mirror of
https://github.com/3b1b/manim.git
synced 2025-08-05 22:03:01 +08:00
Final animation for Hilbert, I think
This commit is contained in:
Grant Sanderson
@ -261,6 +261,25 @@ class Sierpinski(LindenmayerCurve):
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"angle" : -np.pi/3,
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}
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class KochCurve(LindenmayerCurve):
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DEFAULT_CONFIG = {
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"start_color" : BLUE_D,
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"end_color" : WHITE,
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"axiom" : "A--A--A--",
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"rule" : {
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"A" : "A+A--A+A"
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},
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"radius" : 4,
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"scale_factor" : 3,
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"start_step" : RIGHT,
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"angle" : np.pi/3
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}
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def __init__(self, **kwargs):
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digest_config(self, kwargs)
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self.scale_factor = 2*(1+np.cos(self.angle))
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LindenmayerCurve.__init__(self, **kwargs)
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class StellarCurve(LindenmayerCurve):
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DEFAULT_CONFIG = {
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@ -319,21 +338,31 @@ class SpaceFillingCurveScene(Scene):
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return CurveClass, int(order_str)
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class TransformOverIncreasingOrders(SpaceFillingCurveScene):
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def construct(self, CurveClass, max_order):
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def setup(self, CurveClass):
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sample = CurveClass(order = 1)
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self.curve = Line(sample.radius*LEFT, sample.radius*RIGHT)
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self.curve = Line(3*LEFT, 3*RIGHT)
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self.curve.gradient_highlight(
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sample.start_color,
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sample.end_color
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)
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for order in range(1, max_order):
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new_curve = CurveClass(order = order)
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self.play(
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Transform(self.curve, new_curve),
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run_time = 3/np.sqrt(order),
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)
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self.CurveClass = CurveClass
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self.order = 0
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def construct(self, CurveClass, max_order):
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self.setup(CurveClass)
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while self.order < max_order:
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self.increase_order()
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self.dither()
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def increase_order(self, *other_anims):
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self.order += 1
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new_curve = self.CurveClass(order = self.order)
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self.play(
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Transform(self.curve, new_curve),
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*other_anims,
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run_time = 3/np.sqrt(self.order)
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)
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class DrawSpaceFillingCurve(SpaceFillingCurveScene):
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def construct(self, CurveClass, order):
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347
hilbert/fractal_porn.py
Normal file
347
hilbert/fractal_porn.py
Normal file
@ -0,0 +1,347 @@
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from mobject import Mobject, Point, Mobject1D
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from scene import Scene
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from animation.transform import \
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Transform, ShimmerIn, FadeIn, FadeOut, ApplyMethod
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from animation.simple_animations import \
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ShowCreation, DelayByOrder
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from topics.geometry import Line, Arc, Arrow
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from mobject.tex_mobject import TexMobject, TextMobject
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from helpers import *
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from hilbert.curves import *
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class Intro(TransformOverIncreasingOrders):
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@staticmethod
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def args_to_string(*args):
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return ""
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@staticmethod
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def string_to_args(string):
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raise Exception("string_to_args Not Implemented!")
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def construct(self):
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words1 = TextMobject(
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"If you watched my video about Hilbert's space-filling curve\\dots"
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)
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words2 = TextMobject(
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"\\dots you might be curious to see what a few other space-filling curves look like."
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)
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words2.scale(0.8)
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for words in words1, words2:
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words.to_edge(UP, buff = 0.2)
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self.setup(HilbertCurve)
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self.play(ShimmerIn(words1))
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for x in range(4):
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self.increase_order()
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self.remove(words1)
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self.increase_order(
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ShimmerIn(words2)
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)
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for x in range(4):
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self.increase_order()
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class BringInPeano(Intro):
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def construct(self):
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words1 = TextMobject("""
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For each one, see if you can figure out what
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the pattern of construction is.
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""")
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words2 = TextMobject("""
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This one is the Peano curve.
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""")
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words3 = TextMobject("""
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It is the original space-filling curve.
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""")
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self.setup(PeanoCurve)
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self.play(ShimmerIn(words1))
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self.dither(5)
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self.remove(words1)
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self.add(words2.to_edge(UP))
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for x in range(3):
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self.increase_order()
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self.remove(words2)
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self.increase_order(ShimmerIn(words3.to_edge(UP)))
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for x in range(2):
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self.increase_order()
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class FillOtherShapes(Intro):
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def construct(self):
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words1 = TextMobject("""
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But of course, there's no reason we should limit
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ourselves to filling in squares.
