Tips on searching for a pattern

Brian Wichmann

1 Introduction

There are three methods provide to search for a pattern. You should try all three so that you have a basic knowledge of the system.

The system stores some basic geometric properties and details of the source. Hence one can search for specific geometric properties or use a text search.

The simplest search method to use is that of the tree search, but it can be rather slow in locating a pattern.

2 Geometric property search

Given a specific pattern, then you need to analysis the geometry to see what features might be useful in a search. The problem is that with over 1,000 patterns to choose from, one needs to search for unusual features.

One can see what properties might be useful in searching for a pattern by examining the geometric properties listed for each pattern already in the system.

Consider the example: click here.

Firstly, you should check that you agree with the properties listed:

The star with an angle of 45° is in the centre (about which there is a rotation of order 4)
The other 8-pointed star with a vertex angle of 90° also has a rotation of order 4.
The properties state there is only one of the two stars above - this is because the symmetry ensures the other copies appear.
There is also reflections vertically and horizontally about the central star which ensure that the symmetry is *442 (p4m).
The five non-regular reflective polygons are: one in light blue, one in dark blue and two in grey blue.
The tiling satisfies the interlace condition (the points at which more than two polygons meet are straight cross-overs). Following the interlaces, one finds two types of infinite interlaces.
The tiling is edge-to-edge since each straight line of a polygon is joined to only one other polygon.
The last property given the number of polygons displayed is useless for locating a pattern, since that merely depends upon the scale of the pattern.

All of the other properties can be inserted into the form for the comprehensive search. This obviously locates the tiling above, but could, in general find other tilings (but not in this case).

In practice, when working from a photograph (say) you may not be able to determine all the properties - in that case, one should enter only those for which you are certain. In this case, the same result would be obtained if you did not enter the symmetry group.

You can now experiment and find out which individual properties reduce the number to the smallest. For instance:

Just giving the symmetry group produces 6255 tilings.
Just giving the two-colour condition with no finite and two infinite interlaces gives 126 tilings.
Giving the tiling angle as 45 degrees gives 453 tilings.

Hence it is a combination of several properties which enables a search to reduce the result to a reasonable number which can be inspected by hand.

If you look at the statistical summary, you will notice a very uneven distribution for every property. This implies that there are no simple rules as to what properties will be most effective in locating a pattern. The only solution is to try various properties until a suitable combination is found.

3 Textual properties

To search for all the tilings in the collection from the Alhambra is easy - just type Alhambra into the text search box in the comprehensive search.

However, one tiling is not as expected, see click here. This is from the Alhambra Palace Hotel and was thought not to be an authentic classical Islamic pattern. It is actually authentic but not in the Alhambra Palace itself. Hence text searches need to be used with care.

Now consider trying to find the tilings from Morocco - the obvious choice being a text search with the text Morocco. This gives only 18 tilings. Looking at click here, shows that the books by Paccard and DeGeorge are relevant. These two publications can be used in the comprehensive search to locate more Moroccan tilings. Actually, typing Fez into a text search yields 31 tilings, but Fes yields 11 tilings. The inconsistent spelling is due to copying the spelling in the source documents, rather than attempting some consistency.

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