def show_diameter(self):
exceptions = [
self.circle, self.tangent_line, self.pc_line,
self.right_angle_symbol
]
everything = set(self.mobjects).difference(exceptions)
everything_copy = Mobject(*everything).copy()
light_everything = everything_copy.copy()
dark_everything = everything_copy.copy()
dark_everything.fade(0.8)
bottom_point = np.array(self.c_point)
bottom_point += 2 * self.radius * DOWN
diameter = Line(bottom_point, self.c_point)
brace = Brace(diameter, RIGHT)
diameter_word = TextMobject("Diameter")
d_mob = TexMobject("D")
diameter_word.next_to(brace)
d_mob.next_to(diameter)
self.remove(*everything)
self.play(Transform(everything_copy, dark_everything))
self.dither()
self.play(ShowCreation(diameter))
self.play(GrowFromCenter(brace))
self.play(ShimmerIn(diameter_word))
self.dither()
self.play(*[Transform(mob, d_mob) for mob in brace, diameter_word])
self.remove(brace, diameter_word)
self.add(d_mob)
self.play(Transform(everything_copy, light_everything))
self.remove(everything_copy)
self.add(*everything)
self.d_mob = d_mob
self.bottom_point = bottom_point
def show_diameter(self):
exceptions = [
self.circle,
self.tangent_line,
self.pc_line,
self.right_angle_symbol
]
everything = set(self.mobjects).difference(exceptions)
everything_copy = Mobject(*everything).copy()
light_everything = everything_copy.copy()
dark_everything = everything_copy.copy()
dark_everything.fade(0.8)
bottom_point = np.array(self.c_point)
bottom_point += 2*self.radius*DOWN
diameter = Line(bottom_point, self.c_point)
brace = Brace(diameter, RIGHT)
diameter_word = TextMobject("Diameter")
d_mob = TexMobject("D")
diameter_word.next_to(brace)
d_mob.next_to(diameter)
self.remove(*everything)
self.play(Transform(everything_copy, dark_everything))
self.dither()
self.play(ShowCreation(diameter))
self.play(GrowFromCenter(brace))
self.play(ShimmerIn(diameter_word))
self.dither()
self.play(*[
Transform(mob, d_mob)
for mob in brace, diameter_word
])
self.remove(brace, diameter_word)
self.add(d_mob)
self.play(Transform(everything_copy, light_everything))
self.remove(everything_copy)
self.add(*everything)
self.d_mob = d_mob
self.bottom_point = bottom_point
def construct(self):
text = TextMobject([
"PHC", "_n", "(", "x", ")$",
" has a limit point ", "as $n \\to \\infty$",
"\\\\ for all $x$"
])
parts = text.split()
parts[-1].next_to(Mobject(*parts[:-1]), DOWN)
parts[-1].highlight(BLUE)
parts[3].highlight(BLUE)
parts[1].highlight()
parts[-2].highlight()
text.to_edge(UP)
curve = UnitInterval()
curve.sort_points(lambda p : p[0])
vals = np.arange(0.1, 1, 0.1)
dots = Mobject(*[
Dot(curve.number_to_point(val))
for val in vals
])
curve.add_numbers(0, 1)
starter_dots = dots.copy().ingest_submobjects()
starter_dots.shift(2*UP)
self.add(curve, text)
self.wait()
self.play(DelayByOrder(ApplyMethod(starter_dots.shift, 2*DOWN)))
self.wait()
self.remove(starter_dots)
self.add(dots)
for num in range(1, 10):
new_curve = HilbertCurve(order = num)
new_curve.scale(0.8)
new_dots = Mobject(*[
Dot(new_curve.points[int(val*new_curve.get_num_points())])
for val in vals
])
self.play(
Transform(curve, new_curve),
Transform(dots, new_dots),
)
def construct(self):
text = TextMobject([
"PHC", "_n", "(", "x", ")$",
" has a limit point ", "as $n \\to \\infty$",
"\\\\ for all $x$"
])
parts = text.split()
parts[-1].next_to(Mobject(*parts[:-1]), DOWN)
parts[-1].highlight(BLUE)
parts[3].highlight(BLUE)
parts[1].highlight()
parts[-2].highlight()
text.to_edge(UP)
curve = UnitInterval()
curve.sort_points(lambda p : p[0])
vals = np.arange(0.1, 1, 0.1)
dots = Mobject(*[
Dot(curve.number_to_point(val))
for val in vals
])
curve.add_numbers(0, 1)
starter_dots = dots.copy().ingest_sub_mobjects()
starter_dots.shift(2*UP)
self.add(curve, text)
self.dither()
self.play(DelayByOrder(ApplyMethod(starter_dots.shift, 2*DOWN)))
self.dither()
self.remove(starter_dots)
self.add(dots)
for num in range(1, 10):
new_curve = HilbertCurve(order = num)
new_curve.scale(0.8)
new_dots = Mobject(*[
Dot(new_curve.points[int(val*new_curve.get_num_points())])
for val in vals
])
self.play(
Transform(curve, new_curve),
Transform(dots, new_dots),
)
def construct(self):
n_terms = 4
def func((x, y, ignore)):
z = complex(x, y)
if (np.abs(x%1 - 0.5)<0.01 and y < 0.01) or np.abs(z)<0.01:
return ORIGIN
out_z = 1./(2*np.tan(np.pi*z)*(z**2))
return out_z.real*RIGHT - out_z.imag*UP
arrows = Mobject(*[
Arrow(ORIGIN, np.sqrt(2)*point)
for point in compass_directions(4, RIGHT+UP)
])
arrows.highlight(YELLOW)
arrows.ingest_submobjects()
all_arrows = Mobject(*[
arrows.copy().scale(0.3/(x)).shift(x*RIGHT)
for x in range(1, n_terms+2)
])
terms = TexMobject([
"\\dfrac{1}{%d^2} + "%(x+1)
for x in range(n_terms)
]+["\\cdots"])
terms.shift(2*UP)
plane = NumberPlane(color = BLUE_E)
axes = Mobject(NumberLine(), NumberLine().rotate(np.pi/2))
axes.highlight(WHITE)
for term in terms.split():
self.play(ShimmerIn(term, run_time = 0.5))
self.dither()
self.play(ShowCreation(plane), ShowCreation(axes))
self.play(*[
Transform(*pair)
for pair in zip(terms.split(), all_arrows.split())
])
self.play(PhaseFlow(
func, plane,
run_time = 5,
virtual_time = 8
))
