Complex Surfaces

I wrote a separate version of formula toy that handles complex functions. So, you can type in a function like: f=sqrt(g). Both f and g are expected to be complex functions:

    g = u + iv

and

    f = w + ix

where u is the real component of g, v is the imaginary component of g, etc.

To draw this surface we need 4 axes, so formula toy uses a color gradient for the 4th axis. We name these as follows:
– fR – the real component of f.
– fI – the imaginary component of f.
– gR – the real component of g.
– gI – the imaginary component of g.

And you can choose which complex axis maps to which cartesian axis.

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f=sqrt(g)

This flexible way of doing the mappings allows for simple multi-valued functions/Riemann surfaces:

30

f=log(g)

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f=atan(g)

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Lambert W function

Click on the images to open the surface in formula toy. More details here.

 

 

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