def setup(self):
self.input_color = YELLOW_C
self.output_color = RED
def spiril(t):
theta = 2*np.pi*t
return t*np.cos(theta)*RIGHT+t*np.sin(theta)*UP
self.spiril1 = ParametricFunction(
lambda t : 1.5*RIGHT + DOWN + 2*spiril(t),
density = 5*DEFAULT_POINT_DENSITY_1D,
)
self.spiril2 = ParametricFunction(
lambda t : 5.5*RIGHT + UP - 2*spiril(1-t),
density = 5*DEFAULT_POINT_DENSITY_1D,
)
Mobject.align_data(self.spiril1, self.spiril2)
self.output = Mobject(self.spiril1, self.spiril2)
self.output.ingest_submobjects()
self.output.highlight(GREEN_A)
self.interval = UnitInterval()
self.interval.scale_to_fit_width(SPACE_WIDTH-1)
self.interval.to_edge(LEFT)
self.input_dot = Dot(color = self.input_color)
self.output_dot = self.input_dot.copy().highlight(self.output_color)
left, right = self.interval.get_left(), self.interval.get_right()
self.input_homotopy = lambda (x, y, z, t) : (x, y, t) + interpolate(left, right, t)
output_size = self.output.get_num_points()-1
output_points = self.output.points
self.output_homotopy = lambda (x, y, z, t) : (x, y, z) + output_points[int(t*output_size)]
def construct(self):
words = TextMobject([
"One does not simply define the limit \\\\ \
of a sequence of", "curves", "\\dots"
])
top_words = TextMobject(["curves", "are functions"]).to_edge(UP)
curves1 = words.split()[1]
curves2 = top_words.split()[0]
words.ingest_submobjects()
number = TexMobject("0.27")
pair = TexMobject("(0.53, 0.02)")
pair.next_to(number, buff=2)
arrow = Arrow(number, pair)
Mobject(number, arrow, pair).center().shift(UP)
number_line = UnitInterval()
number_line.stretch_to_fit_width(5)
number_line.to_edge(LEFT).shift(DOWN)
grid = Grid(4, 4).scale(0.4)
grid.next_to(number_line, buff=2)
low_arrow = Arrow(number_line, grid)
self.play(ShimmerIn(words))
self.dither()
self.play(FadeOut(words), ApplyMethod(curves1.replace, curves2),
ShimmerIn(top_words.split()[1]))
self.dither()
self.play(FadeIn(number))
self.play(ShowCreation(arrow))
self.play(FadeIn(pair))
self.dither()
self.play(ShowCreation(number_line))
self.play(ShowCreation(low_arrow))
self.play(ShowCreation(grid))
self.dither()
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.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].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 get_freq_line():
return UnitInterval().shift(2*DOWN) ##Change?
