def series_of_videos(self, chapters):
icon = SVGMobject("video_icon")
icon.center()
icon.scale_to_fit_width(2 * SPACE_WIDTH / 12.)
icon.set_stroke(color=WHITE, width=0)
icons = [icon.copy() for chapter in chapters.split()]
colors = Color(BLUE_A).range_to(BLUE_D, len(icons))
for icon, color in zip(icons, colors):
icon.set_fill(color, opacity=1)
icons = VMobject(*icons)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
icons.shift(UP)
randy = Randolph()
randy.to_corner()
bubble = randy.get_bubble()
new_icons = icons.copy().scale(0.2)
bubble.position_mobject_inside(new_icons)
self.play(Transform(
chapters,
icons,
path_arc=np.pi / 2,
))
self.clear()
self.add(icons)
self.play(FadeIn(randy))
self.play(Blink(randy))
self.wait()
self.play(ShowCreation(bubble), Transform(icons, new_icons))
self.remove(icons)
bubble.make_green_screen()
self.wait()
def handle_mathy(self, creatures):
self.fade_all_but(creatures, 2)
physy, compy, mathy = creatures
v_color = YELLOW
w_color = BLUE
sum_color = GREEN
v_arrow = Vector([1, 1])
w_arrow = Vector([2, 1])
w_arrow.shift(v_arrow.get_end())
sum_arrow = Vector(w_arrow.get_end())
arrows = VMobject(v_arrow, w_arrow, sum_arrow)
arrows.scale(0.7)
arrows.to_edge(LEFT, buff = 2)
v_array = matrix_to_mobject([3, -5])
w_array = matrix_to_mobject([2, 1])
sum_array = matrix_to_mobject(["3+2", "-5+1"])
arrays = VMobject(
v_array, TexMobject("+"), w_array, TexMobject("="), sum_array
)
arrays.arrange_submobjects(RIGHT)
arrays.scale(0.75)
arrays.to_edge(RIGHT).shift(UP)
v_sym = TexMobject("\\vec{\\textbf{v}}")
w_sym = TexMobject("\\vec{\\textbf{w}}")
syms = VMobject(v_sym, TexMobject("+"), w_sym)
syms.arrange_submobjects(RIGHT)
syms.center().shift(2*UP)
statement = TextMobject("We'll ignore him \\\\ for now")
statement.highlight(PINK)
statement.scale_to_fit_width(arrays.get_width())
statement.next_to(arrays, DOWN, buff = 1.5)
circle = Circle()
circle.shift(syms.get_bottom())
VMobject(v_arrow, v_array, v_sym).highlight(v_color)
VMobject(w_arrow, w_array, w_sym).highlight(w_color)
VMobject(sum_arrow, sum_array).highlight(sum_color)
self.play(
Write(syms), Write(arrays),
ShowCreation(arrows, submobject_mode = "one_at_a_time"),
ApplyMethod(mathy.change_mode, "pondering"),
run_time = 2
)
self.play(Blink(mathy))
self.add_scaling(arrows, syms, arrays)
self.play(Write(statement))
self.play(ApplyMethod(mathy.change_mode, "sad"))
self.dither()
self.play(
ShowCreation(circle),
ApplyMethod(mathy.change_mode, "plain")
)
self.dither()
def handle_mathy(self, creatures):
self.fade_all_but(creatures, 2)
physy, compy, mathy = creatures
v_color = YELLOW
w_color = BLUE
sum_color = GREEN
v_arrow = Vector([1, 1])
w_arrow = Vector([2, 1])
w_arrow.shift(v_arrow.get_end())
sum_arrow = Vector(w_arrow.get_end())
arrows = VMobject(v_arrow, w_arrow, sum_arrow)
