Information on the Tiling Database

by

Brian Wichmann

with assistance from Tony Lee

Contents

1  Introduction
2  Sources
    2.1  Copyright
3  Acknowledgements
4  Browsing
5  The main search facility
6  The simple search facility
7  The Tree search facility
8  Special collections
If you have comments on this Internet site, please email the author at the address above. Contributions are also requested. High quality digital photographs of tiling patterns that should be in this collection would be much appreciated.

1  Introduction

This site consists of a data base and search facilities to locate items in the collection. Unlike most data bases, the items are images, but ones that have substantial structure. This structure is recorded in the data base making searching and retrieval possible.

2  Sources

Currently, almost all of the material recorded here has been extracted from publications. Hence for every item, there is a list of publications that refers to it. The complete list of publications is in the list. Each publication is referenced by text string enclosed in square brackets.
In those cases in which the author has been provided with information that has not been published or placed on the Internet, the `publication' [pc] is used (standing for personal communication).
If you want an ordinary publication containing the great majority of the information here, you can purchase on-line the CD/booklet: [1].

2.1  Copyright

The contents of this site are licensed under a Creative Commons License.
If we have, by accident, infringed your copyright, please notify us and we will remove the offending item.
If we have, but accident, not correctly attributed work to yourself, please notify use and we will amend the offending item.

3  Acknowledgements

Thanks to World Scientific Publishing Co Pte Ltd for publishing The World of Patterns [ISBN: 981-02-4619-6 (pbk); © 2001], which has provided a basis for this Internet system.
This site is actually hosted by Perspective Technologies Ltd, the Directors of whom are the two youngest sons of the author of this system.
The list of sources shows the large number of people who have effectively contributed to this work via their publications.
People who have contributed includes (alphabetically):
Various facilities have made undertaking this work possible including: GNAT Ada compiler, MySql, Graphic Converter, Python, Fugu and all of this software on an Apple computer.
Producing the publication list would hardly have been possible without the National Art Library on-line catalogue.

4  Browsing

The simplest way to browse the collection is to use the facility on the home page to display a random selection of 20 patterns. Click here to use it! Click on any of the small GIFs to obtain the full details of the pattern. Clicking on the same GIF again produces the high quality PDF version of the pattern.
The other method of browsing the collection is to use the slideshow. Click here to use it! This display in a large format provides a selection of patterns which shows the variety within the collection. For each such item in the slideshow, one can obtain the full details and also an explanation as to how to use the search facilities (see below) to find other similar patterns.
The another method of browsing the collection to examine some classes of similar patterns. Click here to use it!
Yet another method of browsing the collection to examine the statistics page. The numbers of patterns having a specific property is actually a hypertext link to an individual pattern having that property. Click here to use it!
If your main interest is in Islamic patterns, then the very best such patterns are shown on the entry page to the system. These are called gold star patterns. Click here to use it! Wait for each pattern to be displayed in random order.

5  The main search facility

This search uses an HTML form to specify a number of conditions that a tiling pattern must satisfy. Unlike many Internet searches, this one obtains an exact match. If you request a pentagon, then the pattern has to have an exact regular pentagon - one that looks as if it might be regular, but is not, will not do. As an example with inexact pentagons, see.
To satisfy the conditions, all of them must be satisfied. Hence, when combining unusual conditions, it may well be that no tiling pattern satisfies the conditions you have given. To refine a search, the HTML back facility can be used to edit the existing search options. Otherwise the Reset button can be used to start again.
One cannot specify a search for the absence of something. Hence one may get a tiling pattern with a regular octagon even though that was not requested.
Three options are available for presenting the results, always as a list. Small images are available for quick identification, a list of titles, and lastly, a list of the tilings with the reference information for each one. This last option is useful for checking all the references to a specific publication.
Note that the text search is somewhat slower than the other forms of searching.
Now try using the facility by clicking here to use it! See how many patterns there are with 14-point stars.

6  The simple search facility

This facility aims to be as simple as possible. The user just needs to select the shapes present in the pattern - the shapes being regular polygons and regular star polygons. Only the major polygons and star polygons are listed.
The search finds the tilings with only the selected regular shapes present. Hence if a search is made for tilings containing equilateral triangles and hexagons, then tiling containing those and squares will not be included. This implies that the search logic is different from the main search facility.
Now try using the facility by clicking here to use it! See how many patterns there are with both equilateral triangles and hexagons (but no other regular figures).

7  The Tree search facility

This facility allows to locate a pattern by answering simple questions about it. When relatively few patterns are left, all are displayed for making the final selection.
Now try using the facility by clicking here to use it! Take any pattern and see if you can find it. If you have a photo of an interesting pattern and fail to find it, please email be about it!

8  Special collections

These are highly specialised collections of patterns which are identified as being special and are handled differently as appropriate. Currently, there are four special collections - one of rectangles tiled by polyominoes, another of prefect colouring, tilings of unique factorization domains and lastly, tilings of squares by similar triangles. For the details, see.

References

[1]
B. A. Wichmann, The World of Patterns, CD and booklet. World Scientific. 2001. ISBN 981-02-4619-6 URL

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