GraphingCalculator 4;
Window 65 46 720 1352;
PaneDivider 389;
FontSizes 16;
BackgroundType 0;
BackgroundColor 10 0 20;
StackPanes 1;
Slider 0 360;
SliderSteps 360;
SliderControlValue 351;
SliderMoving 1;
T 0.45 5;
U 0.45 5;
V 0 6.283185307179586;
4D.Show4DxyPlane 0;
4D.Show4Daxes 0;
4D.Depth 2.1830909743;
4D.View -0.09765045939399754 0.8772120647637984 -0.008483983936123055 0.4699908544092599 -0.05643319744173717 -0.3822360089141598 0.5859821967222206 0.7122750822806383 0.9380244813455552 -0.03252834363471611 -0.2363904797693493 0.2513394523921611 -0.3277037601262058 -0.2886806778793827 -0.7750305982430081 0.4567288950819757;
4D.Speed1 0.5454153912482278;
4D.Speed2 0.5454153912482286;
4D.Axis1 -1 0 0;
4D.Axis2 1 0 0;
Text "COMPLEX FUNCTIONS u+iv = w(x+iy) = w(z)
http://home.scarlet.be/~pin12499/qbComplex.html
by Guido 'wugi' Wuyts (Google wugi + qbcomplex)";
Color 8;
Expr c=cos([2*pi*(n/360)]),b=sin([2*pi*(n/360)]);
Color 5;
MathPaneSlider 87;
Expr m=slider([0.45,5]);
Color 7;
MathPaneSlider 200;
Expr l=slider([0,2*pi+0.1]);
Expr 'mred'=slider([0.44,5]);
Color 2;
MathPaneSlider 200;
Expr 'lred'=slider([0,2*pi+0.1]);
Color 3;
Expr 'mblu'=slider([0.45,5]);
Color 4;
MathPaneSlider 200;
Expr 'lblu'=slider([0,2*pi+0.3]);
Text "
COMPLEX ""DOUBLE""-HYPERBOLA w = 1/z^2
z unit plane in green, w unit plane in magenta.
With parameter curves in blue and red.
With characteristic curves in yellow: the real curve ""y = 1/x^2"" and the inner ""double loop circle"",  part of the same complex surface.
Notice asymptot w = 0 (yellow blade), and double asymptot z = 0 (silver blades).
Try sliders m and l for surface rendering; 
mred thru lblu for parameter curve rendering;
n for independent rotation along z-plane.";
Color 6;
Expr vector(x,y,u,v)=vector(u*cos([v+2*pi*(n/360)]),u*sin([v+2*pi*(n/360)]),1/(u*u)*cos([-(2*v)]),1/(u*u)*sin([-(2*v)])),leq(1,u),leq(u,m),leq(v,l);
Color 7;
Expr vector(x,y,u,v)=vector(1/u*cos([v+2*pi*(n/360)]),1/u*sin([v+2*pi*(n/360)]),u*u*cos([-(2*v)]),u*u*sin([-(2*v)])),geq(1/u,1/m),geq(1,1/u),leq(v,l),geq(1/u,0.44);
Text "
";
Color 4;
Expr vector(0,0,0,0),vector(c,b,0,0),vector(c-b,b+c,0,0),vector(-b,c,0,0),vector(0,0,0,0);
Expr vector(0,0,0,0),vector(0,0,1,0),vector(0,0,1,1),vector(0,0,0,1),vector(0,0,0,0);
Color 6;
Expr vector(x,y,u,v)=vector(t*cos([a+2*pi*(n/360)]),t*sin([a+2*pi*(n/360)]),1/(t*t)*cos([-(2*a)]),1/(t*t)*sin([-(2*a)])),in(a,set(0,pi));
Color 2;
Expr vector(x,y,u,v)=vector(t*cos([a*(pi/10)+2*pi*(n/360)]),t*sin([a*(pi/10)+2*pi*(n/360)]),1/(t*t)*cos([-(2*a*(pi/10))]),1/(t*t)*sin([-(2*a*(pi/10))])),in(a,set(-1,-2,-3,-4,-5,-6,-7,-8,-9,-10,1,2,3,4,5,6,7,8,9)),geq(t,'mred'),leq(a*(pi/10)+pi,'lred');
Color 3;
Expr vector(x,y,u,v)=vector(a*cos([[t-0.3]*2*(pi/3)+2*pi*(n/360)]),a*sin([[t-0.3]*2*(pi/3)+2*pi*(n/360)]),1/(a*a)*cos([-(2*[t-0.3]*2*(pi/3))]),1/(a*a)*sin([-(2*[t-0.3]*2*(pi/3))])),in(a,set(0.45,0.55,0.65,0.75,0.85,1.5,2,3,4,5)),geq(a,'mblu'),leq([t-0.3]*2*(pi/3),'lblu');
Color 6;
Expr vector(x,y,u,v)=vector(a*cos([2.1*t+2*pi*(n/360)]),a*sin([2.1*t+2*pi*(n/360)]),1/(a*a)*cos([-(2*2.1*t)]),1/(a*a)*sin([-(2*2.1*t)])),in(a,set(1));