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https://github.com/3b1b/manim.git
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Up to initial discussion of scaling
This commit is contained in:
Grant Sanderson
parent
2d4ce0bd88
commit
4225941730
1 changed files with 655 additions and 9 deletions
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@ -28,18 +28,20 @@ from mobject.tex_mobject import *
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class Britain(SVGMobject):
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CONFIG = {
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"file_name" : "Britain.svg",
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"stroke_width" : 1,
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"stroke_color" : WHITE,
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"fill_opacity" : 0,
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"stroke_width" : 0,
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"fill_color" : BLUE_D,
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"fill_opacity" : 1,
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"propogate_style_to_family" : True,
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"height" : 5,
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"mark_paths_closed" : True,
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}
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def __init__(self, **kwargs):
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SVGMobject.__init__(self, **kwargs)
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self.points = self[0].points
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self.submobjects = []
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self.scale_to_fit_height(self.height)
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self.center()
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class KochTest(Scene):
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def construct(self):
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koch = KochCurve(order = 5, stroke_width = 2)
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@ -69,7 +71,7 @@ class SierpinskiTest(Scene):
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class FractalCreation(Scene):
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CONFIG = {
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"fractal_class" : PentagonalFractal,
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"max_order" : 6,
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"max_order" : 5,
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"path_arc" : np.pi/6,
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"submobject_mode" : "lagged_start"
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}
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@ -330,7 +332,11 @@ class SelfSimilarFractalsAsSubset(Scene):
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title.next_to(ORIGIN, RIGHT, buff = LARGE_BUFF)
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title.to_edge(UP, buff = 2*MED_BUFF)
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britain = Britain()
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britain = Britain(
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fill_opacity = 0,
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stroke_width = 2,
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stroke_color = WHITE,
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)
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britain.next_to(self.small_rect, RIGHT)
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britain.shift(2*DOWN)
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@ -354,6 +360,10 @@ class SelfSimilarFractalsAsSubset(Scene):
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self.dither(2)
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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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}
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def construct(self):
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v_line = Line(UP, DOWN).scale(SPACE_HEIGHT)
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smooth = TextMobject("Smooth")
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@ -361,11 +371,647 @@ class ConstrastSmoothAndFractal(Scene):
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fractal = TextMobject("Fractal")
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fractal.shift(SPACE_WIDTH*RIGHT/2)
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VGroup(smooth, fractal).to_edge(UP)
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self.add(v_line, smooth, fractal)
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background_rectangle = Rectangle(
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height = 2*SPACE_HEIGHT,
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width = SPACE_WIDTH,
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)
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background_rectangle.to_edge(RIGHT, buff = 0)
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background_rectangle.set_fill(BLACK, 1)
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background_rectangle.set_stroke(width = 0)
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self.add(v_line, background_rectangle, smooth, fractal)
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britain = Britain()
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britain = Britain(
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fill_opacity = 0,
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stroke_width = 2,
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stroke_color = WHITE,
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)[0]
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anchors = britain.get_anchors()
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smooth_britain =
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smooth_britain = VMobject()
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smooth_britain.set_points_smoothly(anchors[::10])
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smooth_britain.center().shift(SPACE_WIDTH*LEFT/2)
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index = np.argmax(smooth_britain.get_anchors()[:,0])
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smooth_britain.zoom_point = smooth_britain.point_from_proportion(
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self.britain_zoom_point_proportion
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)
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britain.shift(SPACE_WIDTH*RIGHT/2)
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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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britains = VGroup(britain, smooth_britain)
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self.play(*[
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ShowCreation(mob, run_time = 3)
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for mob in britains
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])
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self.play(
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britains.set_fill, BLUE, 1,
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britains.set_stroke, None, 0,
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)
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self.dither()
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self.play(
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ApplyMethod(
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smooth_britain.scale,
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self.scale_factor,
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smooth_britain.zoom_point
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),
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Animation(v_line),
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Animation(background_rectangle),
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ApplyMethod(
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britain.scale,
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self.scale_factor,
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britain.zoom_point
