I'm trying to visualize Boy's surface using Bryant's parametrization, as per the MathWorld article. However, I'm not sure I understand the parametrization, and I don't know how to implement it when the parameter is complex.

z := u + vI
g1 := -(3/2) Im[(z (1 - z^4))/(z^6 + z^3 \[Sqrt]5 - 1)]
g2 := -(3/2) Re[(z (1 + z^4))/(z^6 + z^3 \[Sqrt]5 - 1)]
g3 := Im[(1 + z^6)/(z^6 + z^3 \[Sqrt]5 - 1)] - 1/2
g = g1 + g2 + g3

ParametricPlot3D[
  {g1/g, g2/g, g3/g}, {u, 0, 0.5}, {v, 0, 0.5}
]

Now, I understand that $z=u+v\mathrm{i}$ is the parameter, and that it must range over the closed unit disc, so $u^2+v^2\leq1$. But I don't know how do do this! (I let $u,v$ range between 0 and 0.5, for good measure, but the graphic appears empty.)

In the end I want to end up with exactly this image, for which I've been unable to find the original code.