def construct(self):
val = 0.3
text = TextMobject([
"PHC", "$_n", "(", "%3.1f"%val, ")$",
" has a ", "limit point ", "as $n \\to \\infty$"
])
func_parts = text.copy().split()[:5]
Mobject(*func_parts).center().to_edge(UP)
num_str, val_str = func_parts[1], func_parts[3]
curve = UnitInterval()
curve.sort_points(lambda p : p[0])
dot = Dot().shift(curve.number_to_point(val))
arrow = Arrow(val_str, dot, buff = 0.1)
curve.add_numbers(0, 1)
self.play(ShowCreation(curve))
self.play(
ShimmerIn(val_str),
ShowCreation(arrow),
ShowCreation(dot)
)
self.wait()
self.play(
FadeOut(arrow),
*[
FadeIn(func_parts[i])
for i in 0, 1, 2, 4
]
)
for num in range(2,9):
new_curve = HilbertCurve(order = num)
new_curve.scale(0.8)
new_dot = Dot(new_curve.points[int(val*new_curve.get_num_points())])
new_num_str = TexMobject(str(num)).replace(num_str)
self.play(
Transform(curve, new_curve),
Transform(dot, new_dot),
Transform(num_str, new_num_str)
)
self.wait()
text.to_edge(UP)
text_parts = text.split()
for index in 1, -1:
text_parts[index].set_color()
starters = Mobject(*func_parts + [
Point(mob.get_center(), stroke_width=1)
for mob in text_parts[5:]
])
self.play(Transform(starters, text))
arrow = Arrow(text_parts[-2].get_bottom(), dot, buff = 0.1)
self.play(ShowCreation(arrow))
self.wait()
def construct(self):
val = 0.3
text = TextMobject([
"PHC", "$_n", "(", "%3.1f"%val, ")$",
" has a ", "limit point ", "as $n \\to \\infty$"
])
func_parts = text.copy().split()[:5]
Mobject(*func_parts).center().to_edge(UP)
num_str, val_str = func_parts[1], func_parts[3]
curve = UnitInterval()
curve.sort_points(lambda p : p[0])
dot = Dot().shift(curve.number_to_point(val))
arrow = Arrow(val_str, dot, buff = 0.1)
curve.add_numbers(0, 1)
self.play(ShowCreation(curve))
self.play(
ShimmerIn(val_str),
ShowCreation(arrow),
ShowCreation(dot)
)
self.wait()
self.play(
FadeOut(arrow),
*[
FadeIn(func_parts[i])
for i in 0, 1, 2, 4
]
)
for num in range(2,9):
new_curve = HilbertCurve(order = num)
new_curve.scale(0.8)
new_dot = Dot(new_curve.points[int(val*new_curve.get_num_points())])
new_num_str = TexMobject(str(num)).replace(num_str)
self.play(
Transform(curve, new_curve),
Transform(dot, new_dot),
Transform(num_str, new_num_str)
)
self.wait()
text.to_edge(UP)
text_parts = text.split()
for index in 1, -1:
text_parts[index].highlight()
starters = Mobject(*func_parts + [
Point(mob.get_center(), stroke_width=1)
for mob in text_parts[5:]
])
self.play(Transform(starters, text))
arrow = Arrow(text_parts[-2].get_bottom(), dot, buff = 0.1)
self.play(ShowCreation(arrow))
self.wait()
def construct(self):
val = 0.7
text = TexMobject([
"\\text{HC}(", "x", ")",
"=\\lim_{n \\to \\infty}\\text{PHC}_n(", "x", ")"
])
text.to_edge(UP)
x1 = text.split()[1]
x2 = text.split()[-2]
x2.set_color(BLUE)
explanation = TextMobject("Actual Hilbert curve function")
exp_arrow = Arrow(explanation, text.split()[0])
curve = UnitInterval()
dot = Dot(curve.number_to_point(val))
x_arrow = Arrow(x1.get_bottom(), dot, buff = 0)
curve.sort_points(lambda p : p[0])
curve.add_numbers(0, 1)
self.add(*text.split()[:3])
self.play(
ShimmerIn(explanation),
ShowCreation(exp_arrow)
)
self.wait()
self.remove(explanation, exp_arrow)
self.play(ShowCreation(curve))
self.play(
ApplyMethod(x1.set_color, BLUE),
ShowCreation(x_arrow),
ShowCreation(dot)
)
self.wait()
self.remove(x_arrow)
limit = Mobject(*text.split()[3:]).ingest_submobjects()
limit.stroke_width = 1
self.play(ShimmerIn(limit))
for num in range(1, 9):
new_curve = HilbertCurve(order = num)
new_curve.scale(0.8)
new_dot = Dot(new_curve.points[int(val*new_curve.get_num_points())])
self.play(
Transform(curve, new_curve),
Transform(dot, new_dot),
)
def construct(self):
val = 0.7
text = TexMobject([
"\\text{HC}(", "x", ")",
"=\\lim_{n \\to \\infty}\\text{PHC}_n(", "x", ")"
])
text.to_edge(UP)
x1 = text.split()[1]
x2 = text.split()[-2]
x2.highlight(BLUE)
explanation = TextMobject("Actual Hilbert curve function")
exp_arrow = Arrow(explanation, text.split()[0])
curve = UnitInterval()
dot = Dot(curve.number_to_point(val))
x_arrow = Arrow(x1.get_bottom(), dot, buff = 0)
curve.sort_points(lambda p : p[0])
curve.add_numbers(0, 1)
self.add(*text.split()[:3])
self.play(
ShimmerIn(explanation),
ShowCreation(exp_arrow)
)
self.wait()
self.remove(explanation, exp_arrow)
self.play(ShowCreation(curve))
self.play(
ApplyMethod(x1.highlight, BLUE),
ShowCreation(x_arrow),
ShowCreation(dot)
)
self.wait()
self.remove(x_arrow)
limit = Mobject(*text.split()[3:]).ingest_submobjects()
limit.stroke_width = 1
self.play(ShimmerIn(limit))
for num in range(1, 9):
new_curve = HilbertCurve(order = num)
new_curve.scale(0.8)
new_dot = Dot(new_curve.points[int(val*new_curve.get_num_points())])
self.play(
Transform(curve, new_curve),
Transform(dot, new_dot),
)
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].set_color(BLUE)
parts[3].set_color(BLUE)
parts[1].set_color()
parts[-2].set_color()
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_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),
)