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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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)
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self.dither(2)
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class ShowIdealizations(Scene):
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def construct(self):
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arrow = DoubleArrow(SPACE_WIDTH*LEFT, SPACE_WIDTH*RIGHT)
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arrow.shift(DOWN)
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left_words = TextMobject("Idealization \\\\ as smooth")
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middle_words = TextMobject("Nature")
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right_words = TextMobject("""
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Idealization
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as perfectly
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self-similar
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""")
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for words in left_words, middle_words, right_words:
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words.scale(0.8)
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words.next_to(arrow, DOWN)
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left_words.to_edge(LEFT)
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right_words.to_edge(RIGHT)
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self.add(arrow, left_words, middle_words, right_words)
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britain = Britain()[0]
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britain.scale_to_fit_height(4)
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britain.next_to(arrow, UP)
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anchors = britain.get_anchors()
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smooth_britain = VMobject()
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smooth_britain.set_points_smoothly(anchors[::10])
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smooth_britain.set_stroke(width = 0)
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smooth_britain.set_fill(BLUE_D, opacity = 1)
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smooth_britain.next_to(arrow, UP)
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smooth_britain.to_edge(LEFT)
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koch_snowflake = KochSnowFlake(order = 5, monochromatic = True)
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koch_snowflake.set_stroke(width = 0)
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koch_snowflake.set_fill(BLUE_D, opacity = 1)
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koch_snowflake.scale_to_fit_height(3)
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koch_snowflake.rotate(2*np.pi/3)
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koch_snowflake.next_to(arrow, UP)
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koch_snowflake.to_edge(RIGHT)
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VGroup(smooth_britain, britain, koch_snowflake).gradient_highlight(
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BLUE_B, BLUE_D
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)
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self.play(FadeIn(britain))
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self.dither()
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self.play(Transform(britain.copy(), smooth_britain))
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self.dither()
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self.play(Transform(britain.copy(), koch_snowflake))
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self.dither()
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self.dither(2)
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class SayFractalDimension(TeacherStudentsScene):
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def construct(self):
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self.teacher_says("Fractal dimension")
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self.change_student_modes("confused", "hesitant", "pondering")
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self.dither(3)
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class ExamplesOfDimension(Scene):
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def construct(self):
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labels = VGroup(*[
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TextMobject("%s-dimensional"%s)
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for s in "1.585", "1.262", "1.21"
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])
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fractals = VGroup(*[
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Sierpinski(order = 7),
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KochSnowFlake(order = 5),
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Britain(stroke_width = 2, fill_opacity = 0)
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])
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for fractal, vect in zip(fractals, [LEFT, ORIGIN, RIGHT]):
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fractal.to_edge(vect)
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fractals[2].shift(0.5*UP)
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fractals[1].shift(0.5*RIGHT)
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for fractal, label, vect in zip(fractals, labels, [DOWN, UP, DOWN]):
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label.next_to(fractal, vect)
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label.shift_onto_screen()
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self.play(
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ShowCreation(fractal),
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Write(label),
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run_time = 3
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)
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self.dither()
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self.dither()
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class DimensionForNaturalNumbers(Scene):
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def construct(self):
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labels = VGroup(*[
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TextMobject("%d-dimensional"%d)
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for d in 1, 2, 3
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])
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for label, vect in zip(labels, [LEFT, ORIGIN, RIGHT]):
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label.to_edge(vect)
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labels.shift(2*DOWN)
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line = Line(DOWN+LEFT, 3*UP+RIGHT, color = BLUE)
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line.next_to(labels[0], UP)
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self.play(
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Write(labels[0]),
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ShowCreation(line)
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)
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self.dither()
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for label in labels[1:]:
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self.play(Write(label))
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self.dither()
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class Show2DPlanein3D(Scene):
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def construct(self):
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pass
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class ShowCubeIn3D(Scene):
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def construct(self):
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pass
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class OfCourseItsMadeUp(TeacherStudentsScene):
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def construct(self):
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self.teacher_says("""
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Fractal dimension
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\\emph{is} a made up concept...
