√(x²−1)(x²−k²).      x,k∈ℂ (actually just going over the unit…

√(x²−1)(x²−k²).      x,k∈ℂ

(actually just going over the unit circle, not all of ℂ)

edit: hey, are these showing up as moving gif’s for you?

< !-- more -->

code:

   require(animation)
    source(wegert.R)    #where I define "plat" and "Z", standard for all Wegert plots
    i = complex(imaginary=1)
    hyperbola <- function(x,k=i) sqrt( (x^2-1) * (x^2-k^2) )
    saveGIF({
        for (param in 1:100/30) {
            plat(Z, function(x) hyperbola(x,k=complex(argument=param)) )
            }
        }, movie.name="hyperbola", nmax=100)

more gifs: http://ge.tt/2Lh48dw1