def get_subdivision_braces_and_labels(
self, parts, labels, direction,
buff=SMALL_BUFF,
min_num_quads=1
):
label_mobs = VGroup()
braces = VGroup()
for label, part in zip(labels, parts):
brace = Brace(
part, direction,
min_num_quads=min_num_quads,
buff=buff
)
if isinstance(label, Mobject):
label_mob = label
else:
label_mob = TexMobject(label)
label_mob.scale(self.default_label_scale_val)
label_mob.next_to(brace, direction, buff)
braces.add(brace)
label_mobs.add(label_mob)
parts.braces = braces
parts.labels = label_mobs
parts.label_kwargs = {
"labels": label_mobs.copy(),
"direction": direction,
"buff": buff,
}
return VGroup(parts.braces, parts.labels)
def get_number_design(self, value, symbol):
num = int(value)
n_rows = {
2 : 2,
3 : 3,
4 : 2,
5 : 2,
6 : 3,
7 : 3,
8 : 3,
9 : 4,
10 : 4,
}[num]
n_cols = 1 if num in [2, 3] else 2
insertion_indices = {
5 : [0],
7 : [0],
8 : [0, 1],
9 : [1],
10 : [0, 2],
}.get(num, [])
top = self.get_top() + symbol.get_height()*DOWN
bottom = self.get_bottom() + symbol.get_height()*UP
column_points = [
interpolate(top, bottom, alpha)
for alpha in np.linspace(0, 1, n_rows)
]
design = VGroup(*[
symbol.copy().move_to(point)
for point in column_points
])
if n_cols == 2:
space = 0.2*self.get_width()
column_copy = design.copy().shift(space*RIGHT)
design.shift(space*LEFT)
design.add(*column_copy)
design.add(*[
symbol.copy().move_to(
center_of_mass(column_points[i:i+2])
)
for i in insertion_indices
])
for symbol in design:
if symbol.get_center()[1] < self.get_center()[1]:
symbol.rotate_in_place(np.pi)
return design
def get_number_design(self, value, symbol):
num = int(value)
n_rows = {
2: 2,
3: 3,
4: 2,
5: 2,
6: 3,
7: 3,
8: 3,
9: 4,
10: 4,
}[num]
n_cols = 1 if num in [2, 3] else 2
insertion_indices = {
5: [0],
7: [0],
8: [0, 1],
9: [1],
10: [0, 2],
}.get(num, [])
top = self.get_top() + symbol.get_height() * DOWN
bottom = self.get_bottom() + symbol.get_height() * UP
column_points = [
interpolate(top, bottom, alpha)
for alpha in np.linspace(0, 1, n_rows)
]
design = VGroup(*[
symbol.copy().move_to(point)
for point in column_points
])
if n_cols == 2:
space = 0.2 * self.get_width()
column_copy = design.copy().shift(space * RIGHT)
design.shift(space * LEFT)
design.add(*column_copy)
design.add(*[
symbol.copy().move_to(
center_of_mass(column_points[i:i + 2])
)
for i in insertion_indices
])
for symbol in design:
if symbol.get_center()[1] < self.get_center()[1]:
symbol.rotate_in_place(np.pi)
return design
def get_corner_numbers(self, value, symbol):
value_mob = TextMobject(value)
width = self.get_width() / self.card_width_to_corner_num_width
height = self.get_height() / self.card_height_to_corner_num_height
value_mob.scale_to_fit_width(width)
value_mob.stretch_to_fit_height(height)
value_mob.next_to(self.get_corner(UP + LEFT),
DOWN + RIGHT,
buff=MED_LARGE_BUFF * width)
value_mob.set_color(symbol.get_color())
corner_symbol = symbol.copy()
corner_symbol.scale_to_fit_width(width)
corner_symbol.next_to(value_mob, DOWN, buff=MED_SMALL_BUFF * width)
corner_group = VGroup(value_mob, corner_symbol)
opposite_corner_group = corner_group.copy()
opposite_corner_group.rotate(np.pi, about_point=self.get_center())
return VGroup(corner_group, opposite_corner_group)