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""")
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words2 = TextMobject("""
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Here's a simple triangle-filling curve I defined
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in a style reflective of a Hilbert curve.
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""")
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words1.to_edge(UP)
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words2.scale(0.8).to_edge(UP, buff = 0.2)
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self.setup(TriangleFillingCurve)
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self.play(ShimmerIn(words1))
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for x in range(3):
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self.increase_order()
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self.remove(words1)
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self.add(words2)
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for x in range(5):
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self.increase_order()
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class SmallerFlowSnake(FlowSnake):
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DEFAULT_CONFIG = {
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"radius" : 4
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}
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class MostDelightfulName(Intro):
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def construct(self):
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words1 = TextMobject("""
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This one has the most delightful name,
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thanks to mathematician/programmer Bill Gosper:
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""")
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words2 = TextMobject("``Flow Snake''")
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words3 = TextMobject("""
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What makes this one particularly interesting
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is that the boundary itself is a fractal.
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""")
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for words in words1, words2, words3:
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words.to_edge(UP)
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self.setup(SmallerFlowSnake)
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self.play(ShimmerIn(words1))
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for x in range(3):
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self.increase_order()
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self.remove(words1)
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self.add(words2)
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for x in range(3):
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self.increase_order()
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self.remove(words2)
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self.play(ShimmerIn(words3))
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class SurpriseFractal(Intro):
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def construct(self):
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words = TextMobject("""
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It might come as a surprise how some well-known
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fractals can be described with curves.
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""")
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words.to_edge(UP)
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self.setup(Sierpinski)
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self.add(TextMobject("Speaking of other fractals\\dots"))
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self.dither(3)
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self.clear()
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self.play(ShimmerIn(words))
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for x in range(9):
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self.increase_order()
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class IntroduceKoch(Intro):
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def construct(self):
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words = map(TextMobject, [
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"This is another famous fractal.",
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"The ``Koch Snowflake''",
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"Let's finish things off by seeing how to turn \
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this into a space-filling curve"
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])
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for text in words:
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text.to_edge(UP)
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self.setup(KochCurve)
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self.add(words[0])
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for x in range(3):
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self.increase_order()
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self.remove(words[0])
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self.add(words[1])
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for x in range(4):
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self.increase_order()
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self.remove(words[1])
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self.add(words[2])
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self.dither(6)
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class StraightKoch(KochCurve):
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DEFAULT_CONFIG = {
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"axiom" : "A"
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}
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class SharperKoch(StraightKoch):
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DEFAULT_CONFIG = {
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"angle" : 0.9*np.pi/2,
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}
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class DullerKoch(StraightKoch):
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DEFAULT_CONFIG = {
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"angle" : np.pi/6,
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}
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class SpaceFillingKoch(StraightKoch):
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DEFAULT_CONFIG = {
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"angle" : np.pi/2,
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}
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class FromKochToSpaceFilling(Scene):
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def construct(self):
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self.max_order = 7
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self.revisit_koch()
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self.show_angles()
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self.show_change_side_by_side()
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def revisit_koch(self):
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words = map(TextMobject, [
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"First, look at how one section of this curve is made.",
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"This pattern of four lines is the ``seed''",
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"With each iteration, every straight line is \
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replaced with an appropriately small copy of the seed",
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])
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for text in words:
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text.to_edge(UP)
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self.add(words[0])
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curve = StraightKoch(order = self.max_order)
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self.play(Transform(
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curve,
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StraightKoch(order = 1),
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run_time = 5
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))
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self.remove(words[0])
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self.add(words[1])
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self.dither(4)
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self.remove(words[1])
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self.add(words[2])
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self.dither(3)
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for order in range(2, self.max_order):
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self.play(Transform(
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curve,
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StraightKoch(order = order)
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))
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if order == 2:
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self.dither(2)
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elif order == 3:
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self.dither()
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self.clear()
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def show_angles(self):
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words = TextMobject("""
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Let's see what happens as we change
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the angle in this seed
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""")
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words.to_edge(UP)
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koch, sharper_koch, duller_koch = curves = [
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CurveClass(order = 1)
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for CurveClass in StraightKoch, SharperKoch, DullerKoch
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]
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arcs = [
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Arc(
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2*(np.pi/2 - curve.angle),
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radius = r,
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start_angle = np.pi+curve.angle
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).shift(curve.points[curve.get_num_points()/2])
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for curve, r in zip(curves, [0.6, 0.7, 0.4])
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]
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theta = TexMobject("\\theta")
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theta.shift(arcs[0].get_center()+2.5*DOWN)
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arrow = Arrow(theta, arcs[0])
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self.add(words, koch)
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self.play(ShowCreation(arcs[0]))
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self.play(
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ShowCreation(arrow),
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ShimmerIn(theta)
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)
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self.dither(2)
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self.remove(theta, arrow)
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self.play(
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Transform(koch, duller_koch),
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Transform(arcs[0], arcs[2]),
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)
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self.play(
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Transform(koch, sharper_koch),
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Transform(arcs[0], arcs[1]),
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)
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self.clear()
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def show_change_side_by_side(self):
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seed = TextMobject("Seed")
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seed.shift(3*LEFT+2*DOWN)
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fractal = TextMobject("Fractal")
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fractal.shift(3*RIGHT+2*DOWN)
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words = map(TextMobject, [
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"A sharper angle results in a richer curve",
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"A more obtuse angle gives a sparser curve",
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"And as the angle approaches 0\\dots",
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"We have a new space-filling curve."
