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84 lines
2.4 KiB
Python
84 lines
2.4 KiB
Python
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import numpy as np
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import itertools as it
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from helpers import *
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from mobject.tex_mobject import TexMobject, TextMobject, Brace
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from mobject import Mobject
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from mobject.image_mobject import ImageMobject
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from topics.three_dimensions import Stars
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from animation import Animation
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from animation.transform import \
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Transform, CounterclockwiseTransform, ApplyPointwiseFunction,\
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FadeIn, FadeOut, GrowFromCenter, ApplyFunction, ApplyMethod, \
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ShimmerIn
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from animation.simple_animations import \
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ShowCreation, Homotopy, PhaseFlow, ApplyToCenters, DelayByOrder, \
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ShowPassingFlash
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from animation.playground import TurnInsideOut, Vibrate
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from topics.geometry import \
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Line, Circle, Square, Grid, Rectangle, Arrow, Dot, Point, \
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Arc, FilledRectangle
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from topics.characters import Randolph, Mathematician
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from topics.functions import ParametricFunction, FunctionGraph
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from topics.number_line import NumberLine, NumberPlane
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from mobject.region import Region, region_from_polygon_vertices
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from scene import Scene
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class PhysicalIntuition(Scene):
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def construct(self):
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n_terms = 4
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def func((x, y, ignore)):
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z = complex(x, y)
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if (np.abs(x%1 - 0.5)<0.01 and y < 0.01) or np.abs(z)<0.01:
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return ORIGIN
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out_z = 1./(2*np.tan(np.pi*z)*(z**2))
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return out_z.real*RIGHT - out_z.imag*UP
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arrows = Mobject(*[
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Arrow(ORIGIN, np.sqrt(2)*point)
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for point in compass_directions(4, RIGHT+UP)
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])
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arrows.highlight(YELLOW)
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arrows.ingest_sub_mobjects()
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all_arrows = Mobject(*[
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arrows.copy().scale(0.3/(x)).shift(x*RIGHT)
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for x in range(1, n_terms+2)
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])
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terms = TexMobject([
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"\\dfrac{1}{%d^2} + "%(x+1)
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for x in range(n_terms)
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]+["\\cdots"])
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terms.shift(2*UP)
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plane = NumberPlane(color = BLUE_E)
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axes = Mobject(NumberLine(), NumberLine().rotate(np.pi/2))
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axes.highlight(WHITE)
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for term in terms.split():
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self.play(ShimmerIn(term, run_time = 0.5))
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self.dither()
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self.play(ShowCreation(plane), ShowCreation(axes))
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self.play(*[
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Transform(*pair)
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for pair in zip(terms.split(), all_arrows.split())
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])
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self.play(PhaseFlow(
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func, plane,
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run_time = 5,
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virtual_time = 8
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))
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