Ontwerpen van patronen

Najaar 2017

Dit patroon op een isometrisch grid ontwierp ik najaar 2017. De zevenhoeken zijn regelmatig, de andere vijf vormen hebben minstens één symmetrie-as.

Het patroon behoort tot een in de Islamitische ontwerptraditie schaars voorkomende symmetriegroep met drievoudige rotatiesymmetrieën, maar zonder zesvoudige.

Download onderstaande pdf van het ontwerp in zwart-wit om er zelf mee aan de slag te kunnen gaan.


A new pattern with regular heptagons
17 11 02 New pattern with heptagons on i
Adobe Acrobat document 300.7 KB

Voorjaar 2014

A competition was held about one of my new designs

The winner of the competition is José Bradamonte. He handed in a hand-drawn hexagonal solution with a weaving and slightly curved lines. Congratulations José!

This solution clearly shows the symmetries of the pattern: Threefold rotational symmetry around both the big and the small sixpointed stars and reflection symmetries in three directions.

This pattern belongs to a newly discovered category of patterns that belongs to a wallpapergroup that was very scarcely used in Islamic design.


Here is a part of a tessellation consisting of sixpointed stars (two sizes), fivepointed stars, hexagons (three types which have almost equal shapes) and, in the middle, a tile with the shape of an incomplete star and a hexagonal empty space in the middle.

With these seven different tiles the plane can be tessellated. This can be done by yourself by printing the pdf below.


Dit is een deel van een vlakverdeling die bestaat uit zespuntige sterren (twee groottes), vijfpuntige sterren, zeshoeken (drie types die bijna gelijke vormen hebben) en, in het midden, een tegel met de vorm van een onvolledige ster met een zeshoekige open ruimte in het midden.

Met deze zeven tegels kun je het hele vlak vullen, zoals te zien is in de twee tekeningen hierboven.

Print de pdf hieronder om je eigen tekening te maken.


drawing sheet for competition
Print this page and take part in the competition
Adobe Acrobat document 132.1 KB

P.S. An advice: Use tracing paper (overtrekpapier of patroonpapier) to expand the drawing. Success!

Spring 2014: A late-fourteenth century design with tens and sevens

(This pattern was my own design, late fourteenth century on the Islamic calendar.)

Pre-study; drawing without use of ruler (may 2014)
Pre-study; drawing without use of ruler (may 2014)

Multiple-design of a pattern with octagons

These patterns were designed with the use of drawing in a 16th century manuscript. In this drawing, a subgrid consisting of two types of hexagons is used resulting in a pattern with regular heptagons. I made use of the same subgrid to design patterns with regular octagons. (feb 2014)

Turn-angle 22.5 degrees
Turn-angle 22.5 degrees
turn-angle 30 degrees
turn-angle 30 degrees
Turn-angle 33.5 degrees
Turn-angle 33.5 degrees
In this ppt you find a series of patterns in black-and-white for a range of 'turn-angles'.
Subtle movement of octagons.pptx
Microsoft Power Point presentatie 4.5 MB

Winter 2014: Design of a pattern with 4-, 7-, 8- and 16-pointed stars

Impossible combination of regular 4-, 7-, 8- and 16-pointed stars and triangles
Impossible combination of regular 4-, 7-, 8- and 16-pointed stars and triangles

This tessellation suggests the possibility of combining these various 'perfect' stars in this way. However, the stars aren't exactly regular! There are small imperfections making this combination possible.

Mathematically speaking: The 16-pointed stars do not have an exact 16-fold rotational symmetry and the 7-pointed stars do not exactly have 7-fold rotational symmetry.

These types of mosaics, with slight irregularities were produced in the Seljuk period (11th-13th century Persia) also. Mr Peter Cromwell wrote an article about this, to be published in 2014.

