def __init__(self,
eq1,
eq2,
regex,
regex2=None,
map_list=None,
align_char=None):
# align equations
if align_char:
difference_vec = \
self.mob_from_char(eq1, eq1.tex_string, align_char).get_center() - \
self.mob_from_char(eq2, eq2.tex_string, align_char).get_center()
else:
difference_vec = eq1.get_center() - eq2.get_center()
eq2.shift(difference_vec)
if regex2 is None:
g1 = self.split_by_regex(eq1, regex)
g2 = self.split_by_regex(eq2, regex)
assert (len(g1.submobjects) == len(g2.submobjects))
trans = ReplacementTransform(g1, g2)
AnimationGroup.__init__(self, trans)
else:
assert (map_list)
g1 = self.split_by_regex(eq1, regex)
g2 = self.split_by_regex(eq2, regex2)
self.g1 = g1
self.g2 = g2
G1 = VGroup()
G2 = VGroup()
F1 = Group()
F2 = Group()
g1_nodes = set(pair[0] for pair in map_list)
g2_nodes = set(pair[1] for pair in map_list)
while map_list:
l1 = [g1.submobjects[map_list[0][0]]]
l2 = [g2.submobjects[map_list[0][1]]]
new_list = []
for i in range(1, len(map_list)):
if map_list[i][0] == map_list[0][0]:
l2.append(g2.submobjects[map_list[i][1]])
elif map_list[i][1] == map_list[0][1]:
l1.append(g1.submobjects[map_list[i][0]])
else:
new_list.append(map_list[i])
map_list = new_list
G1.submobjects.append(VGroup(*l1))
G2.submobjects.append(VGroup(*l2))
for i in range(len(g1.submobjects)):
if i not in g1_nodes:
F1.submobjects.append(g1.submobjects[i])
for i in range(len(g2.submobjects)):
if i not in g2_nodes:
F2.submobjects.append(g2.submobjects[i])
self.g1 = g1
self.g2 = g2
trans = ReplacementTransform(G1, G2)
fadeout = FadeOut(F1)
fadein = FadeIn(F2)
AnimationGroup.__init__(self, trans, fadeout, fadein)
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 construct(self):
author = TextMobject("@Solara570")
support = TextMobject("(Powered by @3Blue1Brown)")
author.scale(1.8)
support.match_width(author)
group = VGroup(author, support)
group.arrange_submobjects(DOWN)
group.to_corner(RIGHT+DOWN)
self.play(FadeIn(group))
self.wait(2)
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 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 show_comments(self):
height = 1.5
simple, but, trap = texts = TextMobject("简单直观", "但是", "暗藏陷阱")
texts.scale(1.5)
texts.arrange_submobjects(DOWN, buff = 0.8)
tick = TickButton()
tick.set_height(height)
tick.next_to(simple, RIGHT)
danger = DangerSign()
danger.set_height(height)
danger.next_to(trap, LEFT)
words = [(simple, tick), (but, ), (danger, trap)]
colors = [GREEN, WHITE, RED]
for word, color in zip(words, colors):
VGroup(word).set_color(color)
self.play(FadeIn(VGroup(word)), run_time = 1)
self.wait(0.5)
self.wait()
self.words = words
def update_mobject(self, new_mob, animate=True):
"""
Returns a list of animations of the mobject being updated
"""
ret = []
if animate:
if type(self.mobject) == Line and type(new_mob) == Arrow:
ret.extend([
FadeOut(self.mobject, parent=self),
FadeIn(new_mob, parent=self),
])
else:
ret.extend(
[ReplacementTransform(self.mobject, new_mob, parent=self)])
else:
if hasattr(self, "mobject"):
self.remove(self.mobject)
self.add(new_mob)
self.mobject = new_mob
return ret
def get_digit_increment_animations(self):
result = []
self.number += 1
is_next_digit = self.is_next_digit()
if is_next_digit: self.max_place += 1
new_number_mob = self.get_number_mob(self.number)
new_number_mob.move_to(self.number_mob, RIGHT)
if is_next_digit:
self.add_configuration()
place = len(new_number_mob.split()) - 1
result.append(FadeIn(self.dot_templates[place]))
