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uniswap.py
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uniswap.py
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from manim import *
import numpy as np
from math import e
UNISWAP_PINK = ManimColor('#FE0079')
UNISWAP_GREEN = ManimColor('#00fe83')
UNISWAP_BLUE = ManimColor('#007bfe')
UNISWAP_ORANGE = ManimColor('#fe8300')
BG_COLOR = ManimColor('#0F0E17')
class PriceChange(MovingCameraScene):
def construct(self):
self.camera.background_color = BG_COLOR
self.camera.frame.save_state()
# +---------------+
# | UNISWAP INTRO |
# +---------------+
unilogo = SVGMobject("uni-logo.svg").scale(1.75)
self.wait()
self.play(Write(unilogo))
self.wait()
plotlim = 5
ax = Axes(
x_range=(0, plotlim, 1),
y_range=(0, plotlim, 1),
x_length=plotlim,
y_length=plotlim,
tips=False,
axis_config={"include_numbers": False},
x_axis_config={"include_ticks" : False},
y_axis_config={"include_ticks" : False},
)
xreserves = Tex("X reserves", color=WHITE).move_to(ax.c2p(plotlim/2,0)).shift(DOWN*0.5)
yreserves = Tex("Y reserves", color=WHITE).rotate(PI/2).move_to(ax.c2p(0,plotlim/2)).shift(LEFT*0.5)
reserves = VGroup(xreserves, yreserves)
curve = ax.plot(
lambda x: 1/x,
x_range=[0.2, plotlim],
use_smoothing=True,
color=UNISWAP_PINK
)
equation = MathTex("x\\cdot y = k", color=UNISWAP_PINK).move_to(ax.c2p(plotlim*0.65, plotlim*0.6))
vg1 = VGroup(curve, equation)
x = ValueTracker(1)
d1 = always_redraw(lambda: Dot(radius=0.15).set_color(BLUE_C).move_to(ax.c2p(x.get_value(), 1/x.get_value())))
chart_vg = VGroup(ax, vg1, reserves, unilogo, d1)
self.play(Write(ax), Write(xreserves), Write(yreserves))
self.play(Write(curve), Unwrite(unilogo), run_time=1.25)
self.play(Write(equation))
self.wait()
self.play(self.camera.frame.animate.scale(0.5).move_to(ax.c2p(1, 1.5)))
self.play(Write(d1))
self.play(Flash(d1, color=BLUE_C, line_length=0.1, flash_radius=0.1+SMALL_BUFF))
self.play(x.animate.set_value(0.35), rate_func=rate_functions.ease_in_out_cubic, run_time=1.25)
self.play(x.animate.set_value(3.5), rate_func=rate_functions.ease_in_out_cubic, run_time=1.25)
self.play(x.animate.set_value(1), rate_func=rate_functions.ease_in_out_cubic, run_time=1.25)
self.wait()
self.play(Restore(self.camera.frame), chart_vg.animate.move_to(ORIGIN).shift(LEFT*3))
self.wait()
# +-------------------+
# | NUMERICAL EXAMPLE |
# +-------------------+
dx_buy_dy_1 = MathTex("(x+dx)\\cdot(y-dy)", "=", "k").move_to(RIGHT*4 + UP*3).scale(0.75)
dx_buy_dy_2 = MathTex("xy-xdy+ydx-dxdy", "=", "k").move_to(dx_buy_dy_1).scale(0.75).shift(DOWN*0.5 + LEFT*0.4)