Persian-style geometric pattern designed by students in may 2012

Two students Daphne de Ridder and Thomas Mast from Texel who did the course on Islamic patterns won the Texel 2012 design competition. Their work is reproduced electronically in triplex. Therefore I drew their design using 'Geogebra'. The result is shown here. The colourful end result of the students (They called their work 'Lente', meaning 'Spring') can be found at leerlingen presenteren hun werk.

The pattern has a typical Persian style and it wouldn't surprise me if the design was made before during the middle ages in the Persian region thus making the student's design a 'reinvention' of a pattern designed centuries ago. Its basic pattern consists of squares, hexagons and dodecagons hence the many four-, six- and twelvefold local or total rotation symmetries.

Here's a photograph of the mosaic in triplex. I published a series of photo's showing the production process at van leerlingontwerp naar kunstwerk.

Summer 2012: Design of a pattern with regular heptagons

Regular heptagon pattern, designed july 6th 2012 with the program geogebra
Regular heptagon pattern, designed july 6th 2012 with the program geogebra

Spring 2012: Persian-style geometric pattern

With the drawing programme 'Geogebra' I designed this Persian-style pattern with regular eight- and ninepointed stars. The pattern has reflection and glide reflection symmetries, four- and twofold rotational symetries and local eight- and ninefold rotational symmetries. Besides the two starshaped tiles there are three other types of tiles. Two of them have one axis of symmetry, the third one has two axes of symmetry.

For information about the design technique used and in case you wish to use this design for any goal, please contact me.

Spring 2011

Design of a slowly changing pattern in collaboration with Dutch students, 2011
Design of a slowly changing pattern in collaboration with Dutch students, 2011

Recent Activities, News

Recensie van Snijpunt Isfahan

Lees hier

First prototype of new aperiodic puzzle

The developing process is continued. click here.

Ars et Mathesisdag 2019

During the art- and maths day (Ars et Mathesisdag), 24 november 2018, I gave a lecture about analyzing historical geometric patterns and trying to find new ones.

Timelapse construction

A great timelapse construction by Ameet Hindocha. More can be found on the website Ambigraph

Article online available

The journal For the Learning of Mathematics made my 2014 article 'Learning geometry by designing Persian mosaics' online available: See https://flm-journal.org/Articles/2E0CB6E94D76C79C2F341680D60F17.pdf

Een kritische recensie van Snijpunt Isfahan

Here you find my reflections on  a very critical review of Snijpunt Isfahan by a mathematician (in Dutch)

March 30 2018 Lecture

Lecture in Dutch

Two new 'floral'patterns

24 March 2018

Based upon the famous Alhambra pattern with circle segments. Click on the picture below to go there

14 feb 2018 Event about  'Snijpunt Isfahan' at Spui25

Look here

Interview by Dolf Jansen

Dolf Jansen interviewed Maite and me (in Dutch) during the radio program 'Spijkers met Koppen', to hear and watch the interview, klick here

Interview by Coen Verbraak

Coen Verbraak interviewed Maite and me about Maite's book 'Snijpunt Isfahan' (in Dutch), to hear and watch the interview, klick here

Official opening of Museum Gallery RAT (Recomposed Art Texel)

May 13 2017 we celebrated the opening of our new location Burgwal 20 Den Burg. Here you find artwork composed with beachcombed materials by Maria Roelofsen and my design studio for making new pattern compositions based upon the Islamic design tradition. For further information also look at www.museumgalerierat.nl

A new floral design with worksheet. Click on the picture to find more information about the Khatai Flower.

March 24th 2017

Heart cloud sun

Workshop in Amsterdam

21 august 2016 11.30-13.00

In the Tropenmuseum I delivered a workshop on the Islamic design tradition of geometric patterns in Dutch, further information here

New poem in Dutch:

Één Jaar

                                 May 6th 2016

Floral designs

A new subject is being developed and information will be available on this website: floral designs. I started today with the lotus flower. Click on the lotus below to visit the right tab.

