def vector_to_coords(self, vector, integer_labels=True, clean_up=True):
starting_mobjects = list(self.mobjects)
show_creation = False
if isinstance(vector, Arrow):
arrow = vector
vector = arrow.get_end()[:2]
else:
arrow = Vector(vector)
show_creation = True
array = vector_coordinate_label(arrow, integer_labels=integer_labels)
x_line = Line(ORIGIN, vector[0] * RIGHT)
y_line = Line(x_line.get_end(), arrow.get_end())
x_line.set_color(X_COLOR)
y_line.set_color(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten()
x_coord_start = self.position_x_coordinate(
x_coord.copy(), x_line, vector
)
y_coord_start = self.position_y_coordinate(
y_coord.copy(), y_line, vector
)
brackets = array.get_brackets()
if show_creation:
self.play(ShowCreation(arrow))
self.play(
ShowCreation(x_line),
Write(x_coord_start),
run_time=1
)
self.play(
ShowCreation(y_line),
Write(y_coord_start),
run_time=1
)
self.wait()
self.play(
Transform(x_coord_start, x_coord, submobject_mode="all_at_once"),
Transform(y_coord_start, y_coord, submobject_mode="all_at_once"),
Write(brackets, run_time=1),
)
self.wait()
self.remove(x_coord_start, y_coord_start, brackets)
self.add(array)
if clean_up:
self.clear()
self.add(*starting_mobjects)
return array, x_line, y_line
def tex(self, latex):
eq = TextMobject(latex)
anims = []
anims.append(Write(eq))
for mobject in self.mobjects:
anims.append(ApplyMethod(mobject.shift, 2 * UP))
self.play(*anims)
def coords_to_vector(self,
vector,
coords_start=2 * RIGHT + 2 * UP,
clean_up=True):
starting_mobjects = list(self.mobjects)
array = Matrix(vector)
array.shift(coords_start)
arrow = Vector(vector)
x_line = Line(ORIGIN, vector[0] * RIGHT)
y_line = Line(x_line.get_end(), arrow.get_end())
x_line.set_color(X_COLOR)
y_line.set_color(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten()
self.play(Write(array, run_time=1))
self.wait()
self.play(
ApplyFunction(
lambda x: self.position_x_coordinate(x, x_line, vector),
x_coord))
self.play(ShowCreation(x_line))
self.play(
ApplyFunction(
lambda y: self.position_y_coordinate(y, y_line, vector),
y_coord), FadeOut(array.get_brackets()))
y_coord, brackets = self.get_mobjects_from_last_animation()
self.play(ShowCreation(y_line))
self.play(ShowCreation(arrow))
self.wait()
if clean_up:
self.clear()
self.add(*starting_mobjects)
def construct(self):
# Generate transformation animations of the twin dragon curve
anims = list()
fractal = VMobject()
fractal.shift(UP)
for order in range(-1, self.max_order + 1):
new_fractal = TwinDragon(order=order)
new_fractal.shift(UP)
run_time = 0.5 if order >= 0 else 0
anims.append(
Transform(
fractal,
new_fractal,
submobject_mode="all_at_once",
run_time=run_time,
))
fractal = new_fractal
# Add the channel name
text = TextMobject("Solara570")
text.scale(2).to_edge(DOWN, buff=1.2)
# Now sit back and watch
self.play(
Succession(*anims, rate_func=smooth),
Write(text, lag_factor=2.5),
run_time=4.5,
)
def add_T_label(self,
x_val,
side=RIGHT,
label=None,
color=WHITE,
animated=False,
**kwargs):
triangle = RegularPolygon(n=3, start_angle=np.pi / 2)
triangle.scale_to_fit_height(MED_SMALL_BUFF)
triangle.move_to(self.coords_to_point(x_val, 0), UP)
triangle.set_fill(color, 1)
triangle.set_stroke(width=0)
if label == None:
T_label = TexMobject(self.variable_point_label, fill_color=color)
else:
T_label = TexMobject(label, fill_color=color)
