Moroccan Geomety: S8 Class: 8-fold maakous w/ kandeel & B&L, tessellated

   

Moroccan Geometry: S8 Class: 8-fold maakous with kandeel & "B" & "L", tessellated

This 8-fold design yielded a tessellation of 15 tiles on an 18"x12" page, with a center tile and no half-tiles. The Qandeel w ba w la (jellyfish with "B" and "L") is outside the 22.5°-turned Seal of Solomon/Looza/Sfet figures which comprise the middle of the drawing, but inside the corner seal of solomon, which each tile contains one-fourth of, and which is completed at the corners by four tiles. Other shapes include the Sfet L'herba, or bayonet/spear, and another form based on the Qandeel, known as the Bou Mnikher Mashrook, or Squashed Little Nose. This shape and the Sfet L'herba line the outside border of each tile, and so only half the shape is within the tile itself, and is completed by the adjacent tiles on each side. 

The arrangement consists of circles arranged diagonally, including 5 center circles arrange like the 5 on a die, and extend 1 additional full circle to the left and right for a total of 7 circles. Each of these circles contains 8 adjacent smaller circles arranged around its circumference and 1 smaller circle in the center. Construction lines are based on divisions of these circles. There are 8 spaces in the interstitial areas between and outside of the large circles, 3 each on the top and bottom rows, and 2 on the middle row. These spaces will contain a single small circle, like the center circle within the larger circles, and that will be used to create the 8 additional tiles.

1.  Draw a circle in the middle of the page. Find the horizontal axis and draw it from one end of the page to the other. Then use a compass with a wider radius to find the vertical axis, and draw it end-to-end. Next, use the original compass to find the points along the diagonal axes, and draw those axes end-to-end. Then draw a pair of adjacent circles with identical radii along each diagonal axis, and finally two more circles along the horizontal axis adjacent to each pair of circles you just drew. Note that although there are only 7 circles, there are 8 intersitial spaces between and to the left and right of each circle. These intersititial spaces will yield a complete tile when combined with the adjacent circles. You may wish to draw the upper and lower horizontal borders, which will intersect the outer circles where the diagonals cross

Divide each of the circles into eighths, marking where the axes cross the circumference and intersect the center. You can now draw the left and right borders of the drawing.

1.

2. Find the midpoint on any circle between 2 adjacent eighth marks, and mark that with the dividers. Now set a compass with a radius slightly less than the divider distance, such that when you draw adjacent circles, they just meet without overlapping. Once you are satisfied with the radius, draw pairs of circles at opposite ends of each circle, and continue to do this for each circle, first along the vertical axis, then the horizontal, then each of the diagonals, always checking to make sure the adjacent circles do not overlap. Finally, draw one more circle of the same smaller radius at the center of each large circle. 

2.

3. If necessary, number the circles from the previous step, 1 at the top, proceeding clockwise. Placing the edge of the ruler so that it is touching the centers of circles 1 and 2, make 3 marks, at the outer edges of circles 1 & 2, and at the point where the circles connect. Proceed to do the same with circles, 2 & 3, 3 & 4, etc., all the way to circles 8 & 1. Each circle will now have 4 marks, 2 of which are shared with its adjacent circles.

3.

3.

4. Skipping 2 circles, line the ruler’s edge to the centers of circles 1 & 4, and make 4 marks, 2 on each circle. Moving the ruler to the left, proceed to circles 5 & 8, repeating the 4 marks. Then rotate the page and do circles 2 & 5, and 1 & 6. Rotate again and do circles 3 & 6, and 2 & 7, then rotate again and do circles 4 & 7, and 3 & 8. Thus you are making 4 marks on each circle, and dividing these circles into eighths.

4. 

4.

5. Now that the circles have been divided, you can draw the construction lines. Aligning the ruler parallel to the vertical axis on circle 3, connect the mark on either side of the vertical axis for circle 3 to the mark below it, running the lines to the edge of the page. Although the points are not numbered, that would be points 1 & 4 and 8 & 5. Continue, moving the ruler to the left but parallel to the vertical axis, and draw lines through those same points in circles 2 & 4, 1 & 5, 8 & 6, and circle 7. Do not run your lines through the small center circle, just interrupt them and continue from the other side of the circle.

5.

6. Repeat the procedure along the horizontal access and each of the diagonal axes.

6. 

6.

7. Mark the points where the 4 axes intersect the small center circle, 1 through 8, with 1 at the top. Now draw lines to connect the points 1 to 4, 2 to 5, 3 to 6, 4 to 7, 5 to 8, 6 to 1, 7 to 2, 8 to 3, continuing the lines until they meet the first construction line outside the small center circle. Thus each point will have two lines through it. 

To avoid cluttering up the center, leave a gap in each line segment between the two intervening axes. For example, when drawing the line segment connecting 1 to 4, leave a gap between the NE-SW axes and the E-W axis. When connecting 2 to 5, leave a gap between the E-W axis and the SE-NW axis, etc.

7.

7.

These lines will form the 22.5 rotated seal of Solomon, the surrounding loozat, the looza tips of the qandeel bil ba w la (in the corners), and the looza tips of the Bou Mnikher Mashrook (in the middle of each side). The base of the looza is the point where the neighboring Sfet sagheers stop. Label these marks A to P, A being slightly to the right of the vertical axis, P being slightly to the left.

8. Again, skipping 2 points, hold the ruler from points N to K, and draw line segments between the top 2 horizontals and bottom 2 horizontal lines that intersect the ruler, while leaving a gap between the diagonal lines . Likewise do the same with points C-F. Then points B-O & G-J. Turn the page 45° and do L-I & A-D and then P-M & E-H, but this time don't leave a gap in the line segments. This completes the outer sides of "ba w la" legs of the qandeel w ba w la and the outside point (actually beyond the scope of this tessellation and into the neighboring one) of the Sfet L'Herba.

 

8.

8.

9. Now you are ready to highlight the pattern.

10. Repeat for each of the large circles in the tessellated design. Notice that in the interstitial space between circles, some of the construction lines are already run through. In the center of the space, draw another small circle, connect the axis lines both horizontally, vertically, and diagonally, repeat step 7, and connect any other lines to complete the qandeel w ba w la and the bou mnikher mashrook shapes.

10a. 

10a. 

10b.

You're now ready to ink the lines and shapes of the finished tessellation.

Ink colors for the shapes:

1. Khatem Slimanya (rotated 22°): 1 part Ultramarine (504) +2 parts Sky Blue (551) + 1 Primary Cyan (572), with Pearl Blue (820) wash
2. Looza: Primary Yellow (275) w/ Pearl Yellow (818) wash
3. Sfet Sgheer: same as 1.
4. Kandeel w ba w la: same as 2
5. Bou Mnikher Mashrook (squashed little nose): Titanium White (105), with Pearl White (817) wash
6. Square intersection of #5: Oxide Black (735), with Graphite (840) wash
7. Khatem Slimanya: same as 1.
8. Sfet L'herba: same as 1.

First do the blue areas

Next, do the yellow areas and the black intersections

Next, do the pearlescent blue and yellow washes over their respective areas, and do the white areas washed with pearlescent white.

Finally, go over the lines once more to clean up and sharpen the figures, and correct any egregious errors..