Non-repeating patterns

There are 230 non-repeating patterns.
These can be conveniently divided into four further groups.
The first group are those which have a distinct spiral structure. An example of such a pattern is:
The second group are those tilings of a rectangle by polyominoes, and example of which is:
The third group are those tilings of a square into similar triangles, and example of which is:
The other group has no such spiral structure - an example of which is:
Now you must choose:

v43