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])
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for text in words:
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text.to_edge(UP)
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sharper, duller, space_filling = [
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CurveClass(order = 1).shift(3*LEFT)
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for CurveClass in SharperKoch, DullerKoch, SpaceFillingKoch
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]
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shaper_f, duller_f, space_filling_f = [
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CurveClass(order = self.max_order).shift(3*RIGHT)
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for CurveClass in SharperKoch, DullerKoch, SpaceFillingKoch
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]
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self.add(words[0])
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left_curve = SharperKoch(order = 1)
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right_curve = SharperKoch(order = 1)
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self.play(
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Transform(left_curve, sharper),
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ApplyMethod(right_curve.shift, 3*RIGHT),
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)
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self.play(
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Transform(
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right_curve,
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SharperKoch(order = 2).shift(3*RIGHT)
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),
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ShimmerIn(seed),
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ShimmerIn(fractal)
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)
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for order in range(3, self.max_order):
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self.play(Transform(
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right_curve,
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SharperKoch(order = order).shift(3*RIGHT)
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))
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self.remove(words[0])
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self.add(words[1])
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kwargs = {
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"run_time" : 4,
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}
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self.play(
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Transform(left_curve, duller, **kwargs),
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Transform(right_curve, duller_f, **kwargs)
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)
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self.dither()
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kwargs["run_time"] = 7
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kwargs["rate_func"] = None
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self.remove(words[1])
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self.add(words[2])
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self.play(
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Transform(left_curve, space_filling, **kwargs),
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Transform(right_curve, space_filling_f, **kwargs)
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)
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self.remove(words[2])
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self.add(words[3])
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self.dither()
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@ -18,7 +18,7 @@ from animation.playground import Vibrate
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from topics.geometry import \
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Line, Dot, Arrow, Grid, Square, Point
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from topics.characters import \
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ThoughtBubble, SpeechBubble, Mathematician
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ThoughtBubble, SpeechBubble, Mathematician, Randolph
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from topics.number_line import UnitInterval
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from topics.three_dimensions import Stars
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@ -151,6 +151,23 @@ class PostponePhilosophizing(Scene):
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self.dither()
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class GrowHilbertWithName(Scene):
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def construct(self):
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curve = HilbertCurve(order = 1)
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words = TextMobject("``Hilbert Curve''")
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words.to_edge(UP, buff = 0.2)
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self.play(
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ShimmerIn(words),
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Transform(curve, HilbertCurve(order = 2)),
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run_time = 2
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)
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for n in range(3, 8):
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self.play(
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Transform(curve, HilbertCurve(order = n)),
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run_time = 5. /n
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)
|
||||
|
||||
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class SectionOne(Scene):
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def construct(self):
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self.add(TextMobject("Section 1: Seeing with your ears"))
|
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@ -189,6 +206,16 @@ class ImageToSound(Scene):
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rate_func = rush_from
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))
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||||
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class LinksInDescription(Scene):
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||||
def construct(self):
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||||
text = TextMobject("""
|
||||
See links in the description for more on
|
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sight via sound.
|
||||
""")
|
||||
self.play(ShimmerIn(text))
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||||
self.play(ShowCreation(Arrow(text, 3*DOWN)))
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||||
self.dither(2)
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||||
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||||
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||||
class ImageDataIsTwoDimensional(Scene):
|
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def construct(self):
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||||
@ -923,6 +950,22 @@ class ImagineItWorks(Scene):
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self.add(TextMobject("Image your project succeeds..."))
