
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ApplyMethod(pi.look, DOWN)
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for pi in self.get_everyone()
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])
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self.dither(3)
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class DifferentSlopesAtDifferentScales(IntroduceLogLogPlot):
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def construct(self):
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self.setup_axes(animate = False)
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self.x_axis_label_mob[-2].highlight(BLUE)
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self.y_axis_label_mob[-2].highlight(YELLOW)
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self.graph_function(
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lambda x : 0.01*(x-5)**3 + 0.3*x + 3
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)
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self.remove(self.graph)
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words = TextMobject("""
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Different slopes
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at different scales
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""")
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words.to_edge(RIGHT)
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arrows = VGroup(*[
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Arrow(words.get_left(), self.input_to_graph_point(x))
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for x in 1, 7, 12
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])
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data_points = [
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self.input_to_graph_point(x) + ((random.random()-0.5)/x)*UP
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for x in np.arange(1, 8, 0.7)
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self.input_to_graph_point(x) + (0.3*(random.random()-0.5))*UP
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for x in np.arange(1, self.x_max, 0.7)
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]
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data_dots = VGroup(*[
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Dot(point, radius = 0.05, color = YELLOW)
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for point in data_points
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])
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self.play(ShowCreation(data_dots, run_time = 3))
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self.play(ShowCreation(data_dots, run_time = 2))
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self.play(ShowCreation(self.graph))
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self.dither()
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self.play(
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Write(words),
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ShowCreation(arrows)
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)
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self.dither()
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class HoldUpCoilExample(TeacherStudentsScene):
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def construct(self):
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self.play(
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self.get_teacher().change_mode, "raise_right_hand",
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self.get_teacher().look, UP+LEFT
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)
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self.dither(5)
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self.change_student_modes(*["thinking"]*3)
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self.dither(5)
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class ListDimensionTypes(PiCreatureScene):
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CONFIG = {
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"use_morty" : False,
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}
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def construct(self):
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types = VGroup(*map(TextMobject, [
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"Box counting dimension",
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"Information dimension",
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"Hausdorff dimension",
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"Packing dimension"
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]))
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types.arrange_submobjects(DOWN, aligned_edge = LEFT)
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for text in types:
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self.play(
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Write(text, run_time = 1),
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self.pi_creature.change_mode, "pondering"
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)
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self.dither(3)
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class ZoomInOnBritain(Scene):
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CONFIG = {
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@ -2262,6 +2459,13 @@ class ZoomInOnBritain(Scene):
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)
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self.dither()
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class NoteTheConstantSlope(Scene):
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def construct(self):
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words = TextMobject("Note the \\\\ constant slope")
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words.highlight(YELLOW)
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self.play(Write(words))
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self.dither(2)
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class FromHandwavyToQuantitative(Scene):
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def construct(self):
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randy = Randolph()
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@ -2293,45 +2497,79 @@ class FromHandwavyToQuantitative(Scene):
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class WhatSlopeDoesLogLogPlotApproach(IntroduceLogLogPlot):
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CONFIG = {
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"words" : "What slope does \\\\ this approach?"
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"words" : "What slope does \\\\ this approach?",
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"x_max" : 20,
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"y_max" : 15,
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}
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def construct(self):
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self.setup_axes(animate = False)
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self.x_axis_label_mob[-2].highlight(BLUE)
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self.y_axis_label_mob[-2].highlight(YELLOW)
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graph = self.graph_function(
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lambda x : (1-np.exp(-x))*x
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)
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self.remove(graph)
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spacing = 0.5
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x_range = np.arange(1, self.x_max, spacing)
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randomness = [
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0.5*np.exp(-x/2)+spacing*(0.8 + random.random()/(x**(0.5)))
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for x in x_range
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]
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cum_sums = np.cumsum(randomness)
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data_points = [
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self.input_to_graph_point(x) + (0.2*(random.random()-0.5)/x)*UP
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for x in np.arange(1, 12, 0.2)
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self.coords_to_point(x, cum_sum)
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for x, cum_sum in zip(x_range, cum_sums)
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]
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data_dots = VGroup(*[
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Dot(point, radius = 0.02, color = YELLOW)
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Dot(point, radius = 0.025, color = YELLOW)
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for point in data_points
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])
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words = TextMobject(self.words)
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p1, p2 = [
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self.input_to_graph_point(x)
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for x in 5, 10
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data_dots[int(alpha*len(data_dots))].get_center()
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for alpha in 0.3, 0.5
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]
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words.rotate(Line(p1, p2).get_angle())
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words.next_to(p1, RIGHT, aligned_edge = DOWN, buff = LARGE_BUFF)
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words.next_to(p1, RIGHT, aligned_edge = DOWN, buff = 1.5)
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morty = Mortimer()
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morty.to_corner(DOWN+RIGHT)
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self.add(morty)
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self.play(ShowCreation(data_dots, run_time = 3))
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self.play(ShowCreation(data_dots, run_time = 7))
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self.play(
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Write(words),
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morty.change_mode, "speaking"
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)
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self.play(Blink(morty))
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self.dither()
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class BritainBoxCountHighZoom(BoxCountingWithBritain):
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def construct(self):
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britain = Britain(
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stroke_width = 2,
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fill_opacity = 0
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)
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britain = fractalify(britain, order = 2, dimension = 1.21)
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self.add(self.get_grid())
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self.add(britain)
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for x in range(2):
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self.play(
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britain.scale, 10, britain.point_from_proportion(0.3),
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run_time = 2
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)
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if x == 0:
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a, b = 0.2, 0.5
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else:
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a, b = 0.25, 0.35
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britain.pointwise_become_partial(britain, a, b)
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self.count_britain(britain)
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self.dither()
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def count_britain(self, britain):
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boxes = self.get_highlighted_boxes(britain)
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self.play(ShowCreation(boxes))
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self.dither()
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self.play(FadeOut(boxes))
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class IfBritainWasEventuallySmooth(Scene):
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def construct(self):
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@ -2522,6 +2760,7 @@ class FractalNonFractalFlowChart(Scene):
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randy = Randolph()
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randy.scale_to_fit_height(3)
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randy.to_corner(UP+RIGHT)
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self.add(randy)
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self.add(is_fractal)
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self.dither()
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@ -2597,6 +2836,7 @@ class MortyLookingAtRectangle(Scene):
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affirm_logo = AffirmLogo()[0]
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affirm_logo.to_corner(UP+RIGHT, buff = 2*MED_BUFF)
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affirm_logo.shift(0.5*DOWN)
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self.add(morty)
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affirm_logo.save_state()
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