Drawing an Islamic pattern

1 Introduction

This is a short note which is likely to be expanded at a later date.

Much of an Islamic star pattern is determined directly from its mathematical structure. However, there are often choices to be made which can have a substantial effect on the visual impact.

2 Principles

Even when the mathematical structure does not determine some characteristics of a pattern, choices should be made as a matter of principle:

Reducing the number of distinct polygonal shapes.
Ensure that a polygon has axial symmetry if at all possible.
Ensuring that the internal angles of the polygons are a multiple of an appropriate value. (Most of the Alhambra patterns are a multiple of 22.5 or 45 degrees.)
In general, Islamic patterns in the tiling system will increasingly be based on the proportions seen in the most symmetrical authentic, rather than on previously published, drawings.

In addition to the above, there are aesthetic considerations which are not so straightforward to handle.

Many of the patterns in the CD [1] are not drawn well and are gradually being replaced by superior versions.

3 An example

The example is available of one pattern in two versions. To see the detail, you probably need to click on the small image to look at the PDF file.

version 1: This version has the stars with the petals of a size which leaves little room for the rest of the pattern. There are two heptagons between the two stars which should be contrasted with the second version.
version 2: In this version the heptagon looks regular although it is impossible for it to be accurately regular. Note also that the 6-sided polygons joining the heptagon appear to have axial symmetry (but again cannot be exactly so).
There is no doubt that this version is much closer to the original.

Both versions have been retained so that they can be compared. In general, the inferior version will be replaced by the superior one.

References

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