Frequently Asked Questions

Brian Wichmann


1  Why small GIFs?
2  Why use PDF?
3  Why is colour ignored when determining the symmetry of a pattern?
4  Why no photographs?
5  Why degrees and not radians for angles?
6  The colours of some tilings are poor
7  Why so few mathematical tilings?
8  Why is the style of lines ignored when determining the symmetry of a pattern?
9  Why not use SVG?
10  How are the patterns produced?
11  Can I help?
12  Why can I find something with a string search?
A  Revision record
I cannot pretend that I have a large database of questions to answer here, but this format does provide a mechanism to explain some design choices which may not be obvious.

1  Why small GIFs?

The response to a search query is bound to be a number of individual tilings. Since the number could be quite large, and users may not have a broadband connection to the Internet, small graphics must be used. GIFs are slightly better than JPGs for this purpose. The average size of the GIF's is 7Kb. Around 25 fit on a screen, so that a visual inspection of around 100 tilings is feasible.
The small size of the GIFs means that the more complex patterns, such as the large zellijs from the Alhambra (click on this to see such a pattern), cannot be viewed adequately without going to the PDF version. Hence the size is a compromise and providing an option for large GIFs would be too complex.

2  Why use PDF?

High quality images can only be provided using vector graphics which is supported by PDF. For one pattern, the same detail could not be obtained from a 12Mb GIF. In contrast, the average size of a PDF file is 7Kb (same as the small GIFs).

3  Why is colour ignored when determining the symmetry of a pattern?

Consider the pattern click on this to see the pattern. If the colour was not ignored the pattern would be a repetition of the merging of one yellow, red and green polygons. Hence the rotation of order 6 would be lost. So a key aspect of the structure of patterns would be lost.

4  Why no photographs?

The great majority of photographs that are available are from books which could not be put on this site for copyright reasons. Also, photos would take about 100 times the storage requirements. Lastly, the geometric data about each tiling is produced by the program that produces the graphics - producing this information from a photograph would be a manual and error-prone task. Having links to photos stored elsewhere on the Internet have now been added.
For many patterns, but not all, there is internal documentation which in many cases, includes a photo. This material is not available on the web site but can be requested from me.

5  Why degrees and not radians for angles?

Actually, the angles are held internally as p/q where p and q are integers, being a multiple of 180 degrees. It is felt that degrees is a more natural notation for most users. Note that the comprehensive search only allows for angles in whole degrees or half degrees.

6  The colours of some tilings are poor

Agreed. Many of the colouring derive from [1] and will be redone in due course. Ideally, for the Islamic patterns an actual colour photograph should be used to produce matching colours. In general, such photos are not available.

7  Why so few mathematical tilings?

There are several large sequences of mathematical tilings which could be included. For practical reasons, these sequences need to be available in a computer-readable format which can be converted by program to the format used by the system here. Version 8 included over 100 tiling of rectangles with polyominoes which is the first such specialised collection to be added, see.
In Version 10, tilings are available showing the concept of perfect colouring, see.

8  Why is the style of lines ignored when determining the symmetry of a pattern?

Consider the pattern click on this to see the pattern. Several of the reflections invert the up-and-over interlacing and therefore would not then be a symmetry of the pattern. Hence the structure of the patterns is best captured by ignoring the interlacing line style.

9  Why not use SVG?

The standard for vector graphics could be used instead of PDF, but this would be inappropriate since support for SVG is no where near as good as that for PDF. Alternatively, the ability to output a vector format for a pattern would be useful so that tools like Inkscape could be used to construct variants of an existing pattern. Another vector format is CGM, but this is also poorly supported. There is now a freely available tool that supports SVG, and the generation of SVG is now used to show the dynamic build of a pattern.

10  How are the patterns produced?

Briefly, using my own software. I now have a means of producing documentation which gives the details of construction as a PDF file. I do not plan to put this material on the web site (except for one click on this to see the example), but anybody requesting such documentation can email me for a copy.

11  Can I help?

You can indeed! Probably the most helpful thing is to notify me if you spot any mistakes. Comments are also welcome. Of course, photos of patterns that you think are not included are particularly welcome. All contributions are acknowledged.

12  Why can I find something with a string search?

A string search facility was part of the comprehensive search but cannot always locate material for several reasons: spelling of place names is not consistent, the use of unusual characters is not supported and the text available with a pattern is often not adequate. The use of the publication search or the area lists (see) may be more effective.


B. A. Wichmann, The World of Patterns, CD and booklet. World Scientific. 2001. ISBN 981-02-4619-6 URL (This publication has over 4,000 patterns but in a different format from the on-line system.)
Brian Wichmann and David Wade, Islamic Design: A Mathematical Approach. 2016. ISBN 978-3-319-69977-6. URL (This publication provides and overview of this web site and Patterns in Islamic Art.)