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from manimlib.imports import *
import numpy as np
import math
class graph1(GraphScene):
CONFIG = {
"x_min": -3,
"x_max": 5,
"y_min": -1,
"y_max": 1,
"graph_origin": ORIGIN,
"function_color": RED,
"axes_color": BLUE,
"x_axis_label": "$n$",
"y_axis_label": "$x(n)$",
"x_labeled_nums": range(-3, 6, 1),
"y_axis_height": 7,
"y_tick_frequency": 0.1,
}
def func(self,x,n):
summ=0
for i in range(n+1):
summ+=(1/(math.pow(x,i)))
return summ
def finalFunc(self,x):
if(x!=0):
return 1/(1-(1/(2*x)))
def construct(self):
x_each_unit = self.x_axis_width / (self.x_max - self.x_min)
y_each_unit = self.y_axis_height / (self.y_max - self.y_min)
self.setup_axes(animate=True,scalee=0.8)
function=TextMobject("$X(t)=\sum _{ n=0 }^{ \infty }{ { (0.5) }^{ n }{ z }^{ -n } }$").scale(0.4).shift(5*RIGHT+3*UP).set_color(RED)
self.play(FadeIn(function))
twoDGraph=[]
for i in range(5):
twoDGraph.append(Line(start=(i*x_each_unit,0,0),end=(i*x_each_unit,math.pow(0.5,i)*y_each_unit,0),color=GREEN))
groupGraph=VGroup(self.axes,twoDGraph[0],twoDGraph[1],twoDGraph[2],twoDGraph[3],twoDGraph[4])
self.play(Write(twoDGraph[0]),ShowCreation(twoDGraph[1]),ShowCreation(twoDGraph[2]),ShowCreation(twoDGraph[3]),ShowCreation(twoDGraph[4]))
self.wait(1.2)
self.play(ApplyMethod(groupGraph.scale,0.7))
self.play(ApplyMethod(groupGraph.shift,6*LEFT),ApplyMethod(function.move_to,5*LEFT+3*UP))
someText1=TextMobject("Since it is a","summation","of","infinite terms",", it might").shift(2*RIGHT+2*UP).scale(0.5).set_color_by_tex_to_color_map({"summation":YELLOW,"infinite terms":BLUE})
someText2=TextMobject("Converge","or","Diverge").shift(2*RIGHT+0.5*DOWN+2*UP).scale(0.7).set_color_by_tex_to_color_map({"Converge":GREEN,"Diverge":RED})
someText3=TextMobject("depending upon","$|z|$").shift(2*RIGHT+UP).scale(0.5).set_color_by_tex_to_color_map({"$|z|$":YELLOW})
self.play(Write(someText1))
self.play(FadeIn(someText2))
self.play(Write(someText3))
self.wait(1)
self.play(FadeOut(someText1),FadeOut(someText2),FadeOut(someText3))
self.graph_origin=2*RIGHT+DOWN
self.x_axis_width=6
self.y_axis_height=5
self.y_tick_frequency=1
self.x_axis_label="$|z|$"
self.y_axis_label="$|X(n)|$"
self.x_min=-3
self.x_max=5
self.y_min=-1
self.y_max=5
self.x_labeled_nums=range(-3,6,1)
self.setup_axes(animate=True,scalee=0.6)
x_each_unit = self.x_axis_width / (self.x_max - self.x_min)
y_each_unit = self.y_axis_height / (self.y_max - self.y_min)
rightSideGraphs=[]
xmins=[0,0.25,0.65,0.9,1]
for i in range(5):
rightSideGraphs.append(self.get_graph(lambda x:self.func(x,i),x_min=xmins[i],x_max=5,color=GREEN))
rightSideGraphs.append(self.get_graph(lambda x:1/(1-(1/(2*x))),x_min=0.63,x_max=5,color=GREEN))
graphCoeff=[
TextMobject("$1$").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*2+0.65*UP*y_each_unit*2+DOWN*y_each_unit*0.5).set_color(RED),
TextMobject("$1+\\frac { 1 }{ 2|z| }$").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*2+UP*y_each_unit).set_color(RED),
TextMobject("$1+\\frac { 1 }{ 2|z| } +\\frac { 1 }{ { 2|z| }^{ 2 } } $").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*2+UP*y_each_unit).set_color(RED),
TextMobject("$1+\\frac { 1 }{ 2|z| } +\\frac { 1 }{ { (2|z|) }^{ 2 } } +\\frac { 1 }{ { (2|z|) }^{ 3 } }$").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*2+UP*y_each_unit).set_color(RED),
TextMobject("$1+\\frac { 1 }{ 2|z| } +\\frac { 1 }{ { (2|z|) }^{ 2 } } +\\frac { 1 }{ { (2|z|) }^{ 3 } } +\\frac { 1 }{ (2|z|)^{ 4 } } $").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*2+UP*y_each_unit).set_color(RED),
TextMobject("$\\frac { 1 }{ (1-\\frac { 1 }{ 2z } ) } $").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*2+UP*y_each_unit).set_color(RED)
]
self.play(ReplacementTransform(twoDGraph[0],rightSideGraphs[0]),FadeIn(graphCoeff[0]))
self.wait(0.5)
self.play(FadeOut(rightSideGraphs[0]),ReplacementTransform(twoDGraph[1],rightSideGraphs[1]),ReplacementTransform(graphCoeff[0],graphCoeff[1]))
self.wait(0.5)
self.play(FadeOut(rightSideGraphs[1]),ReplacementTransform(twoDGraph[2],rightSideGraphs[2]),ReplacementTransform(graphCoeff[1],graphCoeff[2]))
self.wait(0.5)
self.play(FadeOut(rightSideGraphs[2]),ReplacementTransform(twoDGraph[3],rightSideGraphs[3]),ReplacementTransform(graphCoeff[2],graphCoeff[3]))
self.wait(0.5)
self.play(FadeOut(rightSideGraphs[3]),ReplacementTransform(twoDGraph[4],rightSideGraphs[4]),ReplacementTransform(graphCoeff[3],graphCoeff[4]))
self.wait(0.5)
self.play(FadeOut(rightSideGraphs[4]),ShowCreation(rightSideGraphs[5]),ReplacementTransform(graphCoeff[4],graphCoeff[5]))
self.wait(2)
# #self.play(FadeOut(self.axes),FadeOut(function),FadeOut(twoDGraph[0]),FadeOut(twoDGraph[1]),FadeOut(twoDGraph[2]))
class graphCont(GraphScene,MovingCameraScene):
CONFIG = {
"x_min": -3,
"x_max": 5,
"y_min": -1,
"y_max": 5,
"graph_origin": 2*RIGHT+DOWN,
"function_color": RED,
"axes_color": BLUE,
"x_axis_label": "$|z|$",
"y_axis_label": "$|X(n)|$",
"x_labeled_nums": range(-3, 6, 1),
"x_axis_width": 6,
"y_axis_height": 5
}
def setup(self):
GraphScene.setup(self)
MovingCameraScene.setup(self)
def construct(self):
x_each_unit = self.x_axis_width / (self.x_max - self.x_min)
y_each_unit = self.y_axis_height / (self.y_max - self.y_min)
coeff=TextMobject("$\\frac { 1 }{ (1-\\frac { 1 }{ 2z } ) } $").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*2+UP*y_each_unit).set_color(RED)
self.setup_axes(scalee=0.6)
graph=self.get_graph(lambda x:1/(1-(1/(2*x))),x_min=0.63,x_max=5,color=GREEN)
self.add(graph)
self.add(coeff)
self.play(ApplyMethod((self.axes).shift,3*LEFT),ApplyMethod(coeff.shift,3*LEFT),ApplyMethod(graph.shift,3*LEFT))
self.wait(1)
dashLine=DashedLine(start=self.graph_origin+3*LEFT+0.5*x_each_unit*RIGHT,end=self.graph_origin+3*LEFT+0.5*x_each_unit*RIGHT+y_each_unit*UP*5,color=YELLOW)
pt=TextMobject("0.5").scale(0.3).shift(self.graph_origin+3*LEFT+0.5*x_each_unit*RIGHT+DOWN*y_each_unit*0.3)
self.play(Write(dashLine))
self.play(Write(pt))
self.wait(0.6)
rectRegion=Rectangle(height=y_each_unit*5,width=x_each_unit*5,fill_color=WHITE,fill_opacity=0.3,opacity=0.3,color=BLACK).shift(1.6*RIGHT*x_each_unit+0.5*DOWN*y_each_unit+1.5*UP)
self.play(ShowCreation(rectRegion))
text=TextMobject("Region Of Convergence!").scale(0.4).shift(4.6*RIGHT+1.5*UP).set_color(GREEN)
self.play(FadeIn(text))
self.wait(2)
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