def get_corner_numbers(self, value, symbol):
value_mob = TextMobject(value)
width = self.get_width() / self.card_width_to_corner_num_width
height = self.get_height() / self.card_height_to_corner_num_height
value_mob.scale_to_fit_width(width)
value_mob.stretch_to_fit_height(height)
value_mob.next_to(
self.get_corner(UP + LEFT), DOWN + RIGHT,
buff=MED_LARGE_BUFF * width
)
value_mob.set_color(symbol.get_color())
corner_symbol = symbol.copy()
corner_symbol.scale_to_fit_width(width)
corner_symbol.next_to(
value_mob, DOWN,
buff=MED_SMALL_BUFF * width
)
corner_group = VGroup(value_mob, corner_symbol)
opposite_corner_group = corner_group.copy()
opposite_corner_group.rotate(
np.pi, about_point=self.get_center()
)
return VGroup(corner_group, opposite_corner_group)
def construct(self):
# Chart on the left
colors = [WHITE, ORANGE, GREEN]
titles = VGroup(*[
TexMobject(text).set_color(color)
for text, color in zip(["n", "p_n", "q_n"], colors)
])
contents = VGroup(*[
VGroup(*[
TexMobject("%d" % num) for num in
[k, central_binomial_coeff(k),
central_binomial_coeff(k)]
]) for k in range(8)
])
titles.arrange_submobjects(RIGHT, buff=1)
for num, line in enumerate(contents):
for k, element in enumerate(line):
buff = 0.6 + 0.8 * num
element.next_to(titles[k], DOWN, aligned_edge=LEFT, buff=buff)
element.set_color(colors[k])
sep_line = Line(ORIGIN, 4.5 * RIGHT, stroke_width=5)
sep_line.next_to(titles, DOWN)
chart = VGroup(titles, contents, sep_line)
chart.set_height(7)
chart.center().to_edge(LEFT)
self.add(chart)
# Figures on the right
std_zero_pos_axis = NumberLine(x_min=-2,
x_max=2,
color=GREY,
unit_size=0.25,
tick_size=0.05)
std_zero_pos_axis.rotate(np.pi / 2)
std_nocross_pos_axis = NumberLine(x_min=-4,
x_max=4,
color=GREY,
unit_size=0.25,
tick_size=0.05)
std_nocross_pos_axis.rotate(np.pi / 2)
std_time_axis = NumberLine(x_min=0,
x_max=5.5,
color=GREY,
unit_size=0.25,
tick_size=0.05)
std_zero_axes = VGroup(std_zero_pos_axis, std_time_axis)
std_nocross_axes = VGroup(std_nocross_pos_axis, std_time_axis)
zero_walks = VGroup()
for sequence in ["UUDD", "UDUD", "UDDU", "DDUU", "DUDU", "DUUD"]:
axes = std_zero_axes.copy()
zero_walk = RandomWalk1DArrow(sequence, step_size=0.25)
zero_walk.move_start_to(axes[0].number_to_point(0))
zero_walks.add(VGroup(axes, zero_walk))
zero_walks.arrange_submobjects_in_grid(2, 3, buff=0.5)
zero_rect = SurroundingRectangle(zero_walks, color=ORANGE, buff=0.4)
zero_walks.add(zero_rect)
nocross_walks = VGroup()
for sequence in ["DDDD", "DDUD", "DDDU", "UUUU", "UUDU", "UUUD"]:
axes = std_nocross_axes.copy()
nocross_walk = RandomWalk1DArrow(sequence, step_size=0.25)
nocross_walk.move_start_to(axes[0].number_to_point(0))
nocross_walks.add(VGroup(axes, nocross_walk))
nocross_walks.arrange_submobjects_in_grid(2, 3, buff=0.5)
nocross_rect = SurroundingRectangle(nocross_walks,
color=GREEN,
buff=0.4)
nocross_walks.add(nocross_rect)
relation = TexMobject("p_2", "=", "q_2", "=", "6")
relation[0].set_color(ORANGE)
relation[2].set_color(GREEN)
relation.scale(1.5)
figure = VGroup(zero_walks, relation, nocross_walks)
figure.arrange_submobjects(DOWN)
figure.set_height(7)
figure.center().to_edge(RIGHT)
self.add(figure)
self.wait()