dx_buy_dy_3 = MathTex("xy+ydx-xdy-dxdy", "=", "k").move_to(dx_buy_dy_1).scale(0.75).shift(DOWN*1 + LEFT*0.4)
dx_buy_dy_4 = MathTex("y(x+dx)-dy(x+dx)", "=", "k").move_to(dx_buy_dy_1).scale(0.75).shift(DOWN*1.5 + LEFT*0.4)
dx_buy_dy_5 = MathTex("y(x+dx)", "=", "k + dy(x+dx)").move_to(dx_buy_dy_1).scale(0.75).shift(DOWN*2 + LEFT*0.4)
dx_buy_dy_6 = MathTex("y(x+dx) - k", "=", "dy(x+dx)").move_to(dx_buy_dy_1).scale(0.75).shift(DOWN*2.5 + LEFT*0.4)
dx_buy_dy_7 = MathTex("dy", "=", "y - \\frac{xy}{x+dx}").move_to(dx_buy_dy_1).scale(0.75).shift(DOWN*3.3)
dx_buy_dy_8 = MathTex("dy", "=", "y\\cdot\\underbrace{\\left(\\frac{x+dx}{x+dx}\\right)}_{1} - \\frac{xy}{x+dx}").move_to(dx_buy_dy_1).scale(0.75).shift(DOWN*4.7 + LEFT*0.6)
dx_buy_dy_9 = MathTex("dy", "=", "\\frac{yx+ydx-xy}{x+dx}").scale(0.75).move_to(dx_buy_dy_1).shift(DOWN*6.1)
dx_buy_dy_10 = MathTex("dy=\\frac{ydx}{x+dx}").scale(0.75).move_to(dx_buy_dy_1).shift(DOWN*2.25)
sr_10 = SurroundingRectangle(dx_buy_dy_10, color=UNISWAP_PINK, buff=0.15)
dx_buy_dy_11 = MathTex("dy","=","\\frac{y\cdot dx(1-\phi)}{x+dx(1-\phi)}").scale(0.75).move_to(dx_buy_dy_1).shift(DOWN*3.75)
sr_11 = SurroundingRectangle(dx_buy_dy_11, color=UNISWAP_PINK, buff=0.15)
self.play(TransformFromCopy(equation, dx_buy_dy_1))
self.play(TransformFromCopy(dx_buy_dy_1, dx_buy_dy_2))
self.play(TransformFromCopy(dx_buy_dy_2, dx_buy_dy_3))
self.play(TransformFromCopy(dx_buy_dy_3, dx_buy_dy_4))
self.play(TransformFromCopy(dx_buy_dy_4, dx_buy_dy_5))
self.play(TransformFromCopy(dx_buy_dy_5, dx_buy_dy_6))
self.play(TransformFromCopy(dx_buy_dy_6, dx_buy_dy_7))
self.play(TransformFromCopy(dx_buy_dy_7, dx_buy_dy_8))
self.play(TransformFromCopy(dx_buy_dy_8, dx_buy_dy_9), run_time=1.5)
self.wait()
self.play(
FadeOut(dx_buy_dy_2),
FadeOut(dx_buy_dy_3),
FadeOut(dx_buy_dy_4),
FadeOut(dx_buy_dy_5),
FadeOut(dx_buy_dy_6),
FadeOut(dx_buy_dy_7),
FadeOut(dx_buy_dy_8),
dx_buy_dy_9.animate.shift(UP*5.1)
)
self.play(TransformFromCopy(dx_buy_dy_9, dx_buy_dy_10))
self.play(Write(sr_10))
self.play(TransformFromCopy(dx_buy_dy_10, dx_buy_dy_11))
self.play(Transform(sr_10, sr_11))
self.wait()
self.play(
FadeOut(dx_buy_dy_9),
FadeOut(dx_buy_dy_10),
FadeOut(dx_buy_dy_1),
dx_buy_dy_11.animate.shift(UP*3.5+RIGHT*0.75),
sr_10.animate.shift(UP*3.55+RIGHT*0.75)
)
self.wait()
self.play(Unwrite(xreserves), Unwrite(yreserves))
self.play(chart_vg.animate.move_to(ORIGIN+DOWN*0.2).scale(1.25))
d1_border = Dot(stroke_width=4, fill_opacity=0, radius=0.15).set_color(BLUE_C).move_to(ax.c2p(1, 1))
self.add(d1_border)