T_label.next_to(triangle, DOWN)
v_line = self.get_vertical_line_to_graph(x_val,
self.v_graph,
color=YELLOW)
if animated:
self.play(DrawBorderThenFill(triangle), ShowCreation(v_line),
Write(T_label, run_time=1), **kwargs)
if np.all(side == LEFT):
self.left_T_label_group = VGroup(T_label, triangle)
self.left_v_line = v_line
self.add(self.left_T_label_group, self.left_v_line)
elif np.all(side == RIGHT):
self.right_T_label_group = VGroup(T_label, triangle)
self.right_v_line = v_line
self.add(self.right_T_label_group, self.right_v_line)
def construct(self):
logo = self.logo
name = self.channel_name
self.play(Write(name, run_time=3, lag_factor=2.5),
*self.get_logo_animations(logo))
self.wait()
def construct(self):
self.quote = self.get_quote()
self.author = self.get_author(self.quote)
self.play(FadeIn(self.quote, **self.fade_in_kwargs))
self.wait(2)
self.play(Write(self.author, run_time=3))
self.wait()
def solve_the_equations(self):
rects = VGroup(*[
CoverRectangle(
equation[0].get_exponent(), stroke_color = color,
text = str(num), text_color = color
)
for equation, color, num in zip(self.equations, self.colors, self.nums)
])
self.play(DrawBorderThenFill(rects))
self.wait()
sps = VGroup()
for equation, num, color in zip(self.equations, self.nums, self.colors):
sp = TexMobject("x", "^{%d}" % num, "=", "%d" % num)
sp[1::2].set_color(color)
sp.scale(2)
sp.next_to(equation, DOWN, buff = 1)
sps.add(sp)
rss = VGroup()
for num, sp, color in zip(self.nums, sps, self.colors):
rs = TexMobject("x", "=", "%d" % num , "^{{1}\\over{%d}}" % num, "=\\sqrt{2}")
for tex in (rs[2], rs[3][2]):
tex.set_color(color)
rs.match_height(sp).move_to(sp)
rss.add(rs)
tf_anims = []
for sp, rs in zip(sps, rss):
tf_anims.append(ReplacementTransform(sp[0], rs[0]))
tf_anims.append(ReplacementTransform(sp[1], rs[3][2], path_arc = -TAU/4))
tf_anims.append(ReplacementTransform(sp[2], rs[1]))
tf_anims.append(ReplacementTransform(sp[3], rs[2]))
tf_anims.append(Write(rs[3][:2]))
self.play(FadeIn(sps))
self.wait()
self.play(AnimationGroup(*tf_anims), run_time = 2)
self.wait()
self.play(Write(VGroup(*[rs[4:] for rs in rss]), submobject_mode = "all_at_once"))
self.wait()
self.play(FadeOut(rects))
self.wait()
self.rss = rss
def ask_to_solve(self):
question = TextMobject("解", "方程（$x>0$）", "：")
solve = TextMobject("解", "：")
for tex in (question, solve):
tex.scale(1.2)
tex.to_corner(LEFT+UP)
self.play(Write(question), run_time = 1)
self.wait()
self.question = question
self.solve = solve
def add_title(self, title, scale_factor=1.5, animate=False):
if not isinstance(title, Mobject):
title = TextMobject(title).scale(scale_factor)
title.to_edge(UP)
title.add_background_rectangle()
if animate:
self.play(Write(title))
self.add_foreground_mobject(title)
self.title = title
return self
def rhs_could_be_any_number(self):
rhs_list = [
"2", # The journey starts here.
"3", # The first number that pops into your head when you hear "2".
"\\pi", # The good ol' pi.
"\\sqrt{2}", # The (most) famous irrational number.
"42", # The answer to everything.
"17.29", # TAXI.CAB
"-1", # A negative number, because why not?
"e", # The (most) famous mathematical constant.
"\\dfrac{3+\\sqrt{13}}{2}", # The bronze ratio... and a fraction.
"570", # 1/3 of the author.
"\\varphi", # The golden ratio.
"g_{64}", # Gigigigigigigigantic...
"0", # And... stop!
