def construct(self):
coords_set = [ORIGIN]
for n in range(int(2*SPACE_WIDTH)):
for vect in UP, RIGHT:
for k in range(n):
new_coords = coords_set[-1]+((-1)**n)*vect
coords_set.append(new_coords)
square = Square(side_length = 1, color = WHITE)
squares = Mobject(*[
square.copy().shift(coords)
for coords in coords_set
]).ingest_submobjects()
self.play(
DelayByOrder(FadeIn(squares)),
run_time = 3
)
curve = HilbertCurve(order = 6).scale(1./6)
all_curves = Mobject(*[
curve.copy().shift(coords)
for coords in coords_set
]).ingest_submobjects()
all_curves.thin_out(10)
self.play(ShowCreation(
all_curves,
rate_func = None,
run_time = 15
))
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):
grid = Grid(64, 64)
space_region = Region()
space_mobject = MobjectFromRegion(space_region, DARK_GREY)
curve = PeanoCurve(order = 5).replace(space_mobject)
line = Line(5*LEFT, 5*RIGHT)
line.gradient_highlight(curve.start_color, curve.end_color)
for mob in grid, space_mobject:
mob.sort_points(np.linalg.norm)
infinitely = TextMobject("Infinitely")
detailed = TextMobject("detailed")
extending = TextMobject("extending")
detailed.next_to(infinitely, RIGHT)
extending.next_to(infinitely, RIGHT)
Mobject(extending, infinitely, detailed).center()
arrows = Mobject(*[
Arrow(2*p, 4*p)
for theta in np.arange(np.pi/6, 2*np.pi, np.pi/3)
for p in [rotate_vector(RIGHT, theta)]
])
self.add(grid)
self.wait()
self.play(Transform(grid, space_mobject, run_time = 5))
self.remove(grid)
self.highlight_region(space_region, DARK_GREY)
self.wait()
self.add(infinitely, detailed)
self.wait()
self.play(DelayByOrder(Transform(detailed, extending)))
self.play(ShowCreation(arrows))
self.wait()
self.clear()
self.highlight_region(space_region, DARK_GREY)
self.play(ShowCreation(line))
self.play(Transform(line, curve, run_time = 5))