# xline = always_redraw(lambda: DashedLine(ax.c2p(x.get_value(), 0), ax.c2p(x.get_value(),1/x.get_value()), color=BLUE_C))
xline = DashedLine(ax.c2p(x.get_value(), 0), ax.c2p(x.get_value(),1/x.get_value()), color=BLUE_C).add_updater(lambda m: m.put_start_and_end_on(ax.c2p(x.get_value(), 0), ax.c2p(x.get_value(),1/x.get_value())))
yline = DashedLine(ax.c2p(0,1/x.get_value()), ax.c2p(x.get_value(),1/x.get_value()), color=BLUE_C).add_updater(lambda m: m.put_start_and_end_on(ax.c2p(0,1/x.get_value()), ax.c2p(x.get_value(),1/x.get_value())))
xline0 = DashedLine(ax.c2p(x.get_value(), 0), ax.c2p(x.get_value(),1/x.get_value()), color=BLUE_C)
yline0 = DashedLine(ax.c2p(0,1/x.get_value()), ax.c2p(x.get_value(),1/x.get_value()), color=BLUE_C)
x_label = MathTex("x", color=BLUE_C).add_updater(lambda m: m.next_to(ax.c2p(x.get_value(), 0),DOWN))
y_label = MathTex("y", color=BLUE_C).add_updater(lambda m: m.next_to(ax.c2p(0, 1/x.get_value()),LEFT))
x0_label = MathTex("x_0", color=BLUE_C).move_to(ax.c2p(x.get_value(), 0)).shift(DOWN*0.35)
y0_label = MathTex("y_0", color=BLUE_C).move_to(ax.c2p(0, 1/x.get_value())).shift(LEFT*0.35)
labels_0 = VGroup(x0_label, y0_label)
self.remove(d1)
d1 = Dot(radius=0.15).set_color(BLUE_C).add_updater(lambda m: m.move_to(ax.c2p(x.get_value(), 1/x.get_value())))
self.add(d1)
self.play(Write(xline), Write(yline), Write(x_label), Write(y_label))
self.wait()
self.add(xline0)
self.add(yline0)
self.play(
x.animate.set_value(0.3).set_color(ORANGE),
x_label.animate.set_color(ORANGE),
y_label.animate.set_color(ORANGE),
xline.animate.set_color(ORANGE),
yline.animate.set_color(ORANGE),
d1.animate.set_color(ORANGE),
FadeIn(x0_label),
FadeIn(y0_label),
run_time=1.5,
rate_func=rate_functions.ease_in_out_cubic
)
dx_buy_dy_12 = MathTex("dy^{+}","=\\frac{y_0\cdot dx^{-}(1-\phi)}{x_0+dx^{-}(1-\phi)}").scale(0.75).move_to(dx_buy_dy_11).shift(LEFT*0.2)
sr_12 = SurroundingRectangle(dx_buy_dy_12, color=UNISWAP_PINK, buff=0.15)
x1_label = MathTex("x_1", color=ORANGE).move_to(ax.c2p(x.get_value(), 0)).shift(DOWN*0.35)
y1_label = MathTex("y_1", color=ORANGE).move_to(ax.c2p(0, 1/x.get_value())).shift(LEFT*0.35)
self.play(
TransformMatchingTex(x_label, x1_label),
TransformMatchingTex(y_label, y1_label),
)
self.wait()
self.play(Wiggle(labels_0), Wiggle(dx_buy_dy_11))
self.play(Transform(sr_10, sr_12), TransformMatchingTex(dx_buy_dy_11, dx_buy_dy_12))
dy_line = Line(ax.c2p(1,1), ax.c2p(1, 1/x.get_value()))
dx_line = Line(ax.c2p(x.get_value(), 1/x.get_value()), ax.c2p(1,1/x.get_value()))
dx_text = MathTex("dx^{-}").scale(0.75).add_updater(lambda m: m.next_to(dx_line, UP).shift(UP*0.5+RIGHT*0.15))
