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, order):
start_color, end_color = RED, GREEN
curve = HilbertCurve(order = order)
line = Line(5*LEFT, 5*RIGHT)
for mob in curve, line:
mob.gradient_highlight(start_color, end_color)
freq_line = get_freq_line()
freq_line.replace(line, stretch = True)
unit = 6./(2**order) #sidelength of pixel
up = unit*UP
right = unit*RIGHT
lower_left = 3*(LEFT+DOWN)
squares = Mobject(*[
Square(
side_length = unit,
color = WHITE
).shift(x*right+y*up)
for x, y in it.product(range(2**order), range(2**order))
])
squares.center()
targets = Mobject()
for square in squares.submobjects:
center = square.get_center()
distances = np.apply_along_axis(
lambda p : np.linalg.norm(p-center),
1,
curve.points
)
index_along_curve = np.argmin(distances)
fraction_along_curve = index_along_curve/float(curve.get_num_points())
target = square.copy().center().scale(0.8/(2**order))
line_index = int(fraction_along_curve*line.get_num_points())
target.shift(line.points[line_index])
targets.add(target)
self.add(squares)
self.play(ShowCreation(
curve,
run_time = 5,
rate_func = None
))
self.dither()
self.play(
Transform(curve, line),
Transform(squares, targets),
run_time = 3
)
self.dither()
self.play(ShowCreation(freq_line))
self.dither()
def construct(self):
start_words = TextMobject([
"``", "Space Filling", "Curve ''",
]).to_edge(TOP, buff = 0.25)
quote, space_filling, curve_quote = start_words.copy().split()
curve_quote.shift(
space_filling.get_left()-\
curve_quote.get_left()
)
space_filling = Point(space_filling.get_center())
end_words = Mobject(*[
quote, space_filling, curve_quote
]).center().to_edge(TOP, buff = 0.25)
space_filling_fractal = TextMobject("""
``Space Filling Fractal''
""").to_edge(UP)
curve = HilbertCurve(order = 2).shift(DOWN)
fine_curve = HilbertCurve(order = 8)
fine_curve.replace(curve)
dots = Mobject(*[
Dot(
curve.points[n*curve.get_num_points()/15],
color = YELLOW_C
)
for n in range(1, 15)
if n not in [4, 11]
])
start_words.shift(2*(UP+LEFT))
self.play(
ApplyMethod(start_words.shift, 2*(DOWN+RIGHT))
)
self.wait()
self.play(Transform(start_words, end_words))
self.wait()
self.play(ShowCreation(curve))
self.wait()
self.play(ShowCreation(
dots,
run_time = 3,
))
self.wait()
self.clear()
self.play(ShowCreation(fine_curve, run_time = 5))
self.wait()
self.play(ShimmerIn(space_filling_fractal))
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):
curve = HilbertCurve(order = 1)
grid = Grid(2, 2, stroke_width=1)
self.add(grid, curve)
for order in range(2, 6):
self.wait()
new_grid = Grid(2**order, 2**order, stroke_width=1)
self.play(
ShowCreation(new_grid),
Animation(curve)
)
self.remove(grid)
grid = new_grid
self.play(Transform(
curve, HilbertCurve(order = order)
))
square = Square(side_length = 6, color = WHITE)
square.corner = Mobject1D()
square.corner.add_line(3*DOWN, ORIGIN)
square.corner.add_line(ORIGIN, 3*RIGHT)
square.digest_mobject_attrs()
square.scale(2**(-5))
square.corner.set_color(
Color(rgb = curve.rgbas[curve.get_num_points()/3])
)
square.shift(
grid.get_corner(UP+LEFT)-\
square.get_corner(UP+LEFT)
)
self.wait()
self.play(
FadeOut(grid),
FadeOut(curve),
FadeIn(square)
)
self.play(
ApplyMethod(square.replace, grid)
)
self.wait()
def construct(self):
start_words = TextMobject([
"``",
"Space Filling",
"Curve ''",
]).to_edge(TOP, buff=0.25)
quote, space_filling, curve_quote = start_words.copy().split()
curve_quote.shift(
space_filling.get_left()-\
curve_quote.get_left()
)
space_filling = Point(space_filling.get_center())
end_words = Mobject(
*[quote, space_filling, curve_quote]).center().to_edge(TOP,
buff=0.25)
space_filling_fractal = TextMobject("""
``Space Filling Fractal''
""").to_edge(UP)
curve = HilbertCurve(order=2).shift(DOWN)
fine_curve = HilbertCurve(order=8)
fine_curve.replace(curve)
dots = Mobject(*[
Dot(curve.points[n * curve.get_num_points() / 15], color=YELLOW_C)
for n in range(1, 15) if n not in [4, 11]
])
start_words.shift(2 * (UP + LEFT))
self.play(ApplyMethod(start_words.shift, 2 * (DOWN + RIGHT)))
self.wait()
self.play(Transform(start_words, end_words))
self.wait()
self.play(ShowCreation(curve))
self.wait()
self.play(ShowCreation(
dots,
run_time=3,
))
self.wait()
self.clear()
self.play(ShowCreation(fine_curve, run_time=5))
self.wait()
self.play(ShimmerIn(space_filling_fractal))
self.wait()
def construct(self):
curve = HilbertCurve(order = 1)
grid = Grid(2, 2, stroke_width=1)
self.add(grid, curve)
for order in range(2, 6):
self.wait()
new_grid = Grid(2**order, 2**order, stroke_width=1)
self.play(
ShowCreation(new_grid),
Animation(curve)
)
self.remove(grid)
grid = new_grid
self.play(Transform(
curve, HilbertCurve(order = order)
))
square = Square(side_length = 6, color = WHITE)
square.corner = Mobject1D()
square.corner.add_line(3*DOWN, ORIGIN)
square.corner.add_line(ORIGIN, 3*RIGHT)
square.digest_mobject_attrs()
square.scale(2**(-5))
square.corner.highlight(
Color(rgb = curve.rgbas[curve.get_num_points()/3])
)
square.shift(
grid.get_corner(UP+LEFT)-\
square.get_corner(UP+LEFT)
)
self.wait()
self.play(
FadeOut(grid),
FadeOut(curve),
FadeIn(square)
)
self.play(
ApplyMethod(square.replace, grid)
)
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].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):
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),
)
def construct(self, order):
start_color, end_color = RED, GREEN
curve = HilbertCurve(order=order)
line = Line(5 * LEFT, 5 * RIGHT)
for mob in curve, line:
mob.set_color_by_gradient(start_color, end_color)
freq_line = get_freq_line()
freq_line.replace(line, stretch=True)
unit = 6. / (2**order) #sidelength of pixel
up = unit * UP
right = unit * RIGHT
lower_left = 3 * (LEFT + DOWN)
squares = Mobject(*[
Square(side_length=unit, color=WHITE).shift(x * right + y * up)
for x, y in it.product(range(2**order), range(2**order))
])
squares.center()
targets = Mobject()
for square in squares.submobjects:
center = square.get_center()
distances = np.apply_along_axis(
lambda p: np.linalg.norm(p - center), 1, curve.points)
index_along_curve = np.argmin(distances)
fraction_along_curve = index_along_curve / float(
curve.get_num_points())
target = square.copy().center().scale(0.8 / (2**order))
line_index = int(fraction_along_curve * line.get_num_points())
target.shift(line.points[line_index])
targets.add(target)
self.add(squares)
self.play(ShowCreation(curve, run_time=5, rate_func=None))
self.wait()
self.play(Transform(curve, line),
Transform(squares, targets),
run_time=3)
self.wait()
self.play(ShowCreation(freq_line))
self.wait()
