mirror of
https://github.com/3b1b/manim.git
synced 2026-04-26 03:00:23 -04:00
AnalyzeFunctionWithTransformations
This commit is contained in:
Grant Sanderson
@@ -214,7 +214,8 @@ class NumberlineTransformationScene(ZoomedScene):
|
||||
sample_dots=None,
|
||||
local_sample_dots=None,
|
||||
target_coordinate_values=None,
|
||||
added_anims=None
|
||||
added_anims=None,
|
||||
**kwargs
|
||||
):
|
||||
zcbr_group = self.zoomed_camera_background_rectangle_group
|
||||
zcbr_anim = self.zoomed_camera_background_rectangle_anim
|
||||
@@ -260,21 +261,35 @@ class NumberlineTransformationScene(ZoomedScene):
|
||||
anims += added_anims
|
||||
anims.append(Animation(zcbr_group))
|
||||
|
||||
self.play(*anims)
|
||||
self.play(*anims, **kwargs)
|
||||
|
||||
# Zooming
|
||||
def zoom_in_on_input(self, x,
|
||||
local_sample_dots=None,
|
||||
local_coordinate_values=None,
|
||||
pop_out=True,
|
||||
first_added_anims=[],
|
||||
second_added_anims=[],
|
||||
first_added_anims=None,
|
||||
first_anim_kwargs=None,
|
||||
second_added_anims=None,
|
||||
second_anim_kwargs=None,
|
||||
zoom_factor=None,
|
||||
):
|
||||
|
||||
first_added_anims = first_added_anims or []
|
||||
first_anim_kwargs = first_anim_kwargs or {}
|
||||
second_added_anims = second_added_anims or []
|
||||
second_anim_kwargs = second_anim_kwargs or {}
|
||||
input_point = self.get_input_point(x)
|
||||
|
||||
# Decide how to move camera frame into place
|
||||
frame = self.zoomed_camera.frame
|
||||
movement = ApplyMethod(frame.move_to, input_point)
|
||||
frame.generate_target()
|
||||
frame.target.move_to(input_point)
|
||||
if zoom_factor:
|
||||
frame.target.scale_to_fit_height(
|
||||
self.zoomed_display.get_height() * zoom_factor
|
||||
)
|
||||
movement = MoveToTarget(frame)
|
||||
zcbr = self.zoomed_camera_background_rectangle
|
||||
zcbr_group = self.zoomed_camera_background_rectangle_group
|
||||
zcbr_anim = self.zoomed_camera_background_rectangle_anim
|
||||
@@ -323,14 +338,15 @@ class NumberlineTransformationScene(ZoomedScene):
|
||||
anims.append(Animation(zcbr_group))
|
||||
if not pop_out:
|
||||
self.activate_zooming(animate=False)
|
||||
self.play(*anims)
|
||||
self.play(*anims, **first_anim_kwargs)
|
||||
|
||||
if not self.zoom_activated and pop_out:
|
||||
self.activate_zooming(animate=False)
|
||||
added_anims = second_added_anims or []
|
||||
self.play(
|
||||
self.get_zoomed_display_pop_out_animation(),
|
||||
*added_anims
|
||||
*added_anims,
|
||||
**second_anim_kwargs
|
||||
)
|
||||
|
||||
def get_local_coordinates(self, line, *x_values, **kwargs):
|
||||
@@ -2264,50 +2280,731 @@ class GraphOnePlusOneOverX(GraphScene):
|
||||
"x_max": 6,
|
||||
"x_axis_width": 12,
|
||||
"y_min": -4,
|
||||
"y_max": 4,
|
||||
"y_max": 5,
|
||||
"y_axis_height": 8,
|
||||
"y_axis_label": None,
|
||||
"graph_origin": ORIGIN,
|
||||
"graph_origin": 0.5 * DOWN,
|
||||
"num_graph_anchor_points": 100,
|
||||
"func_graph_color": GREEN,
|
||||
"identity_graph_color": BLUE,
|
||||
}
|
||||
|
||||
def construct(self):
|
||||
self.add_title()
|
||||
self.setup_axes()
|
||||
self.draw_graphs()
|
||||
self.show_solutions()
|
||||
|
||||
def add_title(self):
|
||||
title = self.title = TexMobject(