dy_text = MathTex("dy^{+}").scale(0.75).add_updater(lambda m: m.next_to(dy_line, RIGHT).shift(RIGHT*0.5))
brace_dx = BraceBetweenPoints(
ax.c2p(x.get_value(),1/x.get_value()),
ax.c2p(1,1/x.get_value()),
direction=UP
)
brace_dy = BraceBetweenPoints(
ax.c2p(1,1),
ax.c2p(1, 1/x.get_value()),
direction=RIGHT
)
self.play(Write(dy_line), Write(dx_line))
self.play(Write(brace_dx), Write(brace_dy), Write(dx_text), Write(dy_text))
self.play(FocusOn(dx_buy_dy_12[0]))
self.play(FocusOn(dy_text))
self.wait(3)
allGroup = VGroup(
chart_vg,
dx_buy_dy_12,
sr_12,
sr_10,
xline,
yline,
xline0,
yline0,
dy_line,
dx_line,
brace_dx,
brace_dy,
dx_text,
dy_text,
x1_label,
y1_label,
x0_label,
y0_label,
d1_border,
d1,
)
self.play(Unwrite(allGroup))
self.wait(2)
class ValueImpermanentLoss(MovingCameraScene):
def construct(self):
self.camera.background_color = BG_COLOR
self.camera.frame.save_state()
unilogo = SVGMobject("uni-logo.svg").scale(1.75)
self.wait()
self.play(Write(unilogo))
self.wait()
plotlim = 5
ax = Axes(
x_range=(0, plotlim, 1),
y_range=(0, plotlim, 1),
x_length=plotlim,
y_length=plotlim,
tips=False,
axis_config={"include_numbers": False},
x_axis_config={"include_ticks" : False},
y_axis_config={"include_ticks" : False},
)
curve = ax.plot(
lambda x: 1/x,
x_range=[0.2, plotlim],
use_smoothing=True,
color=UNISWAP_PINK
)
xreserves = Tex("X reserves", color=WHITE).move_to(ax.c2p(plotlim/2,0)).shift(DOWN*0.5)
yreserves = Tex("Y reserves", color=WHITE).rotate(PI/2).move_to(ax.c2p(0,plotlim/2)).shift(LEFT*0.5)
reserves = VGroup(xreserves, yreserves)
equation = MathTex("x","\\cdot","y","=", "k", color=UNISWAP_PINK).move_to(ax.c2p(plotlim*0.65, plotlim*0.6))
vg1 = VGroup(curve, equation)
x = ValueTracker(1)
d1 = always_redraw(lambda: Dot(radius=0.15).set_color(BLUE_C).move_to(ax.c2p(x.get_value(), 1/x.get_value())))
self.play(Write(ax), Write(xreserves), Write(yreserves))
self.play(Write(curve), Unwrite(unilogo), run_time=1.25)
self.play(Write(equation))
self.wait()
self.play(self.camera.frame.animate.scale(0.75).move_to(ax.c2p(1, 2)), Unwrite(xreserves), Unwrite(yreserves))
self.play(Write(d1))
d1_border = Dot(stroke_width=4, fill_opacity=0, radius=0.15).set_color(BLUE_C).move_to(ax.c2p(1, 1))
d1.z_index = 1
self.play(Flash(d1, color=BLUE_C, line_length=0.1, flash_radius=0.1+SMALL_BUFF))
# +-----------------+
# | PRICE ANIMATION |
# +-----------------+
xline = DashedLine(ax.c2p(x.get_value(), 0), ax.c2p(x.get_value(),1/x.get_value()), color=BLUE_C).add_updater(lambda m: m.put_start_and_end_on(ax.c2p(x.get_value(), 0), ax.c2p(x.get_value(),1/x.get_value())))