                        24th of March 2016

Colour Plates available (not any more since the exhibition ended)

Download my puzzle-/colour plates at this link of the Tropenmuseum Junior 

Short story 'Spiral Figures'

I wrote a short story in Dutch about a child who draws spiral figures at the beach

Students finished newly developed lesson strand on Islamic mosaic design

Click on the picture below and check the two slide shows on the 2015 results. 

The workshop I delivered in 2014 is online since Jan. 2015

A miraculous set of tiles

I found a set of two tiles which can only form a semi-periodical pattern
I found a set of two tiles which can only form a semi-periodical pattern

Patchwork by Marijke Maris-Baan

Marijke Maris-Baan finished her design in patchwork, inspired by the winterworkshop held January 2014 on Texel
Marijke Maris-Baan finished her design in patchwork, inspired by the winterworkshop held January 2014 on Texel

Heptagon construction

A method to construct a near-regular heptagon now published on this site

Result of drawing competition

6 July 2014. The drawing cmpetition was won by José Bradamonte.

Students finished mosaic design course

A  group of about 20 students finished the lesson strand on Persian style mosaics in the beginning of may 2014. You can find some impressions of their activities here

View their endresults here

Result of pre-study

May 2014
May 2014

Article published

2014, March.

My article 'Learning Geometry by Designing Persian Mosaics' is published in issue nr. 100 (March 2014) of the Canadian journal 'For the Learning of Mathematics'.

At the flm-website you can find an Abstract.

Examples of basic patterns

Now available: a set of simple basic patterns (subgrids) to use to design new geometric patterns
Now available: a set of simple basic patterns (subgrids) to use to design new geometric patterns

New pattern design

Click on the picture below to find a series of patterns with octagons

Turn-angle 30 degrees
Turn-angle 30 degrees
Turn-angle 22.5 degrees.
Turn-angle 22.5 degrees.

Workshop 1&2 Feb. 2014

The workshop held on Texel was attended by 13 people in total. Among them: a furniture maker, a designer of lamps, quilters, painters and teachers. See the photo-impression of the workshop

Article in local newspaper Texel

This article (text and photo Pip Barnard) is about my fascination for Islamic geometrical ornamentation and how it can be used in (mathematics) education.

Article in Dutch newspaper

An article about the artwork by Maria Roelofsen and myself was published in the Dutch newspaper 'Reformatorisch Dagblad' on 30 december 2013. (Text Janneke van Reenen-Hak, Photo's Sjaak Verboom)

Publication in dutch magazine 'Experiment NL'

In this magazine on dutch Scientific research an article was published about my work. All those who have a subscription of 'Quest' received this magazine. Four pages with beautiful illustrations!

Work in progress, oktober 2013
Work in progress, oktober 2013

International workshop on Islamic geometric design Istanbul

At the Design Center of Istanbul a six-days congres was organized with lectures and workshops delivered by experts in this field. Incredibly inspiring!


Conference Isfahan, Iran

May 2013. A three day conference for mathematicians and artists on geometric Islamic patterns was held. Lots of inspiring workshops and lectures were delivered.

Workshop Leiden

Workshop for students, Institute for Studies of the Middle East, Leiden University, 27 march 2013

A participant of the workshop designs a geometric pattern
A participant of the workshop designs a geometric pattern

Contribution to piece of art

The use of patterns in a work of art by Maria Roelofsen (march 2013)
The use of patterns in a work of art by Maria Roelofsen (march 2013)

Lecture for maths teachers

During the conference for Maths teachers held december 18th 2012 at the Groningen University I gave a lecture about using islamic mosaics to teach geometry at all levels in secundary schools.


Article Published

June 2012.

In the review for Dutch mathematics teachers called 'Euclides' the article 'Designing Persian Mosaics in the Classroom. Students in the centre of a medieval design tradition' appeared (for the article in Dutch click here).

Maria completed 'the frog'