"N",
]
anything_text = TextMobject("等号右边似乎可以放任何数...")
anything_text.set_color(YELLOW)
anything_text.to_edge(UP)
equations = [
VGroup(ExpTower(order = 5), TexMobject("=", rhs).scale(0.8)).scale(2.5)
for rhs in rhs_list
]
init_equation = equations[0]
init_equation.arrange_submobjects(RIGHT, aligned_edge = DOWN)
init_equation.next_to(anything_text, DOWN, buff = self.tower_edge_buff)
init_equation.to_edge(LEFT, buff = self.tower_edge_buff)
for equation in equations:
equation[0].move_to(init_equation[0])
equation[1][0].move_to(init_equation[1][0])
equation[1][1].move_to(init_equation[1][1], aligned_edge = LEFT)
self.play(FadeIn(init_equation))
self.wait()
self.play(Write(anything_text), run_time = 1)
self.play(
ShowCreationThenDestruction(SurroundingRectangle(init_equation[1][1])),
run_time = 2
)
self.wait()
for k, equation in enumerate(equations):
if k > 0 and k != len(equations)-1:
equation[0].move_to(init_equation[0])
equation[1].move_to(init_equation[1], aligned_edge = LEFT)
self.remove(equations[k-1])
self.add(equations[k])
self.wait(1./3)
elif k == len(equations)-1:
self.wait()
self.play(ReplacementTransform(equations[k-1], equations[k]))
self.wait()
self.anything_text = anything_text
self.equation = equations[-1]
def build_the_tower(self):
highest_order = 6
towers = [
ExpTower(order = k, is_infinite = False)
for k in range(1, highest_order + 1)
]
towers.append(ExpTower(order = highest_order, is_infinite = True))
heights = list(np.linspace(3, 4.5, highest_order + 2))
for tower, height in zip(towers, heights):
tower.set_height(height)
init_tower = towers[0]
final_tower = towers[-1]
self.play(Write(init_tower))
self.wait()
for k, tower in enumerate(towers):
if k < len(towers) - 2:
new_tower = towers[k+1]
new_exponent = new_tower.get_exponent()
new_base = new_tower.get_base()
self.play(
ReplacementTransform(tower, new_exponent),
Write(new_base),
)
self.wait()
else:
xs = final_tower.get_elements()
expdots = final_tower.get_expdots()
sur_rect = SurroundingRectangle(expdots)
self.play(
ReplacementTransform(tower, xs, run_time = 1),
Write(expdots, run_time = 2),
)
self.play(
Indicate(expdots, run_time = 1),
ShowCreationThenDestruction(sur_rect, run_time = 2),
)
self.wait()
break
self.tower = final_tower
self.highest_order = highest_order
def build_the_equation(self):
l_part = self.tower.copy()
r_part = TexMobject("=", "2")
r_part.match_height(l_part.get_base())
equation = VGroup(l_part, r_part)
equation.arrange_submobjects(RIGHT, aligned_edge = DOWN)
self.play(
ReplacementTransform(self.tower, l_part, run_time = 1),
Write(r_part, run_time = 2),
)
self.equation = equation
def rewind_and_play_again(self):
watch_again = TextMobject("再看一遍...")
watch_again.set_color(YELLOW)
rewind, play = buttons = VGroup(*[
Button().get_symbol().set_color(YELLOW).set_height(1)
for Button in (RewindButton, PlayButton)
])
group = VGroup(watch_again, rewind)
group.arrange_submobjects(DOWN, aligned_edge = RIGHT)
group.to_corner(DOWN+RIGHT)
play.move_to(rewind, aligned_edge = RIGHT)
self.play(Write(watch_again), run_time = 0.5)
self.wait()
self.add(rewind)
self.words.reverse()
for word in self.words:
self.play(FadeOut(VGroup(word)), run_time = 0.2)
