I have a book out from the library by Eric Broug which shows how to draw Islamic tile designs. You can buy it here. Eric also has a website with some tutorials. All the designs are drawn with a straight edge and a pair of compasses. No measuring, no set square. I've drawn them in my sketchbook and then coloured and photocopied them so I have multiple copies and different sizes. Above is a small selection covering the dining table.
I'm trying out inverting the black and white areas and combining small and large tiles. The hexagons are easiest to work with and give pleasing compositions. I like leaving blank areas, overlapping the tiles and changing scale and pattern across the paper. I think you can get quite an organic looking design that is composed of very geometric shapes.
The squares are a little trickier to get a pleasing composition. It's difficult to get away from a basic grid design.
These star shapes are mainly based on a pentagon although there is one hexagon based tile here too.
The shapes with 5 or 10 sides are hardest to lay out in a design as they don't naturally tessellate. I'm experimenting with putting them on grids with other shapes in between.
Once I have finished experimenting with these copies I will carve some designs into a lino block to use in my "geographical" sketchbook.
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