yline = DashedLine(ax.c2p(0,1/x.get_value()), ax.c2p(x.get_value(),1/x.get_value()), color=BLUE_C).add_updater(lambda m: m.put_start_and_end_on(ax.c2p(0,1/x.get_value()), ax.c2p(x.get_value(),1/x.get_value())))
xline0 = DashedLine(ax.c2p(x.get_value(), 0), ax.c2p(x.get_value(),1/x.get_value()), color=BLUE_C)
yline0 = DashedLine(ax.c2p(0,1/x.get_value()), ax.c2p(x.get_value(),1/x.get_value()), color=BLUE_C)
x_label = MathTex("x", color=BLUE_C).add_updater(lambda m: m.next_to(ax.c2p(x.get_value(), 0),DOWN))
y_label = MathTex("y", color=BLUE_C).add_updater(lambda m: m.next_to(ax.c2p(0, 1/x.get_value()),LEFT))
x0_label = MathTex("x_0", color=BLUE_C).move_to(ax.c2p(x.get_value(), 0)).shift(DOWN*0.35)
y0_label = MathTex("y_0", color=BLUE_C).move_to(ax.c2p(0, 1/x.get_value())).shift(LEFT*0.35)
new_d1 = Dot(radius=0.15).set_color(BLUE_C).add_updater(lambda m: m.move_to(ax.c2p(x.get_value(), 1/x.get_value())))
new_d1.z_index = 1
self.add(new_d1)
self.remove(d1)
self.play(Write(d1_border),Write(xline), Write(yline), Write(x_label), Write(y_label))
self.remove(d1)
self.wait()
self.add(xline0)
self.add(yline0)
self.play(
x.animate.set_value(0.3).set_color(ORANGE),
x_label.animate.set_color(ORANGE),
y_label.animate.set_color(ORANGE),
xline.animate.set_color(ORANGE),
yline.animate.set_color(ORANGE),
new_d1.animate.set_color(ORANGE),
FadeIn(x0_label),
FadeIn(y0_label),
run_time=1.5,
rate_func=rate_functions.ease_in_out_cubic
)
x1_label = MathTex("x_1", color=ORANGE).move_to(ax.c2p(x.get_value(), 0)).shift(DOWN*0.35)
y1_label = MathTex("y_1", color=ORANGE).move_to(ax.c2p(0, 1/x.get_value())).shift(LEFT*0.35)
self.play(
TransformMatchingTex(x_label, x1_label),
TransformMatchingTex(y_label, y1_label),
)
dy_line = Line(ax.c2p(1,1), ax.c2p(1, 1/x.get_value()))
dy_line.z_index = 0
dx_line = Line(ax.c2p(x.get_value(), 1/x.get_value()), ax.c2p(1, 1/x.get_value()))
dx_line.z_index = 0
brace_dx = Brace(
dx_line,
direction=UP
)
brace_dy = Brace(
dy_line,
direction=RIGHT
)
dx_text = MathTex("dx^{-}").scale(0.75).move_to(brace_dx).shift(UP*0.5+RIGHT*0.15)
dy_text = MathTex("dy^{+}").scale(0.75).move_to(brace_dy).shift(RIGHT*0.5)
self.play(Write(dy_line), Write(dx_line), Write(brace_dx), Write(brace_dy), Write(dx_text), Write(dy_text))
self.wait(2)
new_chart_vg = VGroup(ax, vg1, reserves, unilogo)
self.play(
Unwrite(new_d1),
Unwrite(x0_label),
Unwrite(y0_label),
FadeOut(xline),
Unwrite(yline),
Unwrite(xline0),
Unwrite(yline0),
Unwrite(d1_border),
Unwrite(x1_label),
Unwrite(y1_label),
Unwrite(dy_line), Unwrite(dx_line), Unwrite(brace_dx), Unwrite(brace_dy), Unwrite(dx_text), Unwrite(dy_text)
)
self.wait()