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""")
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self.change_student_modes(*["hesitant"]*3)
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self.dither(2)
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self.teacher_says(
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"""But it's useful!""",
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target_mode = "hooray"
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)
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class FourSelfSimilarShapes(Scene):
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CONFIG = {
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"shape_width" : 2,
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"sierpinski_order" : 6,
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}
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def construct(self):
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titles = self.get_titles()
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shapes = self.get_shapes(titles)
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self.introduce_shapes(titles, shapes)
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self.show_self_similarity(shapes)
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self.mention_measurements()
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def get_titles(self):
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titles = VGroup(*map(TextMobject, [
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"Line", "Square", "Cube", "Sierpinski"
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]))
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for title, x in zip(titles, np.linspace(-0.75, 0.75, 4)):
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title.shift(x*SPACE_WIDTH*RIGHT)
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titles.to_edge(UP)
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return titles
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def get_shapes(self, titles):
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line = VGroup(
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Line(LEFT, ORIGIN),
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Line(ORIGIN, RIGHT)
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)
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line.highlight(BLUE_C)
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square = VGroup(*[
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Square().next_to(ORIGIN, vect, buff = 0)
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for vect in compass_directions(start_vect = DOWN+LEFT)
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])
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square.set_stroke(width = 0)
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square.set_fill(BLUE, 0.7)
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cube = TextMobject("TODO")
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cube.set_fill(opacity = 0)
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sierpinski = Sierpinski(order = self.sierpinski_order)
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shapes = VGroup(line, square, cube, sierpinski)
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for shape, title in zip(shapes, titles):
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shape.scale_to_fit_width(self.shape_width)
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shape.next_to(title, DOWN, buff = MED_BUFF)
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line.shift(DOWN)
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return shapes
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def introduce_shapes(self, titles, shapes):
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line, square, cube, sierpinski = shapes
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brace = Brace(VGroup(*shapes[:3]), DOWN)
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brace_text = brace.get_text("Not fractals")
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self.play(ShowCreation(line))
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self.play(GrowFromCenter(square))
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self.play(FadeIn(cube))
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self.play(ShowCreation(sierpinski))
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self.dither()
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self.play(
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GrowFromCenter(brace),
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FadeIn(brace_text)
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)
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self.dither()
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self.play(*map(FadeOut, [brace, brace_text]))
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self.dither()
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for title in titles:
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self.play(Write(title, run_time = 1))
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self.dither(2)
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def show_self_similarity(self, shapes):
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shapes_copy = shapes.copy()
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self.shapes_copy = shapes_copy
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line, square, cube, sierpinski = shapes_copy
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def break_up(mobject, factor = 1.3):
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mobject.scale_in_place(factor)
