Star Alignment - Geometrical Analysis of a Pattern

Chris Heath Author

An analysis of a tiled wall pattern and frieze from Patio de los Arraynes, Alhambra, Spain. What to look for when reproducing a historic pattern.

Star Alignment

Indirectly, this blog post is about star alignment; not the celestial kind, but the geometrical kind. It's more about interpreting photos of historic patterns. In a sense, there are no hard and fast rules; but there are things to look out for. 

There are assumptions to be made that can set your interpretation of a pattern down the right path, or the wrong path. Many people can't tell the difference, but some will.

Analysis

A shallow analysis can result in a lot of errors that you may not come to realise for a period of time. 

A deeper, more methodical analysis, can reduce the quantity and severity of any errors. 

I know that if I rush my analysis, errors can be embarrassing, especially if I publish a pattern prematurely. Then again, publishing a pattern prematurely can lead to useful feedback which can be the impetus to refine the analysis, and to produce a better, more accurate design.

Above is a pattern from the Patio de los Arrynes, Alhambra, Spain. I'm referring to the pattern of coloured and black squares presented within a diagonal grid. 

For those of you who follow Mohamad Aljanabi's Traditional Method of constructing Islamic geometric patterns, you will know that the obvious diagonal grid is not the grid that we draw and repeat. What we always draw is a rectangle that can be easily repeated in two directions across a surface.

Below is the close up of the tiled pattern. While it doesn't show much of the finished pattern, it was the most detailed photo I could find. The more detailed the photo the better. A high resolution photo reveals so much more information than a low resolution image.

Drawing 1

And here is the problem. It's easy to look at a photo and create a pattern. I did just that with my shallow analysis below. I was in a hurry.

As soon as I posted this image in my Facebook group, I realised it wasn't a good match to the original. I really like it, and it is a nice variation of the design, and it can be drawn using the Traditional Method, but it's not a match to the historic pattern. 

What I do like about it is the separation of the stars from the rotated squares, and how this separation makes the stars more jewel-like in appearance.

Drawing 2

The next step was to align the corners of the stars with the corners of the squares. As in the earlier drawing, the square root of two in the form of the square progression was used to set the placement of the blue lines that are reflected and repeated to form the pattern.

This pattern looked like it might be correct, however, it felt wrong. At this stage I was relying on low resolution images. The stars in drawing No 2 did not feel jewel-like now they were in contact with the squares.

Drawing 3

So it was back to the drawing board (below) with another attempt, again using the square progression.

Now this is better. The stars are separated from the squares. The squares are the correct size; not too small as per drawing 1. The stars retain their jewel like quality because they don't come into contact with the squares. 

Again at this point I was working with low resolution images off the internet. In some photos, the stars looked as per Drawing 2, and in other low resolution photographs, they looked as per Drawing 3. Also some tiles in some of the photos looked like they could be original with their chipped and aged appearance, and some looked almost new with crisp clean edges.

This is where the higher resolution image was useful. Each star is surrounded by a generous amount of grout, whereas the squares are not. It appears that this might have been deliberate in order to give the stars that jewel like quality.

Drawing 4

The next stage was to combine drawings 2 and 3. The smaller star in Drawing 2 is set above the star from Drawing 3. The smaller star being coloured, and the distance between the edges of Stars 2 & 3 determines the width of the grout as shown in drawing No 4, below.

Render

The last stage was to create a coloured render of the pattern. Here it is...

The Frieze

I'd like to acknowledge Ana Delgado, who asked in the Geometrical Design Secrets Facebook group, how to geometrically relate the counterchange band of black and white shapes (frieze) to the all-over pattern of stars and squares in the dado panel beneath it. It was this question that drew my interest to drawing the pattern above.

The counterchange battlement pattern was harder to figure out.

Observations

At first glance, it is easy to make a number of mistakes when drawing this pattern. To see these mistakes, scroll down to Drawing 5 below.

The first mistake is to take a more arithmetical approach to drawing the pattern by dividing a square into a 6 x 6 grid of 36 smaller squares and constructing the pattern on this grid. For a four-fold pattern, it does not make any sense to divide the sides of the square into six equal segments.

The second mistake is to assume the green tiles above the battlement pattern share the same proportions as the green tiles that run beneath the battlement pattern. This is not the case.

The big problem I have with this approach is the contrast between the black tiles and the off-white tiles. The black tiles dominate the pattern and look larger even though they are the same size. It just feels like an optical correction needs to be made.

So how do we make the optical corrections needed to balance the design and to get all the shapes closer in proportion to the historic example?

The answer is to construct the pattern geometrically using the same proportion (√2) that was used to construct the stars and squares earlier. The geometry below is what I used to visually balance the contrast between black and off-white battlement tiles, and to set the heights of the two rows of green tiles. This approach ties all the components of this pattern back to the stars and squares used in the dado panel beneath it.

Below is more analysis of the proportions. This analysis was inspired by some observations of the work above by محمد عبد العزيز.

One of the reasons for writing this post was to point out the dangers of relying on poor quality photos that can be found on the internet. Nothing beats taking your own photos, but for those of us who live on the other side of the planet, other peoples' photos are all we have access to. The trick is to search for the most detailed photos you can find (and credit the photographers if you can).

The other reason is to highlight the dangers of rushing your analysis. I do this all the time and often regret it. However, it does compel me to give it another go and do a deeper analysis. 

One of the things to look out for that should raise alarm bells is the arithmetic approach to constructing patterns. Simply dividing areas such as squares into equal segments creates a static design. It's important to think more in terms of proportion. By using geometrical proportions you can introduce balanced asymmetry into a pattern and give it a more dynamic feel that better reflects what we see in the natural world.

I hope you found this blog post useful and informative.

Categories: Design Graphics, Dynamic Symmetry, Geometric Progression, Geometry, Islamic Geometry, Surface Pattern Design