On The Use of Vocabularies of Geometric Forms in Ornamental Pattern Design


This paper examines the development and use of vocabularies of shapes constructed using geometric principles as a basis for ornamental pattern design. Through a combination of digital fabrication techniques and printmaking, I have developed a process for freely exploring geometric ornamentation based on compatible vocabularies of shapes. The process highlights the correlation between the use of these vocabularies and language as a medium of expression. It can also give an insight into how the universality of the visual expression of mathematical concepts helps us perceive the nature of the world around us.

LINK TO THE ORIGINAL PAPER – the full article is also reproduced below

Keep on reading!

Tenfold Pattern Variations

As many of us enter a period of isolation in the unusual and unsettling situation the world finds itself in, many of us will take the opportunity to spend time learning new skills, a process which can help us both focus and relax at the same time. For me, these qualities have been invaluable ones to develop and geometry has played a central role in this development. The process of drawing geometric designs with ruler & compass can help you find your own centre much as we start drawing a geometric pattern by locating the centre of the first circle, which then defines the structure of the whole pattern. Everything is grounded in this point, as we are grounded in our own centre.

Since becoming immersed in Islamic geometric design I have found myself drawn to overlapping rosettes which appear in a number of forms, particularly within tenfold patterns. This design is slightly unusual as it repeats in a hexagonal unit and the main star or rosette centres are defined by this hexagon rather than the repeat rectangle. I hope you will find this an enjoyable and enlightening construction to spend some time with.

Start by constructing a circle divided into ten. You can find steps to do this in this tutorial and various other places online. Continue with the steps below which show how to establish a repeat rectangle with centre and corners divided into 20ths (18º).

Overlapping tens - Ambigraph Mar 2020_Page_02
Overlapping tens - Ambigraph Mar 2020_Page_03
Overlapping tens - Ambigraph Mar 2020_Page_04
Overlapping tens - Ambigraph Mar 2020_Page_06
Overlapping tens - Ambigraph Mar 2020_Page_07
Overlapping tens - Ambigraph Mar 2020_Page_08

This is a very important base layout and a multitude of tenfold patterns can be constructed from this starting point. Here are three related variations.

For the first two patterns, we need to add some extra circles and divisions as described in the steps below. I have highlighted the basic repeating hexagon in the last slide.

tenfold hexagon repeat R&C-01a
tenfold hexagon repeat R&C-01b
tenfold hexagon repeat R&C-01c
tenfold hexagon repeat R&C-01e
tenfold hexagon repeat R&C-01f

From this layout, although I haven’t outlined every step, you can complete the pattern using existing intersections.. it may take a little comparison between my diagrams and your drawing to see the required connections. The same layout of circles and divisions will yield the two patterns below and, for the explorers among you, perhaps more to discover.

Starting again from the base layout of the rectangle and 1/20th divisions we can go in a different direction to construct a related pattern using different angles and a different vocabulary of shapes. Follow the steps below to establish circles and divisions.

tenfold hexagon repeat R&C-01i
tenfold hexagon repeat R&C-01j
tenfold hexagon repeat R&C-01k
tenfold hexagon repeat R&C-01l
tenfold hexagon repeat R&C-01m

… and the pattern itself.

tenfold hexagon repeat R&C-01n


I hope you enjoy exploring these patterns and that it may lead to your own insights and discoveries. If you post your drawings on Instagram, please tag me @ambigraph so I can see your work. Finally here is an alternative tiling of the repeating hexagonal unit with a jaunty rhythm.

Constructing semi-regular tilings of the plane with ruler & compass

Through discussion with fellow geometers, it seems there is a need for a simple resource showing the steps for drawing all eight semi-regular tilings of the plane using a ruler and compass, so I have compiled the methods presented here. There are, of course, many other ways to approach these tilings depending on your requirements. You can find sequential diagrams below, however if you enjoy print media or would like to support my work and help me fund further book projects, you can purchase a printed booklet version (with free UK delivery).

These tilings underpin many geometric patterns and are essential to understand if not always necessary to construct. If you need help constructing the hexagon and square you can refer to my earlier blog post about constructing regular grids with ruler and compass.

semi reg grid book

New published work

Some of my works have been published in the last month. Firstly, I have written a paper for the latest issue of the Journal of Illustration titled On the use of vocabularies of geometric forms in ornamental pattern design. This has been developed from a talk I gave at the Decriminalising Ornament – the 9th International Illustration Research Symposium and Exhibition at Anglia Ruskin Universiy in 2018.

As it is an academic publication, the cheapest way to access the article is pay per view of a single article for $14.

Secondly, some of my work has been featured in The Drawing Ideas Book by Frances Stanfield. “Refresh your creativity and boost your motivation to draw with the expert help of The Drawing Ideas Book.” Many thanks to Frances for including my work alongside many other great artists.

Art of Islamic Pattern Exhibition at Homerton Hospital

I’m very pleased to be exhibiting two painted geometric drawings as part of this group exhibition at Homerton University Hospital, London organised by Richard Henry and Adam Williamson from Art of Islamic Pattern alongside excellent and varied work in a range of media by a number of other geometric artists. If you would like to attend the private view from 6-8pm on 2nd July, please contact me.

Constructing grids with ruler and compass

In September 2018 I gave a presentation about patterns constructed using grids at the 4th International Workshop on Geometric Patterns in Islamic Art in Istanbul. For the presentation I prepared these timelapse videos demonstrating different methods for constructing grids using ruler and compass and I have posted them here to be of service to a wider audience.

Square and isometric (triangular) grids provide a rich and expansive foundation for the exploration of geometric patterns. They have arisen from the simplest regular divisions of the 2D plane. The triangle and the square are two of the three regular polygons which can tile a 2D plane by themselves. The hexagon is the third but can be seen as a combination of 6 triangles so equates directly with the isometric grid. These first two videos show the basic construction of the hexagon and square from the circle, fundamental constructions in the study of geometric art.


Timelapse geometric drawings for the Qatar National Library

Earlier this year the Qatar National Library opened a new permanent exhibition of artefacts from it’s Heritage Library collection. I was commissioned to make three timelapse videos demonstrating the construction of geometric designs featured in particular artefacts, to be displayed alongside the original pieces. In order to create the films I analysed and reconstructed the three designs and then produced these timelapse films demonstrating how the designs could have been constructed using the traditional tools of ruler and compass. It was an incredibly satisfying challenge which allowed me to incorporate a wide range of skills into one project.

The videos are currently on display the library and the exhibition also features books, manuscripts, historical photographs, maps, globes and travellers’ instruments that tell the story of Qatar, along with the history of science, literature, writing, travel in the region, and much more.