The `gnuplot`

code in this article, creates several frames of a `3D`

torus with a visible structural grid from different viewing angles, like the one in the image below.

torus.gnuplot (compressed) (709 downloads)

In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution.

From Wikipedia https://en.wikipedia.org/wiki/Torus

By modifying the `circles`

and `rings`

variables in the script you can increase and decrease the number of circles and rings that appear on your `torus`

.

The above image was generated using **60 circles** and **30 rings**.

To better explain what a `circle`

and what a `ring`

is, please have a look at the following two examples.

The following torus has **10 circles** and **30 rings**.

The next one has **60 circles** and **10 rings**.

The last torus has **10 circles** and **10 rings**.

Using the script, you can also play around with the `set view`

command and the `for loop`

to change the number of frames that will be produced and what movement should the camera perform before printing.

torus.gnuplot (compressed) (709 downloads)

set terminal pngcairo transparent enhanced font "arial,10" fontscale 1.0 size 700, 400 unset key unset border unset tics set dummy u, v circles=60 rings=30 set parametric set isosamples circles, rings set hidden3d back offset 1 trianglepattern 3 undefined 1 altdiagonal bentover set urange [ -pi : pi ] noreverse nowriteback set vrange [ -pi : pi ] noreverse nowriteback do for [i=1:360/circles] { set view 25, i, 1, 1 set output sprintf('game-of-life-torus.%03.0f.png', i) splot cos(u)+.5*cos(u)*cos(v),sin(u)+.5*sin(u)*cos(v),.5*sin(v) with lines }

torus.gnuplot (compressed) (709 downloads)

Below, you can see two examples of animation we build together using the `gimp`

application.

### Showing one frame at a time.

### Accumulating all frames into one, until the loop is reset.

To create the animation we followed the next steps:

- Executed
`gnuplot torus.gnuplot`

to generated the frames. - Then we started the
`gimp`

and from the menu`File`

we chose the option`Open as layers...`

(`Ctrl`

+`Alt`

+`o`

). - We selected all the images we wanted for our animation and pressed the
`Open`

button. - The
`Layers - Brushes`

window got populated by the new frames. Please note that window you can use that to change the order of the frames (which are now the layers). - Following, from the menu
`File`

we chose the option`Export As...`

(`Shift`

+`Ctrl`

+`E`

), from the pop-up window we selected the type of the file to be`gif`

and pressed the`Export`

button. - At the final pop-up window, we enabled the
`As animation`

checkbox, then at the`Frame disposal where unspecified`

dropdown menu we chose`One frame per layer (replace)`

and hit the`Export`

button which produce the first animation in this article (two images up).

This post is also available in: Greek