The first big change in the labyrinth figure happened in the time of the Roman empire of about 165 B.C. till 400 A.D. Before, for nearly two millenniums only the classical, sometimes called Cretan type, was used.
The Roman type is marked by the division in (mostly four) sectors / quadrants /segments which are completed one after the other, before entering the middle. Besides, the alignment and the external form can be different.
Jeff Saward has explained in one of his books how one can picture the development of the Roman labyrinth from the Classical one, which I tried to reproduce in a previous posting (see below). The following subdivision in three big groups is also from him. Here, I only want to explain it nearer.
The external form or the number of the circuits is not so important for the differentiation of the various groups. The kind of the alignment is what counts.
In the meander-type two simple meanders are completed in each sector, like in the classical labyrinth, even if in other order. In square form this looks thus:
One recognises the narrow relationship and the provenance from the classical labyrinth even better in the diagram:
We have nine circuits. One is used for the circumnavigation of the center and one to change to the next sector. The inner seven circuits are identical with those in the classical labyrinth. One can see clearly the two meanders.
One would have to call this type more exactly two-meander-type or more-meander-type. Since there are still other samples, made with more meanders.
The next type is called spiral-type. It is less complicated and has only one change of direction within each sector. The spiral movement is caused by a meander.
Here as a diagram:
The principle of the alignment is identical with the one in the previous type, even if there are all together less circuits.
Strictly speaking one would have to call this type one-meander-type. Since the spiral is nothing else than a meander.
In the serpentine-type the way inside the sector simply wiggles to and fro.
Here as diagram:
In this type it is quite easy to append more or less circuits.
Example of a labyrinth to walk from our time: Retzbach
The historically known Roman labyrinths can be sorted with some variations into these groups. And according to these criteria can be thought another immense number of variations. Since it does not depend on the external form (angular or round) or the number of the sectors. The original historical labyrinths were often mosaics and served more decorative purposes. Nowadays the labyrinths are mostly put on as walkable objects. There would be still a rich sphere of activity. Since the most frequent new labyrinths are either the classical type or the medieval Chartres type.