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How can we actually define a pattern and why do we consider them so (psychologically) appealing?
There are several theories, that people are basically pattern recognition and matching machines and there is definitely some truth about it. If we for instance look at a mountain or a wild tree, eventually a beach, we can relax into its complexity because of the high fractal dimensions. The nature itself occasionally exhibits repetition and symmetry, such as in crystals.
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So what does this symmetry mean and why is this symmetry so important to us?
Symmetry can be considered as predictable and perfect regularity within pattern. In symmetric pattern, certain aspect(s) of the pattern are produced identically when other aspects of the pattern are changed.
In other words, symmetry is a fundamental part of geometry, nature and shapes. It creates patterns that help us organize our world conceptually. We see symmetry every day, but often don't (consciously) realize it.
It is actually an important and prominent feature of the visual world. It has been studied as a basis for image segmentation and perceptual organisation, but it also plays a role in higher level processes, such as face and object perception.
Confused?
In a world of rush and chaos, we're searching for something still and perfect. After all, even a tower block that once seemed drab and ugly, can, if photographed in the right way, be transformed to a thing of beauty. So yes, that's why pattern and symmetry really matters and goes hand in hand. After all, convince yourself by visiting our little pattern universe.