Are these textile patterns?
no. These are tiles. dome's tile of The Imam Mosque in The Isfahan,Iran.This is related to the Safavid period.16 Century.
You can try to look here http://archive.bridgesmathart.org/2011/bridges2011-681.pdf
There is a commercial macro that can generate patterns, it may work for the Islamic-type designs.
http://corelvba.com/index.php?pages=sym_1
Patti
This looks interesting. I guess it is only possible to make an exact replicate of the original by tracing it by hand, as it is handdrawn and not 100 % symmetrical. But, if it is enough to make just something similar in less time I would start looking at it like this, then tweaking the result to make it look slightly less symmetrical:
PS: I think the Symmetrical macro that pranderson suggested could be useful if you find a way to distort the macro output into a triangle shape or envelope (?).
Another way to approach this...
A Kaleidoscope effect in PhotoPaint (effect is a plugin)