self.wait(0.1)
self.remove(rewind)
self.add(play)
self.play(FadeOut(watch_again), run_time = 0.5)
self.wait(0.5)
self.remove(play)
def reveal_2_is_4(self):
sqrt2_towers = VGroup(*[
ExpTower(element = "\\sqrt{2}", order = 5).match_height(x_tower) \
.move_to(x_tower, aligned_edge = RIGHT)
for x_tower in self.x_towers
])
self.play(
Transform(self.x_towers, sqrt2_towers, submobject_mode = "lagged_start"),
run_time = 2,
)
self.wait()
self.play(FadeOut(self.rss))
self.wait()
two_equals_four = TexMobject("2", "=", "4")
for tex, color in zip(two_equals_four, [GREEN, WHITE, RED]):
tex.set_color(color)
two_equals_four.scale(3)
two_equals_four.to_edge(DOWN, buff = 1)
sources = VGroup(*[
self.equations[i][j][k].copy()
for i, j, k in [(0, 1, 1), (1, 1, 0), (1, 1, 1)]
])
for source, target in zip(sources, two_equals_four):
self.play(Transform(source, target))
self.wait()
fake_qed = FakeQEDSymbol(order = 2, jagged_percentage = 0.3)
fake_qed.next_to(two_equals_four, RIGHT, aligned_edge = DOWN, buff = 1)
self.play(FadeIn(fake_qed))
self.wait()
issue = TextMobject("思考：\\\\问题在哪？")
issue.set_color(YELLOW)
issue.to_corner(RIGHT+DOWN)
self.play(Write(issue), run_time = 1)
self.wait(2)
def label_vector(self, vector, label, animate=True, **kwargs):
label = self.get_vector_label(vector, label, **kwargs)
if animate:
self.play(Write(label, run_time=1))
self.add(label)
return label
def setup_axes(self, animate=False):
# TODO, once eoc is done, refactor this to be less redundant.
x_num_range = float(self.x_max - self.x_min)
self.space_unit_to_x = self.x_axis_width / x_num_range
if self.x_labeled_nums is None:
self.x_labeled_nums = []
if self.x_leftmost_tick is None:
self.x_leftmost_tick = self.x_min
x_axis = NumberLine(x_min=self.x_min,
x_max=self.x_max,
unit_size=self.space_unit_to_x,
tick_frequency=self.x_tick_frequency,
leftmost_tick=self.x_leftmost_tick,
numbers_with_elongated_ticks=self.x_labeled_nums,
color=self.axes_color)
x_axis.shift(self.graph_origin - x_axis.number_to_point(0))
if len(self.x_labeled_nums) > 0:
if self.exclude_zero_label:
self.x_labeled_nums = filter(lambda x: x != 0,
self.x_labeled_nums)
x_axis.add_numbers(*self.x_labeled_nums)
if self.x_axis_label:
x_label = TextMobject(self.x_axis_label)
x_label.next_to(x_axis.get_tick_marks(),
UP + RIGHT,
buff=SMALL_BUFF)
x_label.shift_onto_screen()
x_axis.add(x_label)
self.x_axis_label_mob = x_label
y_num_range = float(self.y_max - self.y_min)
self.space_unit_to_y = self.y_axis_height / y_num_range
if self.y_labeled_nums is None:
self.y_labeled_nums = []
if self.y_bottom_tick is None:
self.y_bottom_tick = self.y_min
y_axis = NumberLine(
x_min=self.y_min,
x_max=self.y_max,
unit_size=self.space_unit_to_y,
tick_frequency=self.y_tick_frequency,
leftmost_tick=self.y_bottom_tick,
numbers_with_elongated_ticks=self.y_labeled_nums,
color=self.axes_color,
line_to_number_vect=LEFT,
)
y_axis.shift(self.graph_origin - y_axis.number_to_point(0))
y_axis.rotate(np.pi / 2, about_point=y_axis.number_to_point(0))
if len(self.y_labeled_nums) > 0:
if self.exclude_zero_label:
self.y_labeled_nums = filter(lambda y: y != 0,
self.y_labeled_nums)
y_axis.add_numbers(*self.y_labeled_nums)