arrows.scale(0.7)
arrows.to_edge(LEFT, buff = 2)
v_array = matrix_to_mobject([3, -5])
w_array = matrix_to_mobject([2, 1])
sum_array = matrix_to_mobject(["3+2", "-5+1"])
arrays = VMobject(
v_array, TexMobject("+"), w_array, TexMobject("="), sum_array
)
arrays.arrange_submobjects(RIGHT)
arrays.scale(0.75)
arrays.to_edge(RIGHT).shift(UP)
v_sym = TexMobject("\\vec{\\textbf{v}}")
w_sym = TexMobject("\\vec{\\textbf{w}}")
syms = VMobject(v_sym, TexMobject("+"), w_sym)
syms.arrange_submobjects(RIGHT)
syms.center().shift(2*UP)
statement = TextMobject("We'll ignore him \\\\ for now")
statement.highlight(PINK)
statement.scale_to_fit_width(arrays.get_width())
statement.next_to(arrays, DOWN, buff = 1.5)
circle = Circle()
circle.shift(syms.get_bottom())
VMobject(v_arrow, v_array, v_sym).highlight(v_color)
VMobject(w_arrow, w_array, w_sym).highlight(w_color)
VMobject(sum_arrow, sum_array).highlight(sum_color)
self.play(
Write(syms), Write(arrays),
ShowCreation(arrows, submobject_mode = "one_at_a_time"),
ApplyMethod(mathy.change_mode, "pondering"),
run_time = 2
)
self.play(Blink(mathy))
self.add_scaling(arrows, syms, arrays)
self.play(Write(statement))
self.play(ApplyMethod(mathy.change_mode, "sad"))
self.wait()
self.play(
ShowCreation(circle),
ApplyMethod(mathy.change_mode, "plain")
)
self.wait()
def construct(self):
v = TexMobject(self.v_str)
v.highlight(YELLOW)
eq = TexMobject("=")
coords = Matrix(["x", "y", "z"])
eq2 = eq.copy()
if self.post_transform:
L, l_paren, r_paren = map(TexMobject, "L()")
parens = VMobject(l_paren, r_paren)
parens.scale(2)
parens.stretch_to_fit_height(
coords.get_height()
)
VMobject(L, l_paren, coords, r_paren).arrange_submobjects(buff = 0.1)
coords.submobjects = [L, l_paren] + coords.submobjects + [r_paren]
lin_comb = VMobject(*map(TexMobject, [
"x", self.i_str, "+",
"y", self.j_str, "+",
"z", self.k_str,
]))
lin_comb.arrange_submobjects(
RIGHT, buff = 0.1,
aligned_edge = ORIGIN if self.post_transform else DOWN
)
lin_comb_parts = np.array(lin_comb.split())
new_x, new_y, new_z = lin_comb_parts[[0, 3, 6]]
i, j, k = lin_comb_parts[[1, 4, 7]]
plusses = lin_comb_parts[[2, 5]]
i.highlight(X_COLOR)
j.highlight(Y_COLOR)
k.highlight(Z_COLOR)
everything = VMobject(v, eq, coords, eq2, lin_comb)
everything.arrange_submobjects(buff = 0.2)
everything.scale_to_fit_width(2*SPACE_WIDTH - 1)
everything.to_edge(DOWN)
if not self.post_transform:
lin_comb.shift(0.35*UP)
self.play(*map(Write, [v, eq, coords]))
self.dither()
self.play(
Transform(
coords.get_entries().copy(),
VMobject(new_x, new_y, new_z),
path_arc = -np.pi,
submobject_mode = "lagged_start"
),
Write(VMobject(*[eq2, i, j, k] + list(plusses))),
run_time = 3
)
self.dither()
def construct(self):
icon = SVGMobject("video_icon")
icon.center()
icon.scale_to_fit_width(2 * SPACE_WIDTH / 12.)