|
||||
"\\text{Solve: }", "1 + \\frac{1}{x}", "=", "x",
|
||||
)
|
||||
title.set_color_by_tex("x", self.identity_graph_color, substring=False)
|
||||
title.set_color_by_tex("frac", self.func_graph_color)
|
||||
title.to_corner(UL)
|
||||
self.add(title)
|
||||
|
||||
def setup_axes(self):
|
||||
GraphScene.setup_axes(self)
|
||||
self.x_axis.add_numbers(*range(-6, 0) + range(1, 7))
|
||||
step = 2
|
||||
self.x_axis.add_numbers(*range(-6, 0, step) + range(step, 7, step))
|
||||
self.y_axis.label_direction = RIGHT
|
||||
self.y_axis.add_numbers(*range(-3, 0) + range(1, 4))
|
||||
self.y_axis.add_numbers(*range(-2, 0, step) + range(step, 4, step))
|
||||
|
||||
def draw_graphs(self):
|
||||
def draw_graphs(self, animate=True):
|
||||
lower_func_graph, upper_func_graph = func_graph = VGroup(*[
|
||||
self.get_graph(
|
||||
lambda x: 1.0 + 1.0 / x,
|
||||
x_min=x_min,
|
||||
x_max=x_max,
|
||||
color=BLUE,
|
||||
color=self.func_graph_color,
|
||||
)
|
||||
for x_min, x_max in (-10, -0.1), (0.1, 10)
|
||||
])
|
||||
func_graph_label = self.get_graph_label(
|
||||
func_graph.label = self.get_graph_label(
|
||||
upper_func_graph, "y = 1 + \\frac{1}{x}",
|
||||
x_val=6, direction=UP
|
||||
x_val=6, direction=UP,
|
||||
)
|
||||
|
||||
identity_graph = self.get_graph(
|
||||
lambda x: x, color=GREEN
|
||||
lambda x: x, color=self.identity_graph_color
|
||||
)
|
||||
identity_graph_label = self.get_graph_label(
|
||||
identity_graph.label = self.get_graph_label(
|
||||
identity_graph, "y = x",
|
||||
x_val=3, direction=UL, buff=SMALL_BUFF
|
||||
)
|
||||
# for label in func_graph_label, identity_graph_label:
|
||||
# label[:2].set_color(WHITE)
|
||||
|
||||
self.play(ShowCreation(func_graph))
|
||||
self.play(Write(func_graph_label))
|
||||
self.play(ShowCreation(identity_graph))
|
||||
self.play(Write(identity_graph_label))
|
||||
if animate:
|
||||
for graph in func_graph, identity_graph:
|
||||
self.play(
|
||||
ShowCreation(graph),
|
||||
Write(graph.label),
|
||||
run_time=2
|
||||
)
|
||||
self.wait()
|
||||
else:
|
||||
self.add(
|
||||
func_graph, func_graph.label,
|
||||
identity_graph, identity_graph.label,
|
||||
)
|
||||
|
||||
self.func_graph = func_graph
|
||||
self.identity_graph = identity_graph
|
||||
|
||||
def show_solutions(self):
|
||||
phi = 0.5 * (1 + np.sqrt(5))
|
||||
phi_bro = 0.5 * (1 - np.sqrt(5))
|
||||
|
||||
lines = VGroup()
|
||||
for num in phi, phi_bro:
|
||||
line = DashedLine(
|
||||
self.coords_to_point(num, 0),
|
||||
self.coords_to_point(num, num),
|
||||
color=WHITE
|
||||
)
|
||||
line_copy = line.copy()
|
||||
line.fade(0.5)
|
||||
line_anim = ShowCreationThenDestruction(
|
||||
line_copy,
|
||||
submobject_mode="lagged_start",
|
||||
run_time=2
|
||||
)
|
||||
line.continual_anim = CycleAnimation(line_anim)
|
||||
lines.add(line)
|
||||
|
||||
phi_line, phi_bro_line = lines
|
||||
|
||||
decimal_kwargs = {
|
||||
"num_decimal_places": 3,
|
||||
"show_ellipsis": True,
|
||||
"color": YELLOW,
|
||||
}
|
||||
arrow_kwargs = {
|
||||
"buff": SMALL_BUFF,
|
||||
"color": WHITE,
|
||||
"tip_length": 0.15,
|
||||
"rectangular_stem_width": 0.025,
|
||||
}
|
||||
|
||||
phi_decimal = DecimalNumber(phi, **decimal_kwargs)