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for submob in mobject:
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submob.scale_in_place(1./factor)
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return mobject
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self.play(line.shift, 3*DOWN)
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self.play(ApplyFunction(break_up, line))
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self.dither()
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brace = Brace(line[0], DOWN)
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brace_text = brace.get_text("1/2")
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self.play(
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GrowFromCenter(brace),
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Write(brace_text)
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)
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brace.add(brace_text)
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self.dither()
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self.play(square.next_to, square, DOWN, LARGE_BUFF)
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self.play(ApplyFunction(break_up, square))
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subsquare = square[0]
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subsquare.save_state()
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self.play(subsquare.replace, shapes[1])
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self.dither()
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self.play(subsquare.restore)
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self.play(brace.next_to, subsquare, DOWN)
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self.dither()
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self.dither(5)#Handle cube
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self.play(sierpinski.next_to, sierpinski, DOWN, LARGE_BUFF)
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self.play(ApplyFunction(break_up, sierpinski))
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self.dither()
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self.play(brace.next_to, sierpinski[0], DOWN)
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self.dither(2)
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self.play(FadeOut(brace))
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def mention_measurements(self):
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line, square, cube, sierpinski = self.shapes_copy
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labels = map(TextMobject, [
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"$1/2$ length",
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"$1/4$ area",
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"$1/8$ volume",
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"You'll see...",
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])
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for label, shape in zip(labels, self.shapes_copy):
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label.next_to(shape, DOWN)
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label.to_edge(DOWN, buff = 2*MED_BUFF)
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if label is labels[-1]:
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label.shift(0.1*UP) #Dumb
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self.play(
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Write(label, run_time = 1),
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shape[0].highlight, YELLOW
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)
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self.dither()
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class BreakUpCubeIn3D(Scene):
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def construct(self):
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pass
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class BrokenUpCubeIn3D(Scene):
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def construct(self):
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pass
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class GeneralWordForMeasurement(Scene):
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def construct(self):
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measure = TextMobject("``Measure''")
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measure.to_edge(UP)
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mass = TextMobject("Mass")
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mass.move_to(measure)
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words = VGroup(*map(TextMobject, [
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"Length", "Area", "Volume"
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]))
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words.arrange_submobjects(RIGHT, buff = 2*LARGE_BUFF)
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words.next_to(measure, DOWN, buff = 2*LARGE_BUFF)
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colors = color_gradient([BLUE_B, BLUE_D], len(words))
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for word, color in zip(words, colors):
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word.highlight(color)
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lines = VGroup(*[
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Line(
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measure.get_bottom(), word.get_top(),
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color = word.get_color(),
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buff = MED_BUFF