self.play(Restore(self.camera.frame), new_chart_vg.animate.move_to(ORIGIN).shift(LEFT*3))
# +-------+
# | CASES |
# +-------+
equation2 = MathTex("x","\\cdot","y","=", "L^2", color=UNISWAP_PINK).move_to(equation.get_center())
self.play(Transform(equation, equation2))
case_p = MathTex("P = \\frac{y}{x}", color=UNISWAP_PINK).scale(0.75)
case_0 = MathTex("x=\\frac{y}{P} = \\frac{L}{\\sqrt{P}}").scale(0.75)
case_1 = MathTex("y=L\\sqrt{P}").scale(0.75)
case_2 = MathTex("\\frac{y^2}{P} = L^2").scale(0.75)
cases = VGroup(case_p, case_0, case_1, case_2).arrange(DOWN, aligned_edge=LEFT)
cases_brace = Brace(cases, direction=LEFT)
cases_braced = VGroup(cases, cases_brace).move_to(ORIGIN).shift(RIGHT*3+UP)
self.play(Write(case_p))
self.play(TransformFromCopy(case_p, case_0))
self.play(TransformFromCopy(case_0, case_1))
self.play(TransformFromCopy(case_1, case_2))
self.play(Write(cases_brace))
self.wait()
self.play(new_chart_vg.animate.shift(UP*1.5+LEFT*1.5).scale(0.75), cases_braced.animate.shift(DOWN*3+LEFT*8.25).scale(0.75))
# +----------+
# | LP VALUE |
# +----------+
lp_value_1 = MathTex("V_{LP}(P) := ", "xP+y", color=UNISWAP_PINK).scale(0.75).move_to(ORIGIN + UP*3)
lp_value_2 = MathTex("= 2\\cdot y").scale(0.75)
lp_value_3 = MathTex("= 2\\cdot \\frac{k}{x}").scale(0.75)
lp_value_4 = MathTex("= 2\\cdot \\frac{L^2}{x}").scale(0.75)
lp_value_5 = MathTex("= 2\\cdot \\frac{L^2}{\\frac{y}{P}}").scale(0.75)
lp_value_6 = MathTex("= 2\\cdot \\frac{L^2\\cdot P}{y}").scale(0.75)
lp_values = VGroup(
lp_value_2,
lp_value_3,
lp_value_4,
lp_value_5,
lp_value_6
).arrange(DOWN, aligned_edge=LEFT).move_to(lp_value_1).shift(RIGHT*0.9 + DOWN*3)
lp_value_7 = MathTex("= 2\\cdot \\frac{L^2\\cdot P}{L\\cdot \\sqrt{P}}").scale(0.75)
lp_value_8 = MathTex("= 2L\\sqrt{P}").move_to(lp_value_1).scale(0.75)
self.play(TransformFromCopy(equation, lp_value_1))
self.play(TransformFromCopy(lp_value_1, lp_value_2))
self.play(TransformFromCopy(lp_value_2, lp_value_3))
self.play(TransformFromCopy(lp_value_3, lp_value_4))
self.play(TransformFromCopy(lp_value_4, lp_value_5))
self.play(TransformFromCopy(lp_value_5, lp_value_6))
self.wait()
self.play(lp_value_6.animate.move_to(lp_value_2).shift(DOWN*0.5+RIGHT*0.5), FadeOut(lp_value_2), FadeOut(lp_value_3), FadeOut(lp_value_4), FadeOut(lp_value_5))
lp_values_2 = VGroup(
lp_value_7,
lp_value_8
).arrange(DOWN, aligned_edge=LEFT).move_to(lp_value_6).shift(DOWN*1.5)
self.play(TransformFromCopy(lp_value_6, lp_value_7))
self.play(TransformFromCopy(lp_value_7, lp_value_8))
self.wait()
lp_value_final = MathTex("V_{LP}(P) := ","2L\\sqrt{P}").move_to(ORIGIN + UP*3).scale(0.75).set_color(UNISWAP_PINK)