|
||||
phi_decimal.next_to(phi_line, DOWN, LARGE_BUFF)
|
||||
phi_arrow = Arrow(
|
||||
phi_decimal[:4].get_top(), phi_line.get_bottom(),
|
||||
**arrow_kwargs
|
||||
)
|
||||
|
||||
phi_bro_decimal = DecimalNumber(phi_bro, **decimal_kwargs)
|
||||
phi_bro_decimal.next_to(phi_bro_line, UP, LARGE_BUFF)
|
||||
phi_bro_decimal.shift(0.5 * LEFT)
|
||||
phi_bro_arrow = Arrow(
|
||||
phi_bro_decimal[:6].get_bottom(), phi_bro_line.get_top(),
|
||||
**arrow_kwargs
|
||||
)
|
||||
|
||||
brother_words = TextMobject(
|
||||
"$\\varphi$'s little brother",
|
||||
tex_to_color_map={"$\\varphi$": YELLOW},
|
||||
arg_separator=""
|
||||
)
|
||||
brother_words.next_to(
|
||||
phi_bro_decimal[-2], UP, buff=MED_SMALL_BUFF,
|
||||
aligned_edge=RIGHT
|
||||
)
|
||||
|
||||
self.add(phi_line.continual_anim)
|
||||
self.play(ShowCreation(phi_line))
|
||||
self.play(
|
||||
Write(phi_decimal),
|
||||
GrowArrow(phi_arrow),
|
||||
)
|
||||
self.wait(4)
|
||||
self.add(phi_bro_line.continual_anim)
|
||||
self.play(ShowCreation(phi_bro_line))
|
||||
self.play(
|
||||
Write(phi_bro_decimal),
|
||||
GrowArrow(phi_bro_arrow),
|
||||
)
|
||||
self.wait(4)
|
||||
self.play(Write(brother_words))
|
||||
self.wait(8)
|
||||
|
||||
|
||||
class NumericalPlayFromOne(ExternallyAnimatedScene):
|
||||
pass
|
||||
|
||||
|
||||
class NumericalPlayFromTau(ExternallyAnimatedScene):
|
||||
pass
|
||||
|
||||
|
||||
class NumericalPlayFromNegPhi(ExternallyAnimatedScene):
|
||||
pass
|
||||
|
||||
|
||||
class NumericalPlayOnNumberLineFromOne(Scene):
|
||||
CONFIG = {
|
||||
"starting_value": 1,
|
||||
"n_jumps": 10,
|
||||
"func": lambda x: 1 + 1.0 / x,
|
||||
"number_line_config": {
|
||||
"x_min": 0,
|
||||
"x_max": 2,
|
||||
"unit_size": 6,
|
||||
"tick_frequency": 0.25,
|
||||
"numbers_with_elongated_ticks": [0, 1, 2]
|
||||
}
|
||||
}
|
||||
|
||||
def construct(self):
|
||||
self.add_number_line()
|
||||
self.add_phi_label()
|
||||
self.add_title()
|
||||
self.bounce_around()
|
||||
|
||||
def add_number_line(self):
|
||||
number_line = NumberLine(**self.number_line_config)
|
||||
number_line.move_to(2 * DOWN)
|
||||
number_line.add_numbers()
|
||||
|
||||
self.add(number_line)
|
||||
self.number_line = number_line
|
||||
|
||||
def add_phi_label(self):
|
||||
number_line = self.number_line
|
||||
phi_point = number_line.number_to_point(
|
||||
(1 + np.sqrt(5)) / 2
|
||||
)
|
||||
phi_dot = Dot(phi_point, color=YELLOW)
|
||||
arrow = Vector(DL)
|
||||
arrow.next_to(phi_point, UR, SMALL_BUFF)
|
||||
phi_label = TexMobject("\\varphi = 1.618\\dots")
|
||||
phi_label.set_color(YELLOW)
|
||||
phi_label.next_to(arrow.get_start(), UP, SMALL_BUFF)
|
||||
|
||||
self.add(phi_dot, phi_label, arrow)
|
||||
|
||||
def add_title(self):
|
||||
title = TexMobject("x \\rightarrow 1 + \\frac{1}{x}")
|
||||
title.to_corner(UL)
|
||||
self.add(title)
|
||||
|
||||
def bounce_around(self):
|
||||
number_line = self.number_line
|
||||
value = self.starting_value
|
||||
point = number_line.number_to_point(value)
|
||||
dot = Dot(point)
|
||||
dot.set_fill(RED, opacity=0.8)
|
||||
arrow = Vector(DR)
|
||||
arrow.next_to(point, UL, buff=SMALL_BUFF)
|
||||
arrow.match_color(dot)
|
||||