icon.set_stroke(color=WHITE, width=0)
icon.set_fill(WHITE, opacity=1)
icons = VMobject(*[icon.copy() for x in range(10)])
icons.submobject_gradient_highlight(BLUE_A, BLUE_D)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
self.play(FadeIn(icons, submobject_mode="lagged_start"), run_time=3)
self.wait()
def construct(self):
title = TextMobject("Questions to ponder")
title.highlight(YELLOW).to_edge(UP)
self.add(title)
questions = VMobject(*map(TextMobject, [
"1. Can you visualize these transformations?",
"2. Can you represent them with matrices?",
"3. How many rows and columns?",
"4. When can you multiply these matrices?",
]))
questions.arrange_submobjects(DOWN, buff=1, aligned_edge=LEFT)
questions.to_edge(LEFT)
for question in questions.split():
self.play(Write(question, run_time=1))
self.wait()
def construct(self):
title = TextMobject("Questions to ponder")
title.highlight(YELLOW).to_edge(UP)
self.add(title)
questions = VMobject(*map(TextMobject, [
"1. Can you visualize these transformations?",
"2. Can you represent them with matrices?",
"3. How many rows and columns?",
"4. When can you multiply these matrices?",
]))
questions.arrange_submobjects(DOWN, buff = 1, aligned_edge = LEFT)
questions.to_edge(LEFT)
for question in questions.split():
self.play(Write(question, run_time = 1))
self.dither()
def construct(self):
icon = SVGMobject("video_icon")
icon.center()
icon.scale_to_fit_width(2*SPACE_WIDTH/12.)
icon.set_stroke(color = WHITE, width = 0)
icon.set_fill(WHITE, opacity = 1)
icons = VMobject(*[icon.copy() for x in range(10)])
icons.submobject_gradient_highlight(BLUE_A, BLUE_D)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
self.play(
FadeIn(icons, submobject_mode = "lagged_start"),
run_time = 3
)
self.dither()
def construct(self):
i_to = TexMobject("\\hat{\\imath} \\to").highlight(X_COLOR)
j_to = TexMobject("\\hat{\\jmath} \\to").highlight(Y_COLOR)
k_to = TexMobject("\\hat{k} \\to").highlight(Z_COLOR)
i_array = Matrix(self.col1)
j_array = Matrix(self.col2)
k_array = Matrix(self.col3)
everything = VMobject(
i_to,
i_array,
TexMobject("=").highlight(BLACK),
j_to,
j_array,
TexMobject("=").highlight(BLACK),
k_to,
k_array,
TexMobject("=").highlight(BLACK),
)
everything.arrange_submobjects(RIGHT, buff=0.1)
everything.scale_to_fit_width(2 * SPACE_WIDTH - 1)
everything.to_edge(DOWN)
i_array.highlight(X_COLOR)
j_array.highlight(Y_COLOR)
k_array.highlight(Z_COLOR)
arrays = [i_array, j_array, k_array]
matrix = Matrix(
reduce(lambda a1, a2: np.append(a1, a2, axis=1),
[m.copy().get_mob_matrix() for m in arrays]))
matrix.to_edge(DOWN)
start_entries = reduce(op.add,
map(lambda a: a.get_entries().split(), arrays))
target_entries = matrix.get_mob_matrix().transpose().flatten()
start_l_bracket = i_array.get_brackets().split()[0]
start_r_bracket = k_array.get_brackets().split()[1]
start_brackets = VMobject(start_l_bracket, start_r_bracket)
target_bracketes = matrix.get_brackets()
for mob in everything.split():
self.play(Write(mob, run_time=1))
self.wait()
self.play(
FadeOut(everything),
Transform(VMobject(*start_entries), VMobject(*target_entries)),
Transform(start_brackets, target_bracketes))
self.wait()
def construct(self):
i_to = TexMobject("\\hat{\\imath} \\to").highlight(X_COLOR)
j_to = TexMobject("\\hat{\\jmath} \\to").highlight(Y_COLOR)
