Homan's 2 Cool Curves:

Pinched Spiral:

"Pinched Spiral" was produced using the following Maple commands:

> x:=sin(t)*cos(t);
> y:=sin(t);
> z:=t^2;

                          x := sin(t) cos(t)


                             y := sin(t)


                                     2
                               z := t

> with(plots):
> spacecurve([x,y,z],t=0..8*Pi,numpoints=1000,
>   axes='BOXED',thickness=2,orientation=[20,75]);

Spikes Galore:

"Spikes Galore" was produced using the following Maple commands:

> x:=3*sin(t)^2+tan(t);
> y:=4*cos(t)^3*tan(t)^2;
> z:=2*sqrt(t);

                                    2
                       x := 3 sin(t)  + tan(t)


                                     3       2
                        y := 4 cos(t)  tan(t)


                                     1/2
                             z := 2 t

> with(plots):
> spacecurve([x,y,z],t=0..10*Pi,numpoints=10000,
>   axes='FRAMED',view=[-30..30,-1..1,0..12],
>   thickness=2,orientation=[70,80]);