start_here = TextMobject("Start here")
|
||||
start_here.next_to(arrow.get_start(), UP, SMALL_BUFF)
|
||||
start_here.match_color(dot)
|
||||
|
||||
self.play(
|
||||
FadeIn(start_here),
|
||||
GrowArrow(arrow),
|
||||
GrowFromPoint(dot, arrow.get_start())
|
||||
)
|
||||
self.play(
|
||||
FadeOut(start_here),
|
||||
FadeOut(arrow)
|
||||
)
|
||||
self.wait()
|
||||
for x in range(self.n_jumps):
|
||||
new_value = self.func(value)
|
||||
new_point = number_line.number_to_point(new_value)
|
||||
if new_value - value > 0:
|
||||
path_arc = -120 * DEGREES
|
||||
else:
|
||||
path_arc = -120 * DEGREES
|
||||
arc = Line(
|
||||
point, new_point,
|
||||
path_arc=path_arc,
|
||||
buff=SMALL_BUFF
|
||||
)
|
||||
self.play(
|
||||
ShowCreationThenDestruction(arc, run_time=1.5),
|
||||
ApplyMethod(
|
||||
dot.move_to, new_point,
|
||||
path_arc=path_arc
|
||||
),
|
||||
)
|
||||
self.wait(0.5)
|
||||
|
||||
value = new_value
|
||||
point = new_point
|
||||
|
||||
|
||||
class NumericalPlayOnNumberLineFromTau(NumericalPlayOnNumberLineFromOne):
|
||||
CONFIG = {
|
||||
"starting_value": TAU,
|
||||
"number_line_config": {
|
||||
"x_min": 0,
|
||||
"x_max": 7,
|
||||
"unit_size": 2,
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
class NumericalPlayOnNumberLineFromMinusPhi(NumericalPlayOnNumberLineFromOne):
|
||||
CONFIG = {
|
||||
"starting_value": -0.61803,
|
||||
"number_line_config": {
|
||||
"x_min": -3,
|
||||
"x_max": 3,
|
||||
"unit_size": 2,
|
||||
"tick_frequency": 0.25,
|
||||
},
|
||||
"n_jumps": 25,
|
||||
}
|
||||
|
||||
def add_phi_label(self):
|
||||
NumericalPlayOnNumberLineFromOne.add_phi_label(self)
|
||||
number_line = self.number_line
|
||||
new_point = number_line.number_to_point(
|
||||
(1 - np.sqrt(5)) / 2
|
||||
)
|
||||
arrow = Vector(DR)
|
||||
arrow.next_to(new_point, UL, SMALL_BUFF)
|
||||
arrow.set_color(RED)
|
||||
new_label = TexMobject("-\\frac{1}{\\varphi} = -0.618\\dots")
|
||||
new_label.set_color(RED)
|
||||
new_label.next_to(arrow.get_start(), UP, SMALL_BUFF)
|
||||
new_label.shift(RIGHT)
|
||||
self.add(new_label, arrow)
|
||||
|
||||
|
||||
class RepeatedApplicationGraphically(GraphOnePlusOneOverX, PiCreatureScene):
|
||||
CONFIG = {
|
||||
"starting_value": 1,
|
||||
"n_jumps": 5,
|
||||
"n_times_to_show_identity_property": 2,
|
||||
}
|
||||
|
||||
def setup(self):
|
||||
GraphOnePlusOneOverX.setup(self)
|
||||
PiCreatureScene.setup(self)
|
||||
|
||||
def construct(self):
|
||||
self.setup_axes()
|
||||
self.draw_graphs(animate=False)
|
||||
self.draw_spider_web()
|
||||
|
||||
def create_pi_creature(self):
|
||||
randy = Randolph(height=2)
|
||||
randy.flip()
|
||||
randy.to_corner(DR)
|
||||
return randy
|
||||
|
||||
def get_new_randy_mode(self):
|
||||
randy = self.pi_creature
|
||||
if not hasattr(self, "n_mode_changes"):
|
||||
self.n_mode_changes = 0
|
||||
else:
|
||||
self.n_mode_changes += 1
|
||||
if self.n_mode_changes % 3 != 0:
|
||||
return randy.get_mode()
|
||||
return random.choice([
|
||||
"confused",
|
||||
"erm",
|
||||
"maybe"
|
||||
])
|
||||
|
||||
def draw_spider_web(self):
|
||||
randy = self.pi_creature
|
||||
func = self.func_graph[0].underlying_function
|
||||
x_val = self.starting_value
