def construct(self, order):
if order == 2:
result_tex = "(0.125, 0.75)"
elif order == 3:
result_tex = "(0.0758, 0.6875)"
phc, arg, result = Tex([
"\\text{PHC}_%d"%order,
"(0.3)",
"= %s"%result_tex
]).to_edge(UP).split()
function = TexText("Function", size = "\\normal")
function.shift(phc.get_center()+DOWN+2*LEFT)
function_arrow = Arrow(function, phc)
line = Line(5*LEFT, 5*RIGHT)
curve = HilbertCurve(order = order)
line.match_colors(curve)
grid = Grid(2**order, 2**order)
grid.fade()
for mob in curve, grid:
mob.scale(0.7)
index = int(0.3*line.get_num_points())
dot1 = Dot(line.get_points()[index])
arrow1 = Arrow(arg, dot1, buff = 0.1)
dot2 = Dot(curve.get_points()[index])
arrow2 = Arrow(result.get_bottom(), dot2, buff = 0.1)
self.add(phc)
self.play(
ShimmerIn(function),
ShowCreation(function_arrow)
)
self.wait()
self.remove(function_arrow, function)
self.play(ShowCreation(line))
self.wait()
self.play(
ShimmerIn(arg),
ShowCreation(arrow1),
ShowCreation(dot1)
)
self.wait()
self.remove(arrow1)
self.play(
FadeIn(grid),
Transform(line, curve),
Transform(dot1, dot2),
run_time = 2
)
self.wait()
self.play(
ShimmerIn(result),
ShowCreation(arrow2)
)
self.wait()
def construct(self):
val = 0.3
text = TexText([
"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.get_points()[int(val*new_curve.get_num_points())])
new_num_str = Tex(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):
start_words = TexText([
"``", "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 = TexText("""
``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.get_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 = Tex([
"\\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 = TexText("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.get_points()[int(val*new_curve.get_num_points())])
self.play(
Transform(curve, new_curve),
Transform(dot, new_dot),
)
def construct(self):
text = TexText([
"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.get_points()[int(val*new_curve.get_num_points())])
for val in vals
])
self.play(
Transform(curve, new_curve),
Transform(dots, new_dots),
)