Riemann Surface: z^(1/2)
GGB script
Re1(x, y) = exp(1 / 2 * log( sqrt( x*x + y*y ) ) ) * cos(1 / 2 * arctan2( y, x ))
Im1(x, y) = exp(1 / 2 * log( sqrt( x*x + y*y ) ) ) * sin(1 / 2 * arctan2( y, x ))
t = Slider(0, 1, 0.1, 1, 100, false, true, false, false)
HRe1(x, y) = 0 * (1-t) + Re1(x, y) * t
HIm1(x, y) = 0 * (1-t) + Im1(x, y) * t
Re2(x, y) = exp(1 / 2 * log( sqrt( x * x + y*y ) ) ) * cos(1 / 2 * (arctan2( y, x ) + 2 pi))
Im2(x, y) = exp(1 / 2 * log( sqrt( x * x + y*y ) ) ) * sin(1 / 2 * (arctan2( y, x )+2 pi))
HRe2(x, y) = 0 * (1-t) + Re2(x, y) * t
HIm2(x, y) = 0 * (1-t) + Im2(x, y) * t
RSRe = Surface(u*cos(v), u*sin(v), HRe1(u*cos(v), u*sin(v)), u, 0, 2, v, -pi, pi-pi/200)
RSIm = Surface(u*cos(v), u*sin(v), HIm1(u*cos(v), u*sin(v)), u,0, 2, v, -pi, pi-pi/200)
RSReN = Surface(u*cos(v), u*sin(v), HRe2(u*cos(v), u*sin(v)), u, 0, 2, v, -pi, pi-pi/200)
RSImN = Surface(u*cos(v), u*sin(v), HIm2(u*cos(v), u*sin(v)), u, 0, 2, v, -pi, pi-pi/200)