|
||||
curr_output = 0
|
||||
dot = Dot(color=RED, fill_opacity=0.7)
|
||||
dot.move_to(self.coords_to_point(x_val, curr_output))
|
||||
|
||||
self.play(FadeInAndShiftFromDirection(dot, 2 * UR))
|
||||
self.wait()
|
||||
|
||||
for n in range(self.n_jumps):
|
||||
new_output = func(x_val)
|
||||
func_graph_point = self.coords_to_point(x_val, new_output)
|
||||
id_graph_point = self.coords_to_point(new_output, new_output)
|
||||
v_line = DashedLine(dot.get_center(), func_graph_point)
|
||||
h_line = DashedLine(func_graph_point, id_graph_point)
|
||||
|
||||
curr_output = new_output
|
||||
x_val = new_output
|
||||
|
||||
for line in v_line, h_line:
|
||||
line_end = line.get_end()
|
||||
self.play(
|
||||
ShowCreation(line),
|
||||
dot.move_to, line_end,
|
||||
randy.change, self.get_new_randy_mode()
|
||||
)
|
||||
self.wait()
|
||||
|
||||
if n < self.n_times_to_show_identity_property:
|
||||
x_point = self.coords_to_point(new_output, 0)
|
||||
y_point = self.coords_to_point(0, new_output)
|
||||
lines = VGroup(*[
|
||||
Line(dot.get_center(), point)
|
||||
for point in x_point, y_point
|
||||
])
|
||||
lines.set_color(YELLOW)
|
||||
self.play(ShowCreationThenDestruction(
|
||||
lines, run_time=2
|
||||
))
|
||||
self.wait(0.25)
|
||||
|
||||
|
||||
class RepeatedApplicationGraphicallyFromNegPhi(RepeatedApplicationGraphically):
|
||||
CONFIG = {
|
||||
"starting_value": -0.61,
|
||||
"n_jumps": 13,
|
||||
"n_times_to_show_identity_property": 0,
|
||||
}
|
||||
|
||||
|
||||
class LetsSwitchToTheTransformationalView(TeacherStudentsScene):
|
||||
def construct(self):
|
||||
self.teacher_says(
|
||||
"Lose the \\\\ graphs!",
|
||||
target_mode="hooray"
|
||||
)
|
||||
self.change_student_modes("hooray", "erm", "surprised")
|
||||
self.wait(5)
|
||||
|
||||
|
||||
class AnalyzeFunctionWithTransformations(NumberlineTransformationScene):
|
||||
CONFIG = {
|
||||
"input_line_zero_point": 0.5 * UP,
|
||||
"output_line_zero_point": 2 * DOWN,
|
||||
"func": lambda x: 1 + 1.0 / x,
|
||||
"num_initial_applications": 10,
|
||||
"num_repeated_local_applications": 7,
|
||||
"zoomed_display_width": 3.5,
|
||||
"zoomed_display_height": 2,
|
||||
"default_mapping_animation_config": {},
|
||||
}
|
||||
|
||||
def construct(self):
|
||||
self.add_function_title()
|
||||
self.repeatedly_apply_function()
|
||||
self.show_phi_and_phi_bro()
|
||||
self.zoom_in_on_phi()
|
||||
self.zoom_in_on_phi_bro()
|
||||
|
||||
def setup_number_lines(self):
|
||||
NumberlineTransformationScene.setup_number_lines(self)
|
||||
for line in self.input_line, self.output_line:
|
||||
VGroup(line.main_line, line.tick_marks).set_stroke(width=2)
|
||||
|
||||
def add_function_title(self):
|
||||
title = TexMobject("f(x)", "=", "1 + \\frac{1}{x}")
|
||||
title.to_edge(UP)
|
||||
self.add(title)
|
||||
self.title = title
|
||||
|
||||
def repeatedly_apply_function(self):
|
||||
input_zero_point = self.input_line.number_to_point(0)
|
||||
output_zero_point = self.output_line.number_to_point(0)
|
||||
sample_dots = self.get_sample_dots(
|
||||
delta_x=0.05,
|
||||
dot_radius=0.05,
|
||||
x_min=-10,
|
||||
x_max=10,
|
||||
)
|
||||
sample_dots.set_stroke(BLACK, 0.5)
|
||||