if self.y_axis_label:
y_label = TextMobject(self.y_axis_label)
y_label.next_to(y_axis.get_tick_marks(),
UP + RIGHT,
buff=SMALL_BUFF)
y_label.shift_onto_screen()
y_axis.add(y_label)
self.y_axis_label_mob = y_label
if animate:
self.play(Write(VGroup(x_axis, y_axis)))
else:
self.add(x_axis, y_axis)
self.x_axis, self.y_axis = self.axes = VGroup(x_axis, y_axis)
self.default_graph_colors = it.cycle(self.default_graph_colors)
def construct(self):
# Setup
axes_group = self.axes_group
pos_axis, time_axis = axes_group[:2]
title_pq = self.title_pq
walk_q = self.walk_q
parts_q = self.parts_q
l_arrow = self.l_arrow
self.add(axes_group, title_pq, walk_q, l_arrow)
walk_q_copy = walk_q.copy()
# Q_4 -> P_4
steps_qp = VGroup(*[
TextMobject(text) for text in [
"1. 找到路径终点的位置坐标$h$", "2. 找到最晚一次穿过$\\frac{h}{2}$的时刻",
"3. 在这个时刻上进行分割", "4. 将第一段水平翻转", "5. 拼接两个片段"
]
])
for step in steps_qp:
step.set_color(YELLOW)
step.add_background_rectangle()
step1_qp, step2_qp, step3_qp, step4_qp, step5_qp = steps_qp
# 1. Find the endpoint
step1_qp.next_to(time_axis.number_to_point(4.5), UP)
end_horiz_line = DashedLine(LEFT_SIDE, RIGHT_SIDE, color=YELLOW)
end_horiz_line.move_to(pos_axis.number_to_point(-4))
end_horiz_line.horizontally_center()
end_brace_line = DashedLine(time_axis.number_to_point(8),
walk_q.get_end_point())
end_brace = Brace(end_brace_line, direction=RIGHT, color=YELLOW)
h = TexMobject("h").set_color(YELLOW)
end_brace.put_at_tip(h)
self.play(Write(step1_qp), ShowCreation(end_horiz_line), run_time=1)
self.play(GrowFromCenter(end_brace), GrowFromCenter(h))
self.wait(1.5)
self.play(FadeOut(step1_qp))
# 2. Find the last time it GOES THROUGH half its final value
half_point = walk_q.get_arrow_end_point(3)
step2_qp.next_to(time_axis.number_to_point(4.5), UP)
half_horiz_line = end_horiz_line.copy().shift(2 * UP)
half_brace_line = DashedLine(time_axis.number_to_point(4), half_point)
half_brace = Brace(half_brace_line, direction=RIGHT, color=YELLOW)
half_h = TexMobject("\\frac{h}{2}").set_color(YELLOW)
half_brace.put_at_tip(half_h)
half_dot = Dot(half_point, color=YELLOW)
self.play(FadeIn(step2_qp), run_time=1)
self.wait(0.5)
self.play(
ReplacementTransform(end_brace, half_brace),
ReplacementTransform(end_horiz_line, half_horiz_line),
ReplacementTransform(h, half_h[0]),
Write(half_h[1:]),
)
self.play(DrawBorderThenFill(half_dot))
self.wait(1.5)
self.play(
FadeOut(VGroup(step2_qp, half_horiz_line, half_brace, half_h)))
# 3. Split
vert_line = DashedLine(2.5 * UP, 2.5 * DOWN, color=YELLOW)
vert_line.move_to(half_point)
step3_qp.next_to(vert_line, UP)
left_part_q, right_part_q = parts_q
self.play(ShowCreation(vert_line), Write(step3_qp), run_time=1)
self.play(
FadeOut(half_dot),
left_part_q.shift,
0.5 * DOWN + 0.5 * LEFT,
right_part_q.shift,
0.5 * UP + 0.5 * RIGHT,
)
self.wait(1.5)
self.play(FadeOut(vert_line), FadeOut(step3_qp))
# 4. Flip the first segment horizontally
flip_axis = DashedLine(2 * UP, 2 * DOWN, color=GREY)
flip_axis.move_to(left_part_q)
step4_qp.next_to(flip_axis, DOWN)
self.play(
ShowCreation(flip_axis),
Write(step4_qp),
run_time=1,
)
self.play(
left_part_q.flip,
Animation(flip_axis),
)
self.wait(1.5)
self.play(FadeOut(step4_qp), FadeOut(flip_axis))