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)
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for word in words
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])
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for word in words:
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self.play(FadeIn(word))
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self.play(ShowCreation(lines, run_time = 2))
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self.dither()
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self.play(Write(measure))
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self.dither(2)
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self.play(Transform(measure, mass))
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self.dither(2)
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class ImagineShapesAsMetal(FourSelfSimilarShapes):
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def construct(self):
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titles = VGroup(*map(VGroup, self.get_titles()))
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shapes = self.get_shapes(titles)
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shapes.shift(DOWN)
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descriptions = VGroup(*[
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TextMobject(*words, arg_separator = "\\\\")
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for shape, words in zip(shapes, [
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["Thin", "wire"],
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["Flat", "sheet"],
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["Solid", "cube"],
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["Sierpinski", "mesh"]
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])
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])
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for title, description in zip(titles, descriptions):
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description.move_to(title, UP)
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title.target = description
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self.add(titles, shapes)
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for shape in shapes:
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shape.generate_target()
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shape.target.highlight(LIGHT_GREY)
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shapes[-1].target.gradient_highlight(GREY, WHITE)
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for shape, title in zip(shapes, titles):
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self.play(
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MoveToTarget(title),
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MoveToTarget(shape)
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)
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self.dither()
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self.dither()
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for shape in shapes:
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self.play(
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shape.scale, 0.5, shape.get_top(),
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run_time = 3,
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rate_func = there_and_back
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)
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self.dither()
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class ScaledLineMass(Scene):
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CONFIG = {
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"title" : "Line",
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"mass_scaling_factor" : "\\frac{1}{2}",
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"shape_width" : 2,
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"break_up_factor" : 1.3,
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"vert_distance" : 2,
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"brace_direction" : DOWN,
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"shape_to_shape_buff" : 2*LARGE_BUFF,
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}
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def construct(self):
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title = TextMobject(self.title)
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title.to_edge(UP)
|
||||
scaling_factor_label = TextMobject(
|
||||
"Scaling factor:", "$\\frac{1}{2}$"
|
||||
)
|
||||
scaling_factor_label[1].highlight(YELLOW)
|
||||
scaling_factor_label.to_edge(LEFT).shift(UP)
|
||||
mass_scaling_label = TextMobject(
|
||||
"Mass scaling factor:", "$%s$"%self.mass_scaling_factor
|
||||
)
|
||||
mass_scaling_label[1].highlight(GREEN)
|
||||
mass_scaling_label.next_to(
|
||||
scaling_factor_label, DOWN,
|
||||
aligned_edge = LEFT,
|
||||
buff = LARGE_BUFF
|
||||
)
|
||||
|
||||
shape = self.get_shape()
|
||||
shape.scale_to_fit_width(self.shape_width)
|
||||
shape.center()
|
||||
shape.shift(SPACE_WIDTH*RIGHT/2 + self.vert_distance*UP)
|
||||
|
||||
big_brace = Brace(shape, self.brace_direction)
|
||||
big_brace_text = big_brace.get_text("$1$")
|
||||
|
||||
shape_copy = shape.copy()
|
||||
shape_copy.next_to(shape, DOWN, buff = self.shape_to_shape_buff)
|
||||
shape_copy.scale_in_place(self.break_up_factor)
|
||||
for submob in shape_copy:
|
||||
submob.scale_in_place(1./self.break_up_factor)
|
||||
|
||||
little_brace = Brace(shape_copy[0], self.brace_direction)
|
||||
little_brace_text = little_brace.get_text("$\\frac{1}{2}$")
|
||||
|
||||
self.add(title, scaling_factor_label, mass_scaling_label[0])