point_func = self.number_func_to_point_func(self.func)
|
||||
arrows = VGroup(*[
|
||||
Arrow(
|
||||
c, point_func(c), buff=SMALL_BUFF,
|
||||
rectangular_stem_width=0.02,
|
||||
tip_length=0.15
|
||||
)
|
||||
for c in map(Mobject.get_center, sample_dots)
|
||||
if np.linalg.norm(c - input_zero_point) > 0.3
|
||||
])
|
||||
arrows.set_fill(WHITE, 0.75)
|
||||
arrows.set_stroke(BLACK, 0.5)
|
||||
|
||||
self.play(LaggedStart(
|
||||
FadeInAndShiftFromDirection, sample_dots,
|
||||
lambda m: (m, UP)
|
||||
))
|
||||
self.play(LaggedStart(GrowArrow, arrows))
|
||||
self.wait()
|
||||
for x in range(self.num_initial_applications):
|
||||
self.apply_function(
|
||||
self.func,
|
||||
apply_function_to_number_line=False,
|
||||
sample_dots=sample_dots
|
||||
)
|
||||
self.wait()
|
||||
|
||||
shift_vect = input_zero_point - output_zero_point
|
||||
shift_vect[0] = 0
|
||||
lower_output_line = self.output_line.copy()
|
||||
upper_output_line = self.output_line.copy()
|
||||
lower_arrows = arrows.copy()
|
||||
upper_arrows = arrows.copy()
|
||||
lower_group = VGroup(lower_output_line, lower_arrows)
|
||||
lower_group.shift(-shift_vect)
|
||||
lower_group.fade(1)
|
||||
|
||||
self.remove(self.output_line, *arrows)
|
||||
self.play(
|
||||
ReplacementTransform(lower_arrows, arrows),
|
||||
ReplacementTransform(lower_output_line, self.output_line),
|
||||
upper_arrows.shift, shift_vect,
|
||||
upper_arrows.fade, 1,
|
||||
upper_output_line.shift, shift_vect,
|
||||
upper_output_line.fade, 1,
|
||||
sample_dots.shift, shift_vect,
|
||||
)
|
||||
self.remove(upper_output_line, upper_arrows)
|
||||
self.wait()
|
||||
self.play(FadeOut(sample_dots))
|
||||
|
||||
self.all_arrows = arrows
|
||||
|
||||
def show_phi_and_phi_bro(self):
|
||||
phi = (1 + np.sqrt(5)) / 2
|
||||
phi_bro = (1 - np.sqrt(5)) / 2
|
||||
|
||||
input_phi_point = self.input_line.number_to_point(phi)
|
||||
output_phi_point = self.output_line.number_to_point(phi)
|
||||
input_phi_bro_point = self.input_line.number_to_point(phi_bro)
|
||||
output_phi_bro_point = self.output_line.number_to_point(phi_bro)
|
||||
|
||||
tick = Line(UP, DOWN)
|
||||
tick.set_stroke(YELLOW, 3)
|
||||
tick.match_height(self.input_line.tick_marks)
|
||||
phi_tick = tick.copy().move_to(input_phi_point, DOWN)
|
||||
phi_bro_tick = tick.copy().move_to(input_phi_bro_point, DOWN)
|
||||
VGroup(phi_tick, phi_bro_tick).shift(SMALL_BUFF * DOWN)
|
||||
|
||||
phi_label = TexMobject("1.618\\dots")
|
||||
phi_label.next_to(phi_tick, UP)
|
||||
phi_bro_label = TexMobject("-0.618\\dots")
|
||||
phi_bro_label.next_to(phi_bro_tick, UP)
|
||||
VGroup(phi_label, phi_bro_label).set_color(YELLOW)
|
||||
|
||||
arrow_kwargs = {
|
||||
"buff": SMALL_BUFF,
|
||||
"rectangular_stem_width": 0.035,
|
||||
"tip_length": 0.2,
|
||||
}
|
||||
phi_arrow = Arrow(phi_tick, output_phi_point, **arrow_kwargs)
|
||||
phi_bro_arrow = Arrow(phi_bro_tick, output_phi_bro_point, **arrow_kwargs)
|
||||
|
||||
self.play(
|
||||
LaggedStart(
|
||||
ApplyMethod, self.all_arrows,
|
||||
lambda m: (m.set_fill, {"opacity": 0.1})
|
||||
),
|
||||
FadeIn(phi_arrow),
|
||||
FadeIn(phi_bro_arrow),
|
||||
)
|
||||
self.play(
|
||||
Write(phi_label),
|
||||
