Zymmetry

Anica Presley

CFC III: Nature

Jessica Frelinghuysen

31 January 2013

Natural Patterns: Symmetry

Symmetry in the general sense refers to proportion and repetition. The term is used by many different professions and areas of study, each with their own specific understanding of its meaning. Biological symmetry refers to the various naturally occurring patterns found in everything from molecules, plants and animals, to the universe as a whole. Humans were fascinated by symmetry long before some of these discoveries were made. Artists, architects, and designers study and manipulate symmetry’s visual implications. However, all human fascination with the subject comes from what can be observed around us. Thus, leading to do in a study of symmetry is to go back to the source, nature. Classification of symmetries varies across the board. However, they can be classified into two groups: point and space. Point groups have one unique point that differs from all others and remains unchanged. Symmetries in the point group include radial and mirror or bi-lateral. Space groups tend to have a repeating shape or pattern within a designated space. This includes wallpaper and stripe pattern symmetries. The most commonly discussed are point groups. Thus, I will begin by explaining the two aforementioned space groups and follow up with point groups.

            Wallpaper symmetry appears more in math than it does in nature. However, a naturally occurring example would be beehives. In wallpaper symmetry a shape or pattern tessellates a plane from a given point or region in a finite amount of space forming wallpaper pieces. There are four different types of symmetries: translations, rotations, reflections, and glide reflections. Translation symmetry involves moving a figure by a vector, or length and direction. Rotational symmetry is the result of rotating a figure about a point. Reflection symmetry is a mirror image produced across an axis that is the same as the original figure but spatially reversed. Glide refection is a combination of translation of a figure that is mirrored across a line. These four groups combine to form seventeen distinct symmetry groups, also known as wallpaper and plane crystallographic groups.

            Stripe pattern symmetry also combines types of symmetries to make up seven patterns. Each pattern has either one or more of the following symmetries: translation(T), horizontal mirror(H), vertical mirror(V), rotational(R), and glide reflection(G). The seven types are T, TR, TV, TG, TRVG, TGH, TRGHV. A naturally occurring example of stripe pattern symmetry is footprints. Human footprints have TG symmetry, while animals on all fours tend to have THG symmetry in their tracks. Trees and snakes are another example of stripe pattern symmetry.

            Radial symmetry is rotational symmetry about a fixed point, the center. There are two forms of radial symmetry; cycle and dihedral. Cyclic is simple rotation a given number of times about the center point. Dihedral refers to both rotations and reflections, with mirrors occurring at each rotation. Examples of radial symmetry are starfish, jellyfish, daisies, and the universe. Things that have radial symmetry tend to be more sedentary, at least when compared to bilateral symmetry.

            Bilateral symmetry is a reflection across a single axis, also commonly known as mirror symmetry. Natural examples of this are orchids, tigers, ants, horses, and elephants. Bilateral symmetry lends and thus is replicated form in vehicles and transit. In animals, bilateral symmetry is demonstrative of forward movement, while in insects like beetles, spiders, and dragonflies it is a sign of forward and back as well as side-to-side movement.

            Each classification has its own purpose and reveals different information about the foundations of life. Wallpaper symmetry tends to show up in packing of particle as well as packaging of products. Stripe pattern symmetry demonstrates growth or journey of an object. Radial symmetry is the essence of our creation as the universe is a rapidly expanding radiation from the center, or what is known as the big bang. Bilateral symmetry is perhaps the most replicated because of its aesthetic nuances and physical implications in movement. The study of symmetry is applicable to virtually anything, and reveals a startling yet enticing magic about the order of the universe.

Works Cited:

Hargittai, István, and Magdolna Hargittai. Symmetry: a Unifying Concept. Bolinas, Calif.: Shelter Publications , 1994.

Senechal, Marjorie, and George M. Fleck. Patterns of Symmetry. Amherst: University of Massachusetts, 1977. Print.

"Symmetry in Nature." Symmetry in Nature. N.p., n.d. Web. 31 Jan. 2013.

Woodger, Joseph Henry. Biological Principles, a Critical Study. London: Routledge & K. Paul, 1948.

Images:

Burlew, Rusty. Fermenting-honey.jpeg. Digital image. Honey Bee Suite. Honey Bee Suite, 25 July 2010. Web. 27 Jan. 2013.

Chap, Chiswick. Tiger-berlin-5 Symmetry. Digital image. File:Tiger-berlin-5 Symmetry.jpg. En.wikipedia.org, 25 Oct. 2012. Web. 27 Jan. 2013. <http://en.wikipedia.org/wiki/File:Tiger-berlin-5_symmetry.jpg>.

Coral Snake. Digital image. The Art of Manliness Guide to Snakes Part 1: Know Thine Enemy. Art of Manliness, 14 July 2008. Web. 27 Jan. 2013.

MwRsoHS.jpeg. Digital image. Bright Petals. RGB Stock, 26 June 2010. Web. 27 Jan. 2013.