I found this as I was looking for aesthetics of symmetry and patters, I found some interesting information.
A Treatise on the Aesthetics of Symmetry
Preface
I was walking along Commonwealth Drive one day in Boston admiring a wrought iron fence when I became introspective, curious as to why I appraised the fence as attractive[I find fences extremely attractive as well!!!]. It had something to do with the inherent symmetrical design. With this in mind, I scrutinized other items that I traveled past exhibiting symmetry. Some were quite provocative, others were nominally patterned, and still others were rather tedious and boring. The conclusions I depict in this essay are anything but scientific.
Even if you concur one hundred percent with everything I describe, be careful when applying this to your own designs. At times the theories that we use to constrain ourselves during design come back to bite us in our rear ends[True]. These ideas have the potential to capture your visual design processes and hold it hostage, incarcerating all of your designs to a central structural consistency. Bad plan. Please apply what you learn from this treatise where its application fits, but don’t force all of your work toward satisfying these observations.
Finally, aesthetics also transpire below, on top of, and beyond symmetry[symmetry and patters appear in nature in many forms, so there is an aesthetic theory that belongs to it]. Some of the most exquisite art and craft that I’ve seen had nothing to with symmetry at all.
Geometric Symmetry: Quick Review
Symmetry has several variants, but the basic symmetrical operations are Translation, Rotation, and Reflection. Translation is simply the movement in a linear direction of a design; here is an example of a translation:
The design above has been translated four times. A rotation is the movement in a circular direction of a design; here is an example of a rotation:
The design above has been rotated six times. Finally a reflection is the inversion of a design across a line; here is an example of a reflection:
The design above has been reflected across both horizontal and vertical lines. Symmetrical operations can be combined; here is an example of a translation combined with a reflection (this is called a Glide Reflection):
Here is an example of a translation combined with a rotation (a Glide Rotation):
What is Boring
Symmetrical operations certainly add some elegance to an otherwise drab design. You can quite easily, however, have too much of a good thing. The following design, for example, is something that I would consider boring:
Too many repeats of the primary simple design bores us[True sometimes!]. What constitutes “too many” or “too few” repeats is a matter of taste and personal opinion. It also has to do with the complexity of the simple design, or motif. Furthermore, it might be affected by the symmetry operation:
The above example is similar to the boring example with too many repeats, however since the symmetrical operation is a Glide Rotation instead of a Translation, it is considerably more interesting.
Ala'a B. 