GrowFromCenter(phi_tick)
|
||||
)
|
||||
self.play(
|
||||
Write(phi_bro_label),
|
||||
GrowFromCenter(phi_bro_tick)
|
||||
)
|
||||
|
||||
self.set_variables_as_attrs(
|
||||
input_phi_point, output_phi_point,
|
||||
input_phi_bro_point, output_phi_bro_point,
|
||||
phi_label, phi_tick,
|
||||
phi_bro_label, phi_bro_tick,
|
||||
phi_arrow, phi_bro_arrow
|
||||
)
|
||||
|
||||
def zoom_in_on_phi(self):
|
||||
phi = (1 + np.sqrt(5)) / 2
|
||||
# phi_point = self.get_input_point(phi)
|
||||
local_sample_dots = self.get_local_sample_dots(
|
||||
phi, dot_radius=0.005, sample_radius=1
|
||||
)
|
||||
local_coordinate_values = [1.55, 1.6, 1.65, 1.7]
|
||||
|
||||
# zcbr = self.zoomed_camera_background_rectangle
|
||||
zcbr_group = self.zoomed_camera_background_rectangle_group
|
||||
zcbr_group.add(self.phi_tick)
|
||||
|
||||
title = self.title
|
||||
deriv_text = TexMobject(
|
||||
"|", "\\frac{df}{dx}(\\varphi)", "|", "< 1",
|
||||
tex_to_color_map={"\\varphi": YELLOW}
|
||||
)
|
||||
deriv_text.get_parts_by_tex("|").match_height(
|
||||
deriv_text, stretch=True
|
||||
)
|
||||
deriv_text.move_to(title, UP)
|
||||
approx_value = TexMobject("\\approx |%.2f|" % (-1 / phi**2))
|
||||
approx_value.move_to(deriv_text)
|
||||
deriv_text_lhs = deriv_text[:-1]
|
||||
deriv_text_rhs = deriv_text[-1]
|
||||
|
||||
self.zoom_in_on_input(
|
||||
phi,
|
||||
local_sample_dots=local_sample_dots,
|
||||
local_coordinate_values=local_coordinate_values
|
||||
)
|
||||
self.wait()
|
||||
self.apply_function(
|
||||
self.func,
|
||||
apply_function_to_number_line=False,
|
||||
local_sample_dots=local_sample_dots,
|
||||
target_coordinate_values=local_coordinate_values,
|
||||
)
|
||||
self.wait()
|
||||
self.play(
|
||||
FadeInFromDown(deriv_text_lhs),
|
||||
FadeInFromDown(deriv_text_rhs),
|
||||
title.to_corner, UL
|
||||
)
|
||||
self.wait()
|
||||
self.play(
|
||||
deriv_text_lhs.next_to, approx_value, LEFT,
|
||||
deriv_text_rhs.next_to, approx_value, RIGHT,
|
||||
FadeIn(approx_value)
|
||||
)
|
||||
self.wait()
|
||||
for n in range(self.num_repeated_local_applications):
|
||||
self.apply_function(
|
||||
self.func,
|
||||
apply_function_to_number_line=False,
|
||||
local_sample_dots=local_sample_dots,
|
||||
path_arc=60 * DEGREES,
|
||||
run_time=2
|
||||
)
|
||||
|
||||
self.deriv_text = VGroup(
|
||||
deriv_text_lhs, deriv_text_rhs, approx_value
|
||||
)
|
||||
|
||||
def zoom_in_on_phi_bro(self):
|
||||
zcbr = self.zoomed_camera_background_rectangle
|
||||
# zcbr_group = self.zoomed_camera_background_rectangle_group
|
||||
zoomed_frame = self.zoomed_camera.frame
|
||||
|
||||
phi_bro = (1 - np.sqrt(5)) / 2
|
||||
# phi_bro_point = self.get_input_point(phi_bro)
|
||||
local_sample_dots = self.get_local_sample_dots(phi_bro)
|
||||
local_coordinate_values = [-0.65, -0.6, -0.55]
|
||||
|
||||
deriv_text = TexMobject(
|
||||
"\\left| \\frac{df}{dx}\\left(\\frac{-1}{\\varphi}\\right) \\right|",
|
||||
"\\approx |%.2f|" % (-1 / (phi_bro**2)),
|
||||
"> 1"
|
||||
)
|
||||
deriv_text.move_to(self.deriv_text, UL)
|
||||
deriv_text[0][10:14].set_color(YELLOW)
|
||||
|
||||
self.play(
|
||||
zoomed_frame.scale_to_fit_height, 4,
|
||||
zoomed_frame.center,
|
||||