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||||
self.dither()
|
||||
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||||
|
||||
class RandyWithHeadphones(Scene):
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||||
def construct(self):
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||||
headphones = ImageMobject("Headphones.png")
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headphones.scale(0.1)
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||||
headphones.stretch(2, 0)
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||||
headphones.shift(1.2*UP+0.05*LEFT)
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headphones.highlight(GREY)
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randy = Randolph()
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self.add(randy, headphones)
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||||
self.dither(2)
|
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self.play(ApplyMethod(randy.blink))
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||||
self.dither(4)
|
||||
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||||
|
||||
class IncreaseResolution(Scene):
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||||
def construct(self):
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||||
grids = [
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||||
@ -1027,7 +1070,7 @@ class TrackSpecificSnakeCurvePoint(TrackSpecificCurvePoint):
|
||||
class NeedToRelearn(Scene):
|
||||
def construct(self):
|
||||
top_words = TextMobject("Different pixel-frequency association")
|
||||
bottom_words = TextMobject("Need to relearn synesthesia")
|
||||
bottom_words = TextMobject("Need to relearn sight-via-sound")
|
||||
top_words.shift(UP)
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||||
bottom_words.shift(DOWN)
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||||
arrow = Arrow(top_words, bottom_words)
|
||||
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||||
@ -700,6 +700,11 @@ class FormalDefinitionOfContinuity(Scene):
|
||||
"Point where the function jumps"
|
||||
)
|
||||
point_description.shift(3*RIGHT)
|
||||
discontinuous_at_A = TextMobject(
|
||||
"``Discontinuous at A''",
|
||||
size = "\\Large"
|
||||
)
|
||||
discontinuous_at_A.shift(2*UP).to_edge(LEFT)
|
||||
text = TextMobject("""
|
||||
Circle around ouput \\\\
|
||||
points can never \\\\
|
||||
@ -724,6 +729,7 @@ class FormalDefinitionOfContinuity(Scene):
|
||||
Homotopy(self.input_homotopy, self.input_dot, **kwargs),
|
||||
Homotopy(self.output_homotopy, self.output_dot, **kwargs)
|
||||
)
|
||||
discontinuous_arrow = Arrow(discontinuous_at_A, self.input_dot)
|
||||
arrow = Arrow(
|
||||
point_description, self.output_dot,
|
||||
buff = 0.05,
|
||||
@ -754,7 +760,12 @@ class FormalDefinitionOfContinuity(Scene):
|
||||
self.remove(input_circle, input_points, output_circle, input_points_copy)
|
||||
self.play(vary_circles)
|
||||
self.dither()
|
||||
self.remove(vary_circles.mobject)
|
||||
self.play(
|
||||
ShimmerIn(discontinuous_at_A),
|
||||
ShowCreation(discontinuous_arrow)
|
||||
)
|
||||
self.dither(3)
|
||||
self.remove(vary_circles.mobject, discontinuous_at_A, discontinuous_arrow)
|
||||
|
||||
def continuous_point(self):
|
||||
pass
|
||||
|
||||
@ -164,7 +164,7 @@ class Randolph(PiCreature):
|
||||
|
||||
class Mortimer(PiCreature):
|
||||
DEFAULT_CONFIG = {
|
||||
"color" : DARK_BROWN
|
||||
"color" : MAROON_E
|
||||
}
|
||||
def __init__(self, **kwargs):
|
||||
PiCreature.__init__(self, **kwargs)
|
||||
|
||||
@ -228,9 +228,8 @@ class XYZAxes(Mobject1D):
|
||||
)
|
||||
self.y_axis = self.x_axis.copy().rotate(np.pi/2, OUT)
|
||||
self.z_axis = self.x_axis.copy().rotate(np.pi/2, DOWN)
|
||||
|
||||
self.digest_mobject_attrs()
|
||||
self.pose_at_angle()
|
||||
|
||||
|
||||
|
||||
class SpaceGrid(Mobject1D):
|
||||
|
||||
Reference in New Issue
Block a user