Tips on searching for a pattern
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
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:
Firstly, you should check that you agree with the properties listed:
All of the other properties can be inserted into the form for the
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:
- 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.
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.
- Just giving the symmetry group produces 6255 tilings.
- Giving the tiling angle as 45 degrees gives 453 tilings.
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 was 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. In this case, the Hotel name has a '-' added so that the search gives the expected