self.play(Transform(lp_value_8, lp_value_final), FadeOut(lp_value_1), FadeOut(lp_value_7), FadeOut(lp_value_6))
self.play(Circumscribe(lp_value_final, color=UNISWAP_PINK))
self.wait()
# +--------------+
# | PRICE CHANGE |
# +--------------+
price_change_0 = MathTex("\\alpha := \\frac{P_T}{P_0}", color=UNISWAP_PINK).move_to(ORIGIN+UP*2+LEFT*0.75).scale(0.75)
price_change_1 = MathTex("\\sqrt{\\frac{P_T}{P_0}} = \\sqrt{\\alpha}").move_to(price_change_0).scale(0.75)
price_change_2 = MathTex("2L\\sqrt{P_T} = 2L\\sqrt{P_0}\\sqrt{\\alpha}").move_to(price_change_0).scale(0.75)
price_change_3 = MathTex("V_{LP}(P_T) = V_{LP}(P_0)\\sqrt{\\alpha}").move_to(price_change_0).scale(0.75)
price_change_4 = MathTex("V_T = V_0\\sqrt{\\alpha}").move_to(price_change_0).scale(0.75).shift(DOWN*2)
price_changes = VGroup(
price_change_1,
price_change_2,
price_change_3,
price_change_4
).arrange(DOWN, aligned_edge=LEFT).move_to(price_change_0).shift(RIGHT*1.2 + DOWN*2)
self.play(Write(price_change_0))
self.play(TransformFromCopy(price_change_0, price_change_1))
self.play(TransformFromCopy(price_change_1, price_change_2))
self.play(TransformFromCopy(price_change_2, price_change_3))
self.play(TransformFromCopy(price_change_3, price_change_4))
self.wait()
self.play(
price_change_4.animate.move_to(price_change_0).shift(RIGHT*0.3),
price_change_0.animate.shift(DOWN*2.9+LEFT*2.5).scale(0.75),
FadeOut(price_change_1), FadeOut(price_change_2),
FadeOut(price_change_3)
)
self.play(Circumscribe(price_change_4, color=UNISWAP_PINK), price_change_4.animate.set_color(UNISWAP_PINK))
# +------------+
# | VALUE HODL |
# +------------+
value_hodl_0 = MathTex("V_{HODL} = \\frac{V_0 + V_0 \\cdot \\alpha}{P} = L\\sqrt{P}(1+\\alpha)", color=UNISWAP_PINK).scale(0.75).move_to(lp_value_final).shift(DOWN*2+RIGHT*1.6)
self.play(Write(value_hodl_0))
self.wait()
self.remove(lp_value_1, lp_value_8)
self.play(
lp_value_final.animate.move_to(case_0).shift(RIGHT*0.225).scale(0.75),
FadeOut(case_0),
price_change_4.animate.move_to(case_1).shift(RIGHT*0.125).scale(0.75),
FadeOut(case_1),
value_hodl_0.animate.move_to(case_2).shift(RIGHT*1.775).scale(0.75),
FadeOut(case_2),
)
# +-------------+
# | LP VS. HODL |
# +-------------+
ax2 = Axes(
x_range=(0, plotlim/2, 0.1),
y_range=(0, plotlim/2-0.5, 0.1),
x_length=plotlim*1.5,
y_length=plotlim*0.5*1.5,
tips=False,
axis_config={"include_numbers": False},
x_axis_config={"include_ticks" : False},
y_axis_config={"include_ticks" : False},
).shift(RIGHT*3+UP*1.7)
alpha_label = MathTex("\\alpha").scale(0.75).move_to(ax2.c2p(plotlim/4, 0)).shift(DOWN*0.25)
