Eric's Excellent Collection of Space Curves:

The Zig-Zag:

"The Zig-Zag" was produced using the following Maple commands:

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

                              x := ln(t)


                             y := sin(t)


                                     2
                               z := t

> with(plots):
> spacecurve([x,y,z],t=0..8*Pi,numpoints=1000,
>   axes='NORMAL',thickness=2,orientation=[55,75]);

Suspended Horseshoes:

"Suspended Horseshoes" was produced using the following Maple commands:

> x:=ln(sin(t));
> y:=t;
> z:=t;

                           x := ln(sin(t))


                                y := t


                                z := t

> spacecurve([x,y,z],t=0..8*Pi,numpoints=1000,
>   axes='NORMAL',thickness=3,orientation=[-5,80]);

The Squiggle:

"The Squiggle" was produced using the following Maple commands:

> x:=t+2*sin(2*t);
> y:=t+2*cos(5*t);
> z:=t;

                         x := t + 2 sin(2 t)


                         y := t + 2 cos(5 t)


                                z := t

> spacecurve([x,y,z],t=0..8*Pi,numpoints=1000,
>   axes='NORMAL',thickness=2,orientation=[-110,45],
>   shading='Z');

Mosquito Flight Plan:

"Mosquito Flight Plan" was produced using the following Maple commands:

> x:=sin(3*t);
> y:=sin(4*t);
> z:=t;

                            x := sin(3 t)


                            y := sin(4 t)


                                z := t

> spacecurve([x,y,z],t=0..2*Pi,numpoints=1000,
>   axes='NORMAL',thickness=2);

Pinched Loop:

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

> x:=cos(t);
> y:=sin(t+sin(5*t));
> z:=cos(t);

                             x := cos(t)


                        y := sin(t + sin(5 t))


                             z := cos(t)

> spacecurve([x,y,z],t=0..2*Pi,numpoints=1000,
>   axes='NORMAL',thickness=2,orientation=[115,75]);