|
||||
self.play(GrowFromCenter(shape))
|
||||
self.play(
|
||||
GrowFromCenter(big_brace),
|
||||
Write(big_brace_text)
|
||||
)
|
||||
self.dither()
|
||||
|
||||
self.play(
|
||||
shape.copy().replace, shape_copy[0]
|
||||
)
|
||||
self.remove(*self.get_mobjects_from_last_animation())
|
||||
self.add(shape_copy[0])
|
||||
self.play(
|
||||
GrowFromCenter(little_brace),
|
||||
Write(little_brace_text)
|
||||
)
|
||||
self.dither()
|
||||
|
||||
self.play(Write(mass_scaling_label[1], run_time = 1))
|
||||
self.dither()
|
||||
self.play(FadeIn(
|
||||
VGroup(*shape_copy[1:]),
|
||||
submobject_mode = "lagged_start"
|
||||
))
|
||||
self.dither()
|
||||
self.play(Transform(
|
||||
shape_copy.copy(), shape
|
||||
))
|
||||
self.dither()
|
||||
|
||||
def get_shape(self):
|
||||
return VGroup(
|
||||
Line(LEFT, ORIGIN),
|
||||
Line(ORIGIN, RIGHT)
|
||||
).highlight(BLUE)
|
||||
|
||||
class ScaledSquareMass(ScaledLineMass):
|
||||
CONFIG = {
|
||||
"title" : "Square",
|
||||
"mass_scaling_factor" : "\\frac{1}{4} = \\left( \\frac{1}{2} \\right)^2",
|
||||
"brace_direction" : LEFT,
|
||||
}
|
||||
def get_shape(self):
|
||||
return VGroup(*[
|
||||
Square(
|
||||
stroke_width = 0,
|
||||
fill_color = BLUE,
|
||||
fill_opacity = 0.7
|
||||
).shift(vect)
|
||||
for vect in compass_directions(start_vect = DOWN+LEFT)
|
||||
])
|
||||
|
||||
class ScaledCubeMass(ScaledLineMass):
|
||||
CONFIG = {
|
||||
"title" : "Cube",
|
||||
"mass_scaling_factor" : "\\frac{1}{8} = \\left( \\frac{1}{2} \\right)^3",
|
||||
}
|
||||
def get_shape(self):
|
||||
return TextMobject("TODO").set_fill(opacity = 0)
|
||||
|
||||
class FormCubeFromSubcubesIn3D(Scene):
|
||||
def construct(self):
|
||||
pass
|
||||
|
||||
class ScaledSierpinskiMass(ScaledLineMass):
|
||||
CONFIG = {
|
||||
"title" : "Sierpinski",
|
||||
"mass_scaling_factor" : "\\frac{1}{3}",
|
||||
"vert_distance" : 2.5,
|
||||
"shape_to_shape_buff" : 1.5*LARGE_BUFF,
|
||||
}
|
||||
def get_shape(self):
|
||||
return Sierpinski(order = 6)
|
||||
|
||||
class DefineTwoDimensional(PiCreatureScene):
|
||||
CONFIG = {
|
||||
"dimension" : "2",
|
||||
"length_color" : GREEN,
|
||||
"dimension_color" : YELLOW,
|
||||
"shape_width" : 2,
|
||||
"scale_factor" : 1.5,
|
||||
}
|
||||
def construct(self):
|
||||
self.add_title()
|
||||
self.add_h_line()
|
||||
self.add_shape()
|
||||
self.add_width_mass_labels()
|
||||
self.show_top_length()
|
||||
self.change_mode("thinking")
|
||||
self.perform_scaling()
|
||||
self.show_dimension()
|
||||
|
||||
def add_title(self):
|
||||
title = TextMobject(
|
||||
self.dimension, "-dimensional",
|
||||
arg_separator = ""
|
||||
)
|
||||
self.dimension_in_title = title[0]
|
||||
self.dimension_in_title.highlight(self.dimension_color)
|
||||
title.to_edge(UP)
|
||||
self.add(title)
|
||||
|
||||
self.title = title
|
||||
|
||||
def add_h_line(self):
|
||||
self.h_line = Line(LEFT, RIGHT).scale(SPACE_WIDTH)
|
||||
self.add(self.h_line)
|
||||
|
||||
def add_shape(self):
|
||||
shape = self.get_shape()
|
||||
shape.scale_to_fit_width(self.shape_width)
|
||||
shape.next_to(self.title, DOWN, buff = 2*MED_BUFF)
|
||||
# self.shape.shift(SPACE_HEIGHT*UP/2)
|
||||
self.mass_color = shape.get_color()
|
||||
self.add(shape)
|
||||
|
||||
self.shape = shape
|
||||
|
||||
def add_width_mass_labels(self):
|
||||
top_length = TextMobject("Length:", "$L$")
|
||||
top_mass = TextMobject("Mass:", "$M$")
|
||||
bottom_length = TextMobject(
|
||||
"Length: ", "$s$", "$L$",
|
||||
arg_separator = ""
|
||||
)
|
||||
bottom_mass = TextMobject(
|
||||
"Mass: ", "$s^%s$"%self.dimension, "$M$",
|
||||
arg_separator = ""
|
||||
)
|
||||
self.dimension_in_exp = VGroup(
|
||||
*bottom_mass[1][-len(self.dimension):]
|
||||
)
|
||||
self.dimension_in_exp.highlight(self.dimension_color)
|
||||
|
||||
top_group = VGroup(top_length, top_mass)
|
||||
bottom_group = VGroup(bottom_length, bottom_mass)
|
||||
for group in top_group, bottom_group:
|
||||
group.arrange_submobjects(
|
||||
DOWN,
|
||||
buff = 2*MED_BUFF,
|
||||
aligned_edge = LEFT
|
||||
)
|
||||
group[0][-1].highlight(self.length_color)
|
||||
group[1][-1].highlight(self.mass_color)
|
||||
|
||||
top_group.next_to(self.h_line, UP, buff = LARGE_BUFF)
|
||||
bottom_group.next_to(self.h_line, DOWN, buff = LARGE_BUFF)
|
||||
for group in top_group, bottom_group:
|
||||
group.to_edge(LEFT)
|
||||
|
||||
self.add(top_group, bottom_group)
|
||||
|
||||
self.top_L = top_length[-1]
|
||||
self.bottom_L = VGroup(*bottom_length[-2:])
|
||||
|
||||
def show_top_length(self):
|
||||
brace = Brace(self.shape, LEFT)
|
||||
top_L = self.top_L.copy()
|
||||
|
||||
self.play(GrowFromCenter(brace))
|
||||
self.play(top_L.next_to, brace, LEFT)
|
||||
self.dither()
|
||||
|
||||
self.brace = brace
|
||||
|
||||
def perform_scaling(self):
|
||||
group = VGroup(self.shape, self.brace).copy()
|
||||
self.play(group.shift, (group.get_top()[1]+MED_BUFF)*DOWN)
|
||||
|
||||
shape, brace = group
|
||||
bottom_L = self.bottom_L.copy()
|
||||
shape.generate_target()
|
||||
shape.target.scale(
|
||||
self.scale_factor,
|
||||
about_point = shape.get_corner(UP+LEFT)
|
||||
)
|
||||
brace.target = Brace(shape.target, LEFT)
|
||||
self.play(*map(MoveToTarget, group))
|
||||
self.play(bottom_L.next_to, brace, LEFT)
|
||||
self.dither()
|
||||
|
||||
def show_dimension(self):
|
||||
top_dimension = self.dimension_in_title.copy()
|
||||
self.play(self.pi_creature.look_at, top_dimension)
|
||||
self.play(
|
||||
top_dimension.replace,
|
||||
self.dimension_in_exp,
|
||||
run_time = 2,
|
||||
)
|
||||
self.dither(3)
|
||||
|
||||
def get_shape(self):
|
||||
return Square(
|
||||
stroke_width = 0,
|
||||
fill_color = BLUE,
|
||||
fill_opacity = 0.7,
|
||||
)
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue