diff options
Diffstat (limited to 'FSF-2020/series-and-transformations/Power Series/script3.py')
| -rw-r--r-- | FSF-2020/series-and-transformations/Power Series/script3.py | 156 |
1 files changed, 156 insertions, 0 deletions
diff --git a/FSF-2020/series-and-transformations/Power Series/script3.py b/FSF-2020/series-and-transformations/Power Series/script3.py new file mode 100644 index 0000000..f710f42 --- /dev/null +++ b/FSF-2020/series-and-transformations/Power Series/script3.py @@ -0,0 +1,156 @@ +from manimlib.imports import* +import math + +class intro(Scene): + def construct(self): + introText1=TextMobject("Let's analyse") + introText2=TextMobject("for") + function_main=TextMobject("$\sum { { (-1) }^{ n }{ x }^{ 2n } }$") + function_main.set_color(GREEN) + introText1.scale(1.2) + introText1.shift(2*UP) + introText2.scale(0.7) + introText2.shift(UP) + function_main.scale(2) + function_main.shift(DOWN) + function_expan=TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }+{ x }^{ 8 }+..$") + function_expan.set_color(RED) + function_expan.scale(1.2) + function_expan.shift(2*UP) + + self.play(Write(introText1)) + self.play(FadeIn(introText2)) + self.wait(0.5) + self.play(Write(function_main)) + self.wait(1) + + self.play(FadeOut(introText1),FadeOut(introText2)) + self.play(ApplyMethod(function_main.shift,3*UP)) + self.wait(0.5) + self.play(ReplacementTransform(function_main,function_expan)) + self.wait(1) + self.play(ApplyMethod(function_expan.scale,0.5)) + function_expan.to_edge(UP+RIGHT) + self.play(ReplacementTransform(function_expan,function_expan)) + self.wait(1) + + +class graphScene(GraphScene): + CONFIG = { + "x_min": -8, + "x_max": 8, + "y_min": -8, + "y_max": 8, + "graph_origin": ORIGIN, + "function_color": RED, + "axes_color": GREEN, + "x_axis_label": "$x$", + "y_axis_label": "$y$", + "exclude_zero_label": True, + "x_labeled_nums": range(-1, 2, 1), + "y_labeled_nums": range(0,2,1) + } + + 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) + + function_expan=TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }+{ x }^{ 8 }+..$") + function_expan.set_color(RED) + function_expan.scale(0.6) + function_expan.to_edge(UP+RIGHT) + self.add(function_expan) + + self.setup_axes(animate=True) + + eqText=[TextMobject("$1$"),TextMobject("$1-{ x }^{ 2 }$"),TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }$"),TextMobject("$1-{ x }^{ 2 }+{ x }^{ 4 }-{ x }^{ 6 }$")] + for i in range(0,len(eqText)): + eqText[i].scale(0.6) + eqText[i].set_color(BLUE) + eqText[i].shift(ORIGIN+UP*2*y_each_unit+RIGHT*3.3*x_each_unit) + eqTextTerm=TextMobject("And so on..!") + eqTextTerm.set_color(BLUE) + eqTextTerm.scale(0.6) + eqTextTerm.shift(ORIGIN+UP*2*y_each_unit+3*RIGHT*x_each_unit) + equation1 = self.get_graph(lambda x : 1,color = RED,x_min = -8,x_max=8) + equation2 = self.get_graph(lambda x : 1-math.pow(x,2),color = RED,x_min = -1.7,x_max=1.7) + equation3 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4),color = RED,x_min = -1.6,x_max=1.6) + equation4 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6),color = RED,x_min = -1.45,x_max=1.45) + equation5 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8),color = RED,x_min = -1.35,x_max=1.35) + equation6 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10),color = RED,x_min = -1.3,x_max=1.3) + equation7 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12),color = RED,x_min = -1.25,x_max=1.25) + equation8 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12)-math.pow(x,14),color = RED,x_min = -1.2,x_max=1.2) + equation9 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12)-math.pow(x,14)+math.pow(x,16),color = RED,x_min = -1.15,x_max=1.15) + equation10 = self.get_graph(lambda x : 1-math.pow(x,2)+math.pow(x,4)-math.pow(x,6)+math.pow(x,8)-math.pow(x,10)+math.pow(x,12)-math.pow(x,14)+math.pow(x,16)-math.pow(x,18),color = RED,x_min = -1.15,x_max=1.15) + + textBtwAnim1=TextMobject("Here the graph just","oscilates") + textBtwAnim1.set_color_by_tex_to_color_map({"oscilates":BLUE}) + textBtwAnim2=TextMobject("after","the","point","(as we add higher order terms)") + textBtwAnim2.set_color_by_tex_to_color_map({"after":BLUE,"point":YELLOW}) + textBtwAnim3=TextMobject("$x=1$") + textBtwAnim1.scale(0.4) + textBtwAnim2.scale(0.4) + textBtwAnim3.scale(1.2) + textBtwAnim1.shift(2.1*DOWN+4.3*RIGHT) + textBtwAnim2.shift(2.4*DOWN+4.1*RIGHT) + textBtwAnim3.shift(2.9*DOWN+4.3*RIGHT) + + self.play(ShowCreation(equation1),run_time=0.8) + self.add(eqText[0]) + self.wait(1) + self.play(ReplacementTransform(equation1,equation2),ReplacementTransform(eqText[0],eqText[1])) + self.wait(0.5) + self.play(ReplacementTransform(equation2,equation3),ReplacementTransform(eqText[1],eqText[2])) + self.wait(0.4) + self.play(ReplacementTransform(equation3,equation4),ReplacementTransform(eqText[2],eqText[3])) + self.wait(0.3) + self.play(FadeOut(eqText[3])) + self.play(FadeIn(eqTextTerm)) + self.play(Write(textBtwAnim1),Write(textBtwAnim2)) + self.play(FadeIn(textBtwAnim3)) + self.play(ReplacementTransform(equation4,equation5)) + self.wait(0.2) + self.play(ReplacementTransform(equation5,equation6)) + self.wait(0.2) + self.play(ReplacementTransform(equation6,equation7)) + self.wait(0.2) + self.play(ReplacementTransform(equation7,equation8)) + self.wait(0.2) + self.play(ReplacementTransform(equation8,equation9)) + self.wait(0.2) + self.play(ReplacementTransform(equation9,equation10)) + self.wait(1) + + self.play(FadeOut(textBtwAnim1),FadeOut(textBtwAnim2),FadeOut(textBtwAnim3),FadeOut(equation10),FadeOut(eqTextTerm)) + self.wait(1) + + convergeLine=Line(start=ORIGIN+x_each_unit*LEFT,end=ORIGIN+x_each_unit*RIGHT,color=WHITE) + divergeLineLeft=Line(start=ORIGIN+x_each_unit*LEFT,end=ORIGIN+x_each_unit*LEFT*8,color=RED) + divergeLineRight=Line(start=ORIGIN+x_each_unit*RIGHT,end=ORIGIN+x_each_unit*8*RIGHT,color=RED) + circle1=Circle(radius=0.01,color=PURPLE_E) + circle2=Circle(radius=0.01,color=PURPLE_E) + circle1.shift(ORIGIN+LEFT*x_each_unit) + circle2.shift(ORIGIN+RIGHT*x_each_unit) + convergeText=TextMobject("Converges") + divergeText1=TextMobject("Diverges") + divergeText2=TextMobject("Diverges") + convergeText.set_color(GREEN) + divergeText1.set_color(RED) + divergeText2.set_color(RED) + convergeText.scale(0.5) + divergeText1.scale(0.5) + divergeText2.scale(0.5) + convergeText.shift(1.6*UP) + divergeText1.shift(0.3*UP+1.5*LEFT) + divergeText2.shift(0.3*UP+1.5*RIGHT) + self.play(Write(divergeLineLeft),Write(divergeLineRight)) + self.play(FadeIn(convergeLine)) + self.wait(0.5) + self.play(FadeOut(self.axes)) + self.play(Write(circle1),Write(circle2)) + self.wait(0.5) + self.play(ApplyMethod(convergeLine.shift,1.3*UP),ApplyMethod(function_expan.shift,5*LEFT+DOWN)) + self.play(FadeIn(convergeText),FadeIn(divergeText1),FadeIn(divergeText2)) + self.wait(2) + |