mirror of
https://github.com/3b1b/manim.git
synced 2025-08-03 04:04:36 +08:00
339 lines
9.2 KiB
Python
339 lines
9.2 KiB
Python
from big_ol_pile_of_manim_imports import *
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from old_projects.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.wait(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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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.wait(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 = list(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.wait(6)
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class StraightKoch(KochCurve):
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CONFIG = {
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"axiom" : "A"
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}
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class SharperKoch(StraightKoch):
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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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CONFIG = {
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"angle" : np.pi/6,
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}
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class SpaceFillingKoch(StraightKoch):
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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 = list(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.wait(4)
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self.remove(words[1])
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self.add(words[2])
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self.wait(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.wait(2)
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elif order == 3:
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self.wait()
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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.wait(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 = list(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.wait()
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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.wait()
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