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Posts Tagged ‘Chartres Type Labyrinth in the Man-in-the-Maze Style’

Fine Tuning

A careful view of the Chartres type labyrinth in the Man-in-the-Maze style (see related posts 1, below) revealed that the design can still be improved. In addition to the not accessible middle, this figure has another 16 smaller segments that are not covered by the pathway. These are highlighted as crossed-through areas in fig. 1. Among others one requirement is that the pathway in a labyrinth should cover as much of the space of the figure as possible and should not let remain any „dead spots“. Such uncovered segments are therefore not liked to be seen in labyrinths.

Figure 1. Segments not Covered by the Pathway

These segments have evolved as a result of the construction of the seed pattern (see related posts 2). However, upon a closer view it turned out that they can be resolved. For this, as shown in fig. 2, the outer delimiting line has to be removed and the wall delimiting the pathway in between must be prolonged further to the inside.

Figure 2. Corrections to the Seed Pattern

The necessary corrections are shown for the segment on low left in orange color. Such corrections must be carried out for all 16 segments in a similar way.

The result can be seen in fig. 3. After these corrections, the labyrinth looks even somewhat more dynamic. Finally, only the one non accessible middle is left over. This is just the same as in the alternating one-arm labyrinths in the MiM-style.

Figure 3. The Final Labyrinth

However, now it cannot anymore be seen easily where the pathway traverses the side-arms. Therefore, the gain in dynamics and unity is associated with a loss in transparency.

Related Posts:

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Finalizing the Labyrinth

Now we have all elements we need (see related posts 2, below) and are able to finalize the Chartres type labyrinth in the Man-in-the-Maze style. These elements are the auxiliary figure and the seed pattern (fig. 1).

Figure 1. Auxiliary Figure and Seed Pattern

 

The auxiliary figure has 90 spokes and 22 rings. In it’s interior there are two rings that are not used for the labyrinth. The reason for this is, that the distance between two spokes would be too narrow and no room would be left for the pathway (related posts 1).

In order to complete the labyrinth we proceed exactly as shown in the first post of this series (related posts 4). First the situation of the center has to be determined (fig. 2).

Figure 2. Situation of the Center

The center lies at the top end of the right half of the seed pattern of the main axis. This is exactly the same as in the one-arm labyrinths in the MiM-style (related posts 4). However, as here are arranged four seed patterns with two halves each on the central auxiliary circle, the center is shifted to the upper end of the eighth part at bottom right.

Figure 3. Step 1, Quadrant IV

In fig. 3 then we draw a wall delimiting the pathway around the center along the lines of the auxiliary figure.

From there we add one wall delimiting the pathway after each other and by this complete the IV th quadrant (fig. 4).

Figure 4. Completion of Quadrant IV

The walls delimiting the path of the IV th quadrant envelop the center and connect the right half of the seed pattern of the main axis with the left half of the seed pattern of the 3rd side-arm.

Next, the walls delimiting the pathway of the other quadrants have to be completed. Where do we have to begin with? This is shown in figure 5.

Figure 5. Step 1, Quadrants I – III

The places where the seed patterns of two different axes connect to each other each are on the innermost, 11th circuit. These places are already well known from the 9th post of this series (related posts 3). They are highlighted with dashed lines. On these spokes lie the inner walls delimiting the pieces of the pathway that have to be connected. So first, we prolong these walls delimiting the pathway until they reach the radius that is highlighted with a dashed circle. On this auxiliary circle lie the inner walls delimiting the 11th circuit.

Figure 6. Step 2, Quadrants I-III

These are then connected with chains of lines along the spokes and rings of the auxiliary figure (fig. 6). These lines represent the outer walls delimiting the path of the 11th circuit and the inner walls delimiting the path of the 10th circuit (fig. 6).

Figures 7 to 9 show, how the other quadrants are completed sequentially

Figure 7. Completion of Quadrant III

 

Figure 8. Completion of Quadrant II

 

Figure 9. Completion of Quadrant I

If we then remove the auxiliary figure, we can easily view the final result (fig. 10).

Figure 10. Labyrinth of the Chartres Type in the Man-in-the-Maze Style

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