k_to = TexMobject("\\hat{k} \\to").highlight(Z_COLOR)
i_array = Matrix(self.col1)
j_array = Matrix(self.col2)
k_array = Matrix(self.col3)
everything = VMobject(
i_to, i_array, TexMobject("=").highlight(BLACK),
j_to, j_array, TexMobject("=").highlight(BLACK),
k_to, k_array, TexMobject("=").highlight(BLACK),
)
everything.arrange_submobjects(RIGHT, buff = 0.1)
everything.scale_to_fit_width(2*SPACE_WIDTH-1)
everything.to_edge(DOWN)
i_array.highlight(X_COLOR)
j_array.highlight(Y_COLOR)
k_array.highlight(Z_COLOR)
arrays = [i_array, j_array, k_array]
matrix = Matrix(reduce(
lambda a1, a2 : np.append(a1, a2, axis = 1),
[m.copy().get_mob_matrix() for m in arrays]
))
matrix.to_edge(DOWN)
start_entries = reduce(op.add, map(
lambda a : a.get_entries().split(),
arrays
))
target_entries = matrix.get_mob_matrix().transpose().flatten()
start_l_bracket = i_array.get_brackets().split()[0]
start_r_bracket = k_array.get_brackets().split()[1]
start_brackets = VMobject(start_l_bracket, start_r_bracket)
target_bracketes = matrix.get_brackets()
for mob in everything.split():
self.play(Write(mob, run_time = 1))
self.dither()
self.play(
FadeOut(everything),
Transform(VMobject(*start_entries), VMobject(*target_entries)),
Transform(start_brackets, target_bracketes)
)
self.dither()
def construct(self):
icons = [VideoIcon() for x in range(10)]
colors = Color(BLUE_A).range_to(BLUE_D, len(icons))
for icon, color in zip(icons, colors):
icon.set_fill(color, opacity=1)
icons = VMobject(*icons)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
icons.shift(UP)
icons = icons.split()
def rate_func_creator(offset):
return lambda a: min(max(2 * (a - offset), 0), 1)
self.play(*[
FadeIn(icon, run_time=5, rate_func=rate_func_creator(offset))
for icon, offset in zip(icons, np.linspace(0, 0.5, len(icons)))
])
self.wait()
def show_matrix(self):
for vect, char in zip([self.i_hat, self.j_hat], ["i", "j"]):
vect.words = TextMobject("$\\hat\\%smath$ lands on" % char,
str(int(vect.get_end()[0])))
direction = UP if vect is self.i_hat else DOWN
vect.words.next_to(vect.get_end(), direction, buff=LARGE_BUFF)
vect.words.highlight(vect.get_color())
matrix = Matrix([[1, 2]])
matrix_words = TextMobject("Transformation matrix: ")
matrix_group = VMobject(matrix_words, matrix)
matrix_group.arrange_submobjects(buff=MED_SMALL_BUFF)
matrix_group.to_edge(UP)
entries = matrix.get_entries()
self.play(Write(matrix_words), Write(matrix.get_brackets()))
for i, vect in enumerate([self.i_hat, self.j_hat]):
self.play(vect.rotate, np.pi / 12, rate_func=wiggle)
self.play(Write(vect.words))
self.dither()
self.play(vect.words[1].copy().move_to, entries[i])
self.dither()
def cs_conception(self, creatures):
self.fade_all_but(creatures, 1)
physy, compy, mathy = creatures
title = TextMobject("Vectors $\\Leftrightarrow$ lists of numbers")
title.to_edge(UP)
vectors = VMobject(*map(matrix_to_mobject, [
[2, 1],
[5, 0, 0, -3],
[2.3, -7.1, 0.1],
]))
vectors.arrange_submobjects(RIGHT, buff=1)
vectors.to_edge(LEFT)
self.play(ApplyMethod(compy.change_mode, "sassy"),
Write(title, run_time=1))
self.play(Write(vectors))
self.dither()
self.play(ApplyMethod(compy.change_mode, "pondering"))
self.house_example(vectors, title)
self.restore_creatures(creatures)
def construct(self):
icons = [VideoIcon() for x in range(10)]
