A 3D Microworld in Comenius Logo

Dorina Fehér
Eötvös Loránd University


The two dimensional Turtle geometry aspect is very close to smaller children’s view in relevance to their own body geometry with respect to ground movements. They can easily think with the Turtle, perform using it and compose geometric structures as two dimensional dynamic representations. When this approach is clear, can be handled well, and a third dimension is ready to inhibit the world of a bit older child, the 3D extended Turtle geometry [1] could be an aid in the same way.


Travelling in three dimensions is a far more difficult task that in the plane and the structures to be built are not just as simple as adding another dimension. Imagining structures, performing movements, visualising objects in 3D are quite uneasy to perform. Thus a visual aid, a simple constructive microworld can be of great help.

The 3D microworld developed contains extensions to the Hungarian Comenius Logo 3.0 [2], that would aid in visualising 3D objects, help in their construction, and allow their view from different aspects. This ability is developed by the creation of new procedures like PITCH, ROLL, YAW [3] allowing 3D specific movements. The visual representation of a three dimensional object in two dimension, is done by parallel projection onto the plane. In order to view an object in space with more realistic flavour, the microworld also contains an eye co-ordinate system, which can be moved in the same manner as the Turtle (PITCH.EYE, ROLL.EYE, YAW.EYE). This produces the image with respect to our position of view, and allows us to travel around our 3D object.

The microworld, apart from the ability of using these newly created commands in procedures, contains easy to use, button driven constructing aids. All commands can be activated through buttons, which can be undone or further evoked to construct a 3D structure. Developed structures can be saved under any name and reused in the same way as any pre-programmed structure. Buttons aid in changing view with respect to our eyes, to help travell around our created object. Some further buttons provide the means of configuring the first line design buttons, produce variations for use.

The microworld can help to illustrate of 3D objects as well as their construction, which is otherwise a very difficult task even for secondary school level. The procedural development of such structures deepen the understanding of 3D aspects and help to grab the essence of the solid form that is very often lost from view otherwise.

The created programmable microworld is open for any variations and constructions using full features of Comenius Logo. It thus can be further developed to fulfil need.


  1. Fehér, D., Modelling in three dimensions, dissertation, Eötvös Loránd University, 1997.
  2. Comenius Logo 3.0 (© localisation M. Turcsányi-Szabó & Kossuth Ltd), from (© Andrej Blaho, Ivan Kalas, Peter Tomcsányi) Kossuth Ltd. 1997.
  3. Abelson, H., diSessa A. A., Turtle Geometry: The computer as a medium for exploring mathematics, MIT Press, 1980.