self.deriv_text.fade, 1,
|
||||
run_time=2
|
||||
)
|
||||
self.wait()
|
||||
zcbr.set_fill(opacity=0)
|
||||
self.zoom_in_on_input(
|
||||
phi_bro,
|
||||
local_sample_dots=local_sample_dots,
|
||||
local_coordinate_values=local_coordinate_values,
|
||||
zoom_factor=self.zoom_factor,
|
||||
first_anim_kwargs={"run_time": 2},
|
||||
)
|
||||
self.wait()
|
||||
self.play(FadeInFromDown(deriv_text))
|
||||
self.wait()
|
||||
zcbr.set_fill(opacity=1)
|
||||
self.apply_function(
|
||||
self.func,
|
||||
apply_function_to_number_line=False,
|
||||
local_sample_dots=local_sample_dots,
|
||||
target_coordinate_values=local_coordinate_values,
|
||||
)
|
||||
self.wait()
|
||||
for n in range(self.num_repeated_local_applications):
|
||||
self.apply_function(
|
||||
self.func,
|
||||
apply_function_to_number_line=False,
|
||||
local_sample_dots=local_sample_dots,
|
||||
path_arc=20 * DEGREES,
|
||||
run_time=2,
|
||||
)
|
||||
|
||||
|
||||
class StabilityAndInstability(AnalyzeFunctionWithTransformations):
|
||||
CONFIG = {
|
||||
"num_initial_applications": 0,
|
||||
}
|
||||
def construct(self):
|
||||
self.force_skipping()
|
||||
self.add_function_title()
|
||||
self.repeatedly_apply_function()
|
||||
self.show_phi_and_phi_bro()
|
||||
self.revert_to_original_skipping_status()
|
||||
|
||||
self.label_stability()
|
||||
|
||||
def label_stability(self):
|
||||
self.title.to_corner(UL)
|
||||
|
||||
stable_label = TextMobject("Stable fixed point")
|
||||
unstable_label = TextMobject("Unstable fixed point")
|
||||
labels = VGroup(stable_label, unstable_label)
|
||||
labels.scale(0.8)
|
||||
stable_label.next_to(self.phi_label, UP, aligned_edge=ORIGIN)
|
||||
unstable_label.next_to(self.phi_bro_label, UP, aligned_edge=ORIGIN)
|
||||
|
||||
phi_point = self.input_phi_point
|
||||
phi_bro_point = self.input_phi_bro_point
|
||||
|
||||
arrow_groups = VGroup()
|
||||
for point in phi_point, phi_bro_point:
|
||||
arrows = VGroup(*filter(
|
||||
lambda a: np.linalg.norm(a.get_start() - point) < 0.75,
|
||||
self.all_arrows
|
||||
)).copy()
|
||||
arrows.set_fill(PINK, 1)
|
||||
arrows.second_anim = LaggedStart(
|
||||
ApplyMethod, arrows,
|
||||
lambda m: (m.set_fill, YELLOW, 1),
|
||||
rate_func=there_and_back_with_pause,
|
||||
lag_ratio=0.7,
|
||||
run_time=2,
|
||||
)
|
||||
arrows.anim = AnimationGroup(*map(GrowArrow, arrows))
|
||||
arrow_groups.add(arrows)
|
||||
phi_arrows, phi_bro_arrows = arrow_groups
|
||||
|
||||
self.add_foreground_mobjects(self.phi_arrow, self.phi_bro_arrow)
|
||||
self.play(
|
||||
Write(stable_label),
|
||||
phi_arrows.anim,
|
||||
)
|
||||
self.play(phi_arrows.second_anim)
|
||||
self.play(
|
||||
Write(unstable_label),
|
||||
phi_bro_arrows.anim,
|
||||
)
|
||||
self.play(phi_bro_arrows.second_anim)
|
||||
self.wait()
|
||||
|
||||
|
||||
class NotBetterThanGraphs(TeacherStudentsScene):
|
||||
def construct(self):
|
||||
self.student_says(
|
||||
"Um, yeah, I'll stick \\\\ with graphs thanks",
|
||||
target_mode="sassy",
|
||||
)
|
||||
self.play(
|
||||
self.teacher.change, "guilty",
|
||||
self.get_student_changes("sad", "sassy", "hesitant")
|
||||
)
|
||||
self.wait(2)
|
||||
|
||||
Reference in New Issue
Block a user