colors = Color(BLUE_A).range_to(BLUE_D, len(icons))
for icon, color in zip(icons, colors):
icon.set_fill(color, opacity = 1)
icons = VMobject(*icons)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
icons.shift(UP)
icons = icons.split()
def rate_func_creator(offset):
return lambda a : min(max(2*(a-offset), 0), 1)
self.play(*[
FadeIn(
icon,
run_time = 5,
rate_func = rate_func_creator(offset)
)
for icon, offset in zip(icons, np.linspace(0, 0.5, len(icons)))
])
self.dither()
def show_matrix(self):
for vect, char in zip([self.i_hat, self.j_hat], ["i", "j"]):
vect.words = TextMobject(
"$\\hat\\%smath$ lands on"%char,
str(int(vect.get_end()[0]))
)
direction = UP if vect is self.i_hat else DOWN
vect.words.next_to(vect.get_end(), direction, buff = LARGE_BUFF)
vect.words.highlight(vect.get_color())
matrix = Matrix([[1, 2]])
matrix_words = TextMobject("Transformation matrix: ")
matrix_group = VMobject(matrix_words, matrix)
matrix_group.arrange_submobjects(buff = MED_SMALL_BUFF)
matrix_group.to_edge(UP)
entries = matrix.get_entries()
self.play(Write(matrix_words), Write(matrix.get_brackets()))
for i, vect in enumerate([self.i_hat, self.j_hat]):
self.play(vect.rotate, np.pi/12, rate_func = wiggle)
self.play(Write(vect.words))
self.dither()
self.play(vect.words[1].copy().move_to, entries[i])
self.dither()
def cs_conception(self, creatures):
self.fade_all_but(creatures, 1)
physy, compy, mathy = creatures
title = TextMobject("Vectors $\\Leftrightarrow$ lists of numbers")
title.to_edge(UP)
vectors = VMobject(*map(matrix_to_mobject, [
[2, 1],
[5, 0, 0, -3],
[2.3, -7.1, 0.1],
]))
vectors.arrange_submobjects(RIGHT, buff = 1)
vectors.to_edge(LEFT)
self.play(
ApplyMethod(compy.change_mode, "sassy"),
Write(title, run_time = 1)
)
self.play(Write(vectors))
self.dither()
self.play(ApplyMethod(compy.change_mode, "pondering"))
self.house_example(vectors, title)
self.restore_creatures(creatures)
def series_of_videos(self, chapters):
icon = SVGMobject("video_icon")
icon.center()
icon.scale_to_fit_width(2*SPACE_WIDTH/12.)
icon.set_stroke(color = WHITE, width = 0)
icons = [icon.copy() for chapter in chapters.split()]
colors = Color(BLUE_A).range_to(BLUE_D, len(icons))
for icon, color in zip(icons, colors):
icon.set_fill(color, opacity = 1)
icons = VMobject(*icons)
icons.arrange_submobjects(RIGHT)
icons.to_edge(LEFT)
icons.shift(UP)
randy = Randolph()
randy.to_corner()
bubble = randy.get_bubble()
new_icons = icons.copy().scale(0.2)
bubble.position_mobject_inside(new_icons)
self.play(Transform(
chapters, icons,
path_arc = np.pi/2,
))
self.clear()
self.add(icons)
self.play(FadeIn(randy))
self.play(Blink(randy))
self.dither()
self.play(
ShowCreation(bubble),
Transform(icons, new_icons)
)
self.remove(icons)
bubble.make_green_screen()
self.dither()
def construct(self):
vect = Matrix(["x", "y"])
vect.get_entries().highlight(YELLOW)
rot_matrix = Matrix([[0, -1], [1, 0]])
rot_matrix.highlight(TEAL)
shear_matrix = Matrix([[1, 1], [0, 1]])
shear_matrix.highlight(PINK)
l_paren, r_paren = map(TexMobject, ["\\Big(", "\\Big)"])
for p in l_paren, r_paren:
p.scale_to_fit_height(1.4*vect.get_height())
long_way = VMobject(
shear_matrix, l_paren, rot_matrix, vect, r_paren
)
long_way.arrange_submobjects(buff = 0.1)
long_way.to_edge(LEFT).shift(UP)
equals = TexMobject("=").next_to(long_way, RIGHT)
