Wednesday, December 9, 2015

Geometric Design for Beginners

The motif we are constructing today comes from a wall carving in Armenia, a culture whose artistic tradition is as ancient and intricate as any. 
The basis of it is simple enough: 16 circles around a central one. There are two things that make it tricky. First, the radius of the central circle is 3/4 of the radius of the 16 circles, and it takes a few steps to establish this relationship. Second, deriving the interweaving bands from the grid lines (see Knots and Weaves) is potentially confusing because there are so many circles. 
Follow the steps carefully and you'll find everything falls into place!
Place a point on a line and draw a small circle. To give you an idea of the scale you need, the total design will fit seven of these circles across.

Bisect the circle.

Place the dry point where the circle cuts the line, and draw a second circle.

Move the point and draw a third then a fourth circle.

Return the point to the centre of the first circle and open it as shown (to include thethird circle). Draw a circle. This is the central circle for the design.

Now open the compass further, to include the fourth small circle. This opening is the radius of the 16 peripheral circles to come. 

Move the dry point to the east or west the central circle, and draw the first of the peripheral circles. The small circles play no further role, so you can rub them out or ignore them from now on.

All of the steps in this section take place on the central circle. Move the dry point opposite its previous position and draw another circle.

Use the north and south poles of the central circle to draw two more circles.

Join the intersections of these four circles, diagonally, to find four more points on the central circle.

Use each of these four points to draw a circle. We now have eight circles.

Join the intersections shown to find eight more points on the circle.

Draw the circles centered on these points. This completes all 16 circles.

This step is to "cordon off" some bits that we no longer need. On your drawing, count the five diamond(ish) shapes highlighted below. With your point in the centre, open the compass to the inner point of the last shape and draw a circle. Everything inside this circle is unwanted and you can rub it out or ignore it.

Now draw a circle that passes through the points of the second of these shapes.

At the intersection of this circle and the diameter, draw a small circle that fits into the shape. It needs to be tangent to the inner sides of the shape (the ones closer to the centre of the design). It won't be tangent to its outer sides.

Draw the same circle all around the design. You may have to find their centres by drawing the corresponding diameters. This completes our base grid.

Inside one of the small circles, draw a tiny circle. The exact diameter is up to you, bearing in mind that the difference between the two determines the thickness of the bands in your final knot. The larger the tiny circle is, the thinner the bands, and vice versa.

Repeat all around.

Now draw two circles. One contains and is tangent to the small circles, and the other contains and is tangent to the tiny circles.

Here is where it gets tricky. Make sure the centres of the 16 circles are still clearly marked, as we're going to use them again.
Place the dry point on one of these centres (the top one as shown here is clearest). If you follow the curve of the circle, you'll notice it is tangent, on the inside, to two small circles. Increase the compass opening slightly so that it's tangent to the two tiny circles inside them
Now draw the parts of the circle that run from the tiny circles to the central "cordoning off" circle. It is of course ok to just draw the full circle, but because the construction is getting so complex, I'm trying to avoid having any more lines than we need.

Repeat all around by simply moving the dry point to the next centre and drawing the same arcs. 

The construction lines for the knot are now complete.

Start by inking the tiny circles and the outermost circle, and then, carefully, ink the parts of the inner circle shown here.

This is the inking pattern that repeats all around the circle to create an interweaving effect. Notice how it goes no further than the "cordoning off" circle. If you feel you may have trouble, start by darkening these lines with a soft pencil to be quite sure of the inking.

Inking completed.

This is our knot once all guidelines are rubbed out:

Colour as desired.
An alternative is to finish with a cloisonné or stained-glass like treatment, where you just fill in the bands without weaving them, and then colour the spaces in-between.
Well done! We have taken the knot-work technique to a new level of intricacy. The more complex these patterns become, the more important it is to take it slowly and be quite focused. Next time we are working on another intermediate tiling pattern, found on the wall of an historic synagogue.