Continued Fractions in Manim

[electrineer1]

Hello, can anyone provide tips on how a continued fraction could be displayed in manim? For example, I'd like to create the fraction f(z) = z + 1/(-z+1/(z+1/(-z+1/(z+1/(-z))))) where z is a complex variable whose magnitude and argument I would adjust during the animation. I would show the absolute magnitude of the result, so |f(z)|.

[uwezi]

sorry, but I don't understand what you want to animate here or how you want to present the result. Come over to Discord for a better discussion environment then here on Github.
https://docs.manim.community/en/stable/faq/general.html?highlight=discord#where-can-i-find-more-resources-for-learning-manim

For just "displaying the continuous fraction" that's quite simple:

class contfrac(Scene):
    def construct(self):
        eqn = MathTex(r"""
 f(z) = z + \frac{1}{-z+\frac{1}{z+\frac{1}{-z+\frac{1}{z+\frac{1}{-z}}}}}
        """)
        self.add(eqn)

[uwezi]

If you just want to show numerical results, perhaps you already know that Python can natively calculate with complex numbers?

class contfrac(Scene):
    def construct(self):
        eqn = MathTex(r"""
 f(z) = z + \frac{1}{-z+\frac{1}{z+\frac{1}{-z+\frac{1}{z+\frac{1}{-z}}}}}
        """)
        self.add(eqn.to_edge(UP, buff=0))
        def cf(z):
            return z + 1/(-z+1/(z+1/(-z+1/(z+1/(-z)))))
        valstr = ""
        for z in [-1, -1j, +1j, +1, 1+1j, 1-1j]:
            try:
                valstr += rf"f({z}) &={np.abs(cf(z)):.07f}\\"
            except:
                valstr += rf"f({z}) &=\text{{NaN}}\\"

        valstex = MathTex(valstr)
        self.add(valstex.to_edge(DOWN,buff=0))