value_label = Tex("value").scale(0.75).move_to(ax2.c2p(0, plotlim/4)).shift(LEFT*0.25).rotate(PI/2)
value_lp_curve = ax2.plot(
lambda x: np.sqrt(x),
x_range=[0.01, plotlim/2],
use_smoothing=True,
color=UNISWAP_ORANGE
)
value_hodl_curve = ax2.plot(
lambda x: (1+x)/2,
x_range=[0.01, plotlim/2],
use_smoothing=True,
color=UNISWAP_BLUE
)
value_0_constant = ax2.plot(
lambda x: 0,
x_range=[0.01, plotlim/2],
use_smoothing=True,
color=WHITE
)
value_impermanent_loss = ax2.plot(
lambda x: 2*np.sqrt(x)/(1+x)-1,
x_range=[0.01, plotlim/2],
use_smoothing=True,
color=WHITE
)
area = ax2.get_area(value_lp_curve, [0.01, 2.5], bounded_graph=value_hodl_curve, color=RED, opacity=1)
impermanent_loss_area = ax2.get_area(
value_impermanent_loss,
[0.01, 2.5],
bounded_graph=value_0_constant,
color=RED,
opacity=1
)
self.play(
Write(ax2),
Write(alpha_label),
Write(value_label)
)
self.play(lp_value_final.animate.set_color(UNISWAP_ORANGE))
self.play(ApplyWave(lp_value_final))
self.play(Create(value_lp_curve))
self.play(value_hodl_0.animate.set_color(UNISWAP_BLUE))
self.play(ApplyWave(value_hodl_0))
self.play(Create(value_hodl_curve))
self.play(Write(area), Unwrite(value_lp_curve), Unwrite(value_hodl_curve))
self.wait()
new_ax_group = VGroup(ax2, alpha_label, value_label, area)
old_ax_group = VGroup(ax, curve, equation)
self.play(FadeOut(old_ax_group), new_ax_group.animate.shift(LEFT*6.25+DOWN*0.25).scale(0.75))
# +------------------+
# | IMPERMANENT LOSS |
# +------------------+
il_0 = MathTex("IL(\\alpha) := \\frac{V_{LP} - V_{HODL}}{V_{HODL}}", color=UNISWAP_PINK).scale(0.75).shift(UP*2.25+RIGHT*3.5)
il_1 = MathTex("= \\frac{V_{LP}}{V_{HODL}}-1").scale(0.75)
il_2 = MathTex("= \\frac{V_0 \\sqrt{\\alpha}}{L\\sqrt{P}(1+\\alpha)}-1").scale(0.75)
il_3 = MathTex("= \\frac{2L\\sqrt{P}\\sqrt{\\alpha}}{L\\sqrt{P}(1+\\alpha)} - 1").scale(0.75)
il_4 = MathTex("= \\frac{2\\sqrt{\\alpha}}{1+\\alpha} - 1").scale(0.75)
il_final = MathTex("IL(\\alpha) := \\frac{2\\sqrt{\\alpha}}{1+\\alpha} - 1", color=UNISWAP_PINK).scale(0.75).move_to(il_0)
il_vgroup = VGroup(il_1, il_2, il_3, il_4).arrange(DOWN, aligned_edge=LEFT).move_to(il_0).shift(RIGHT*0.75+DOWN*3)
self.play(Write(il_0))
self.play(TransformFromCopy(il_0, il_1))
self.play(TransformFromCopy(il_1, il_2))
self.play(TransformFromCopy(il_2, il_3))
self.play(TransformFromCopy(il_3, il_4))
self.play(
FadeOut(il_0),
FadeOut(il_1),
FadeOut(il_2),
FadeOut(il_3),
Transform(il_4, il_final),
)
self.play(Circumscribe(il_final, color=RED_C), il_final.animate.set_color(RED_C))
self.play(lp_value_final.animate.set_color(WHITE), value_hodl_0.animate.set_color(WHITE))
self.wait(2)