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How to Transform Any graph using Complex Function (like we did for Linear Transformation)?

How can I tranform a graph or the whole Number plane using Complex Function?, Like suppose I have f(z)=z^2 =(x^2-y^2)+i(2xy), Now we have U=x^2-y^2 and V=2xy , I am saying that I want to show the transformation X to U and Y to V, I know the Linear Transformation but how to apply the complex Transformation when we have 2 different Functions? And it would be helpful if you can also show how to plot in complex plane? Thank you in Advance

Solution

  • The answer is in the example_scenes.py, in WarpSquare scene.

    class ComplexTransformation(LinearTransformationScene):
    def construct(self):
        square = Square().scale(2)
        function = lambda point: complex_to_R3(R3_to_complex(point)**2)

        self.add_transformable_mobject(square)

        self.apply_nonlinear_transformation(function)

        self.wait()