arrow = Arrow(new_number_mob[place].get_top(),
self.dot_templates[place].get_bottom(),
color=self.digit_place_colors[place])
self.arrows.add(arrow)
result.append(ShowCreation(arrow))
result.append(
Transform(self.number_mob,
new_number_mob,
submobject_mode="lagged_start"))
return result
def construct(self):
# Setup
self.set_camera_orientation(phi = np.pi/3, theta = 3*np.pi/4)
self.begin_ambient_camera_rotation(np.pi/50)
# Part 1: Increasing the order
for order in range(1, self.max_order+1):
if order == 1:
fractal = HilbertCurve3D(order = 1)
self.play(ShowCreation(fractal), run_time = 2)
cur_order = fractal.order
else:
new_fractal = HilbertCurve3D(order = cur_order + 1)
self.play(Transform(fractal, new_fractal))
cur_order = new_fractal.order
self.wait(2)
self.wait(5)
self.play(FadeOut(fractal))
self.wait(3)
# Part 2: Show one-touch construction
self.play(ShowCreation(fractal, run_time = 60))
self.wait(5)
# Part 3: Decreasing the order till it vanishes
for k in reversed(range(1, self.max_order)):
new_fractal = HilbertCurve3D(order = cur_order - 1)
self.play(Transform(fractal, new_fractal))
cur_order = new_fractal.order
self.wait(2)
self.play(Uncreate(fractal), run_time = 1)
# The end
self.stop_ambient_camera_rotation()
self.set_camera_orientation(phi = 0, theta = -np.pi/2)
author = TextMobject("@Solara570")
author.scale(1.5)
author.to_corner(RIGHT+DOWN)
self.play(FadeIn(author), run_time = 1)
self.wait(2)
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 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 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()
def show_the_solution(self):
# Prepare for the solution
pre_solve = VGroup(*self.question[::2])
self.play(
ReplacementTransform(pre_solve, self.solve),
FadeOut(self.question[1]),
run_time = 1,
)
self.wait()
# Manipulate LHS
old_l_part, r_part = self.equation
new_l_part = ExpTower(order = self.highest_order+1, is_infinite = True)
new_l_part.match_height(old_l_part)
new_l_part.next_to(r_part, LEFT, aligned_edge = DOWN)
old_rect, new_rect = rects = [
CoverRectangle(part, text = "2")
for part in (old_l_part, new_l_part.get_exponent())
]
old_two, new_two = twos = [
rect.get_text_mob()
for rect in rects
]
self.play(DrawBorderThenFill(old_rect, run_time = 1))
self.wait()
self.play(
ReplacementTransform(old_l_part, new_l_part),
ReplacementTransform(old_rect, new_rect),
)
self.wait()
new_equation = VGroup(new_l_part, r_part, new_rect)
new_equation.generate_target()
new_equation.target.scale(0.8)
new_equation.target.shift(UP)
self.play(MoveToTarget(new_equation))
self.wait()
# A little bit clean-up
source_eq = VGroup(*[
mob.copy()
for mob in (new_l_part.get_base(), new_two, r_part[0], r_part[1])
])
source_eq.generate_target()
target_eq = TexMobject("x", "^2", "=", "2")
target_eq.scale(3).next_to(source_eq, DOWN, buff = 1)
for k, (old_part, new_part) in enumerate(zip(source_eq.target, target_eq)):
old_part.move_to(new_part)
if k == 1:
old_part.scale(0.5)
old_part.shift(RIGHT/4)
self.play(
FadeOut(new_rect),
MoveToTarget(source_eq),
)
self.wait()
# Reveal the final answer
result = TexMobject("x", "=", "\\sqrt", "2")
result.set_height(source_eq.get_height() * 0.7)
result.move_to(source_eq)
self.play(*[
ReplacementTransform(source_eq[m], result[n], path_arc = angle)
for m, n, angle in [(0, 0, 0), (1, 2, -TAU/3), (2, 1, 0), (3, 3, 0)]
])
self.wait()
qed = QEDSymbol()
qed.next_to(result, RIGHT, aligned_edge = DOWN, buff = 1.5)
self.play(FadeIn(qed))
self.wait()