# 5. Put the pieces together
step5_qp.shift(2.5 * DOWN)
flip_arrow_anims = walk_q.get_flip_arrows_animation(3, color=ORANGE)
self.play(Write(step5_qp), run_time=1)
self.wait(0.5)
self.play(flip_arrow_anims, right_part_q.set_color, ORANGE)
self.wait(0.5)
self.play(
left_part_q.shift,
2.5 * UP + 0.5 * RIGHT,
right_part_q.shift,
3.5 * UP + 0.5 * LEFT,
Animation(step5_qp),
)
self.wait(0.5)
self.play(FadeOut(step5_qp))
self.wait(1.5)
# Now Reset
self.play(FadeOut(walk_q))
self.play(FadeIn(walk_q_copy))
self.wait()
def write_vector_coordinates(self, vector, **kwargs):
coords = vector_coordinate_label(vector, **kwargs)
self.play(Write(coords))
return coords
def construct(self):
# Setup
axes_group = self.axes_group
title_pq = self.title_pq
walk_p = self.walk_p
parts_p = self.parts_p
r_arrow = self.r_arrow
self.add(axes_group, title_pq, walk_p, r_arrow)
walk_p_copy = walk_p.copy()
# P_4 -> Q_4
steps_pq = VGroup(*[
TextMobject(text) for text in [
"1. 第一步是沿着正方向走的", "2. 找到第一次到达最大值的时刻", "3. 在这个时刻上进行分割",
"4. 将第一段水平翻转", "5. 拼接两个片段"
]
])
for step in steps_pq:
step.set_color(YELLOW)
step.add_background_rectangle()
step1_pq, step2_pq, step3_pq, step4_pq, step5_pq = steps_pq
# 1. Check the first step of the walk
step1_circle = Circle(color=YELLOW)
first_arrow = walk_p.get_arrow_by_number(0)
step1_circle.surround(first_arrow)
step1_pq.next_to(step1_circle, RIGHT + DOWN)
self.play(ShowCreation(step1_circle), Write(step1_pq), run_time=1)
self.wait(1.5)
self.play(FadeOut(step1_circle), FadeOut(step1_pq))
# 2. Find the first time it reaches the maximum
peak = walk_p.get_arrow_end_point(3)
horiz_line = DashedLine(2.5 * LEFT, 2.5 * RIGHT, color=YELLOW)
horiz_line.move_to(peak)
dot = Dot(color=YELLOW)
dot.move_to(peak)
step2_pq.next_to(horiz_line, UP)
self.play(ShowCreation(horiz_line),
DrawBorderThenFill(dot),
Write(step2_pq),
run_time=1)
self.wait(1.5)
self.play(FadeOut(horiz_line), FadeOut(step2_pq))
# 3. Split
vert_line = DashedLine(2.5 * UP, 2.5 * DOWN, color=YELLOW)
vert_line.move_to(peak)
step3_pq.next_to(vert_line, DOWN)
left_part_p, right_part_p = parts_p
self.play(ShowCreation(vert_line), Write(step3_pq), run_time=1)
self.play(
FadeOut(dot),
left_part_p.shift,
0.5 * DOWN + 0.5 * LEFT,
right_part_p.shift,
DOWN + 0.5 * RIGHT,
)
self.wait(1.5)
self.play(FadeOut(vert_line), FadeOut(step3_pq))
# 4. Flip the first segment horizontally
flip_axis = DashedLine(2 * UP, 2 * DOWN, color=GREY)
flip_axis.move_to(left_part_p)
step4_pq.next_to(flip_axis, DOWN)
self.play(
ShowCreation(flip_axis),
Write(step4_pq),
run_time=1,
)
self.play(
left_part_p.flip,
Animation(flip_axis),
)
self.wait(1.5)
self.play(FadeOut(step4_pq), FadeOut(flip_axis))
# 5. Put the pieces together
step5_pq.move_to(dot)
flip_arrow_anims = walk_p.get_flip_arrows_animation(3, color=GREEN)
self.play(Write(step5_pq), run_time=1)
self.wait(0.5)
self.play(flip_arrow_anims, right_part_p.set_color, GREEN)
self.wait(0.5)
self.play(
left_part_p.shift,
1.5 * DOWN + 0.5 * RIGHT,
right_part_p.shift,
3 * DOWN + 0.5 * LEFT,
Animation(step5_pq),
)
self.wait(0.5)
self.play(FadeOut(step5_pq))
self.wait(1.5)
# Now Reset
self.play(FadeOut(walk_p))
self.play(FadeIn(walk_p_copy))
self.wait()
