a20200419-1.py

from manimlib.imports import *

class a20200419_1(Scene):
    def construct(self):

        SS = Tex("S")
        SS_u = Tex("u S")
        SS_d = Tex("d S")
        SS.scale(0.7).move_to(LEFT*6+UP*2.5)
        SS_u.scale(0.7).move_to(LEFT*5+UP*3.5)
        SS_d.scale(0.7).move_to(LEFT*5+UP*1.5)

        
        rr = Tex("1")
        rr_u = Tex("r")
        rr_d = Tex("r")
        rr.scale(0.7).move_to(LEFT*1+UP*2.5)
        rr_u.scale(0.7).move_to(RIGHT*0+UP*3.5)
        rr_d.scale(0.7).move_to(RIGHT*0+UP*1.5)

        CC = Tex("?")
        CC_u = Tex("C_u")
        CC_d = Tex("C_d")
        CC.scale(0.7).move_to(RIGHT*4+UP*2.5)
        CC_u.scale(0.7).move_to(RIGHT*5+UP*3.5)
        CC_d.scale(0.7).move_to(RIGHT*5+UP*1.5)

        self.play(
            Write(SS), Write(SS_u), Write(SS_d), 
            Write(rr), Write(rr_u), Write(rr_d),
            Write(CC), Write(CC_u), Write(CC_d))

        rect1 = Rectangle(height=2.5, width=1)
        rect1.set_color(YELLOW)
        rect1.move_to(LEFT*5+UP*2.5)
        self.play(ShowCreation(rect1))

        rect2 = Rectangle(height=2.5, width=1)
        rect2.set_color(RED)
        rect2.move_to(LEFT*0+UP*2.5)
        self.play(ShowCreation(rect2))

        rect3 = Rectangle(height=2.5, width=1)
        rect3.set_color(BLUE)
        rect3.move_to(RIGHT*5+UP*2.5)
        self.play(ShowCreation(rect3))

        formula_1 = Tex(r"""
            \begin{bmatrix} uS \\ \\ dS \end{bmatrix}
            \times
            \Delta
            +
            \begin{bmatrix} r \\ \\ r \end{bmatrix}
            \times
            B
            =
            \begin{bmatrix} C_u \\ \\ C_d \end{bmatrix} 
        """)
        
        formula_1.move_to(DOWN)
        self.play(Write(formula_1))
        self.wait(2)

        formula_2 = Tex(r"""
            \Delta 
            =
            {C_u - C_d 
            \over
            (u-d) S}
            ,
            \quad
            B
            =
            {u C_d - d C_u
            \over
            (u-d) r}
        """
        )
        formula_2.move_to(DOWN)
        self.play(Transform(formula_1, formula_2))
        self.wait(1)

        self.play(FadeOut(rect1), FadeOut(rect2), FadeOut(rect3))

        rect1 = Rectangle(height=1, width=1)
        rect1.set_color(YELLOW)
        rect1.move_to(LEFT*6+UP*2.5)
        self.play(ShowCreation(rect1))

        rect2 = Rectangle(height=1, width=1)
        rect2.set_color(RED)
        rect2.move_to(LEFT*1+UP*2.5)
        self.play(ShowCreation(rect2))

        rect3 = Rectangle(height=1, width=1)
        rect3.set_color(BLUE)
        rect3.move_to(RIGHT*4+UP*2.5)
        self.play(ShowCreation(rect3))

        self.play(Transform(formula_1, formula_2.move_to(UP).scale(0.5)))

        formula_3 = Tex(r"""
            C = S \times 
            \Delta
            +
            1
            \times
            B
        """)

        formula_3_1 = Tex(r"""
            C = S \times 
            \Delta
            +
            1
            \times
            B
        """)
        self.play(Write(formula_3.shift(DOWN)))
        self.wait(2)
        self.play(Transform(formula_3, formula_3_1.move_to(UP*0.5).scale(0.5)))

        formula_4 = Tex(r"""
            C = S \times 
            {C_u - C_d 
            \over
            (u-d) S}
            +
            1
            \times
            {u C_d - d C_u
            \over
            (u-d) r}
        """)
        self.play(Write(formula_4.shift(DOWN*1)))
        self.wait(2)

        formula_5 = Tex(r"""
            = 
            {1 \over r}
            \Big[
            C_u
            \Big(
            {r-d \over u-d}
            \Big)
            +
            C_d
            \Big(
            {u-r \over u-d}
            \Big)
            \Big]
        """)
        self.play(Write(formula_5.shift(DOWN*2.5)))
        self.wait(2)