comp_matrix = Matrix([[1, -1], [1, 0]])
comp_matrix.highlight_columns(X_COLOR, Y_COLOR)
vect_copy = vect.copy()
short_way = VMobject(comp_matrix, vect_copy)
short_way.arrange_submobjects(buff = 0.1)
short_way.next_to(equals, RIGHT)
pairs = [
(rot_matrix, "Rotation"),
(shear_matrix, "Shear"),
(comp_matrix, "Composition"),
]
for matrix, word in pairs:
brace = Brace(matrix)
text = TextMobject(word).next_to(brace, DOWN)
brace.highlight(matrix.get_color())
text.highlight(matrix.get_color())
matrix.add(brace, text)
comp_matrix.split()[-1].submobject_gradient_highlight(TEAL, PINK)
self.add(vect)
groups = [
[rot_matrix],
[l_paren, r_paren, shear_matrix],
[equals, comp_matrix, vect_copy],
]
for group in groups:
self.play(*map(Write, group))
self.dither()
self.play(*map(FadeOut, [l_paren, r_paren, vect, vect_copy]))
comp_matrix.add(equals)
matrices = VMobject(shear_matrix, rot_matrix, comp_matrix)
self.play(ApplyMethod(
matrices.arrange_submobjects, buff = 0.1,
aligned_edge = UP
))
self.dither()
arrow = Arrow(rot_matrix.get_right(), shear_matrix.get_left())
arrow.shift((rot_matrix.get_top()[1]+0.2)*UP)
words = TextMobject("Read right to left")
words.submobjects.reverse()
words.next_to(arrow, UP)
functions = TexMobject("f(g(x))")
functions.next_to(words, UP)
self.play(ShowCreation(arrow))
self.play(Write(words))
self.dither()
self.play(Write(functions))
self.dither()
def construct(self):
vect = Matrix(["x", "y"])
vect.get_entries().highlight(YELLOW)
rot_matrix = Matrix([[0, -1], [1, 0]])
rot_matrix.highlight(TEAL)
shear_matrix = Matrix([[1, 1], [0, 1]])
shear_matrix.highlight(PINK)
l_paren, r_paren = map(TexMobject, ["\\Big(", "\\Big)"])
for p in l_paren, r_paren:
p.scale_to_fit_height(1.4 * vect.get_height())
long_way = VMobject(shear_matrix, l_paren, rot_matrix, vect, r_paren)
long_way.arrange_submobjects(buff=0.1)
long_way.to_edge(LEFT).shift(UP)
equals = TexMobject("=").next_to(long_way, RIGHT)
comp_matrix = Matrix([[1, -1], [1, 0]])
comp_matrix.highlight_columns(X_COLOR, Y_COLOR)
vect_copy = vect.copy()
short_way = VMobject(comp_matrix, vect_copy)
short_way.arrange_submobjects(buff=0.1)
short_way.next_to(equals, RIGHT)
pairs = [
(rot_matrix, "Rotation"),
(shear_matrix, "Shear"),
(comp_matrix, "Composition"),
]
for matrix, word in pairs:
brace = Brace(matrix)
text = TextMobject(word).next_to(brace, DOWN)
brace.highlight(matrix.get_color())
text.highlight(matrix.get_color())
matrix.add(brace, text)
comp_matrix.split()[-1].submobject_gradient_highlight(TEAL, PINK)
self.add(vect)
groups = [
[rot_matrix],
[l_paren, r_paren, shear_matrix],
[equals, comp_matrix, vect_copy],
]
for group in groups:
self.play(*map(Write, group))
self.wait()
self.play(*map(FadeOut, [l_paren, r_paren, vect, vect_copy]))
comp_matrix.add(equals)
matrices = VMobject(shear_matrix, rot_matrix, comp_matrix)
self.play(
ApplyMethod(matrices.arrange_submobjects,
buff=0.1,
aligned_edge=UP))
self.wait()
arrow = Arrow(rot_matrix.get_right(), shear_matrix.get_left())
arrow.shift((rot_matrix.get_top()[1] + 0.2) * UP)
words = TextMobject("Read right to left")
words.submobjects.reverse()
words.next_to(arrow, UP)
functions = TexMobject("f(g(x))")
functions.next_to(words, UP)
self.play(ShowCreation(arrow))
self.play(Write(words))
self.wait()
self.play(Write(functions))
self.wait()
