Here I present two more variants of the seed pattern of the Cretan-type labyrinth. I used the same variants as in this post, but present them in a different order from the simplest to the most complex seed pattern.
Fig. 1 shows the seed patterns of the labyrinth-drawing from Rajasthan. The seed pattern for the walls is coherent. The central cross is distorted but well recognizable. The four angles have mutated to four arcs. And they are not embedded between the arms of the cross, but all are aligned horizontally. The inner two turns lie above, the outer aside and slightly below the horizontal bar.
The seed pattern for the Ariadne’s Thread is less coherent. This is because the turn of the pathway from the first to the fourth circuit covers the whole 3rd quadrant. Therefore, the Ariadne’s Thread is directed somewhere through the middle of this quadrant. By this, the segment representing the opposite outer turns falls apart to two pieces.
The seed patterns of the half-heart shaped labyrinth show four peculiarities (fig. 2).
- They fall apart into two halves. This is due to the layout of this labyrinth, that is not a closed form, but enrolled to a half-open form. The upper half of the seed pattern represents the turns of the pathway that in a closed form would lie on the opposite side next to the turns of this side of the axis.
- As a consequence of the (half-)heart shape, the inner circuits do not describe half an arc but only about one quarter of an arc of a circle. Therefore, the upper inner turns of the pathway are not aligend in parallel with the upper outer turns, but rotated anticlockwise by ca. 1/4 of a circle.
- As a result of the artwork of this labyrinth, the situation at the entrance is ambigous. The pathway can enter from above or from below into the third circuit of the labyrinth. For the course of the pathway to be un-ambigous, a part of the wall is missing. I added this as a dashed line on the seed pattern for the walls.
- Likewise, as a result of the artwork, the major part of the inner space is not accessible, but is separated by the upper boundary of the (half-) heart form. The pathway ends above this boundary, where it reaches the center. By this, all ends of the lower half of the seed pattern are more distant from the center than the ends of the upper half.
Until now the rule for the completion of the seed pattern to the full labyrinth said: “Connect the two ends next to the center with an arc around the center, proceed in the same way with the next two ends and by this add one wall / circuit from the inside out.“ (By the way this also works for both seed patterns combined. First comes the innermost wall, then the innermost circuit, next the second inner wall, then the second inner circuit and so forth.) This rule refers to seed patterns of closed forms.
The rule in the general sense also applies to this variation of a seed pattern of a half-open form. However, the above mentioned specialities must also be considered. As all ends of the upper / opposite half of the seed pattern are closer to the center than the ends of the lower / this-side half, the rule needs to be formulated more precisely as: “connect the nearest end of the upper half to the center with the nearest end of the lower half to the center with a partial arc around the left side of the center.“
As the figure is half-open, the ends of the seed pattern cannot be connected with a full arc, but only with the part of an arc. And, since both halves of the seed pattern are not aligned symmetrically next to each other, it has to be made explicit, that each connection is made between an end of the lower (this-side) and the upper (opposite side) half of the seed pattern. Without being explicitly stated, this is also the case in seed patterns of closed figures. Each arc connects one end of this side with one end of the opposite side of the axis.