Glide reflection in the context of Zigzag

Dickinsonia is a genus of extinct organism that lived during the late Ediacaran period in what is now Australia, China, Russia, and Ukraine. It had a round, approximately bilaterally symmetric body with multiple segments running along it. It could range from a few millimeters to over a meter in length, and likely lived in shallow waters, feeding on the microbial mats that dominated the seascape at the time.

As a member of the Ediacaran biota, its relationships to other organisms has been heavily debated. It was initially proposed to be a jellyfish, and over the years has been claimed to be a land-dwelling lichen, placozoan, or even a giant protist. Currently, the most popular interpretation is that it was a seafloor dwelling animal, perhaps a primitive stem group bilaterian, although this is still contentious. Among other Ediacaran organisms, it shares a close resemblance to other segmented forms like Vendia, Yorgia and Spriggina and has been proposed to be a member of the phylum Proarticulata or alternatively the morphogroup Dickinsoniomorpha. It is disputed whether the segments of Dickinsonia are bilaterally symmetric across the midline, or are offset from each other via glide reflection, or possibly both.

In geometry, a motion is an isometry of a metric space. For instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping associating congruent figures is a motion.

Motions can be divided into direct (also known as proper or rigid) and indirect (or improper) motions.Direct motions include translations and rotations, which preserve the orientation of a chiral shape.Indirect motions include reflections, glide reflections, and Improper rotations, that invert the orientation of a chiral shape.Some geometers define motion in such a way that only direct motions are motions.

Proarticulata (also known as Dickinsoniomorpha) is a phylum of extinct, near-bilaterally symmetrical animals known from fossils found in the Ediacaran (Vendian) marine deposits, and dates to approximately 567 to 550 million years ago. The name comes from the Greek προ (pro-) = "before" and Articulata, i.e. prior to animals with true segmentation such as annelids and arthropods. This phylum was established by Mikhail A. Fedonkin in 1985 for such animals as Dickinsonia, Vendia, Cephalonega, Praecambridium and currently many other Proarticulata are described (see list).

Due to their simplistic morphology, their affinities and mode of life are subject to debate. They are almost universally considered to be metazoans, and due to possessing a clear central axis have been suggested to be stem-bilaterians. In the traditional interpretation, the Proarticulatan body is divided into transverse articulation (division) into isomers as distinct from the transverse articulation segments in annelids and arthropods, as their individual isomers occupy only half the width of their bodies, and are organized in an alternating pattern along the longitudinal axis of their bodies. In other words, one side is not the direct mirror image of its opposite (chirality). Opposite isomers of left and right side are located with displacement of half of their width. This phenomenon is described as the symmetry of gliding reflection. Some recent research suggests that some proarticulatans like Dickinsonia have genuine segments, and the isomerism is superficial and due to taphonomic distortion. However, other researchers dispute this. Displacement of left-right axis is known in bilaterians, notably lancelets.

Charnia is an extinct genus of frond-like lifeforms belonging to the Ediacaran biota with segmented, leaf-like ridges branching alternately to the right and left from a zig-zag medial suture (thus exhibiting glide reflection, or opposite isometry). The genus Charnia was named after Charnwood Forest in Leicestershire, England, where the first fossilised specimen was found; the first species of Charnia described, Charnia masoni, was named after Roger Mason, a schoolboy who was believed to have initially discovered it. Charnia is significant because it was the first Precambrian fossil to be recognized as such.

The living organism grew on the sea floor, 570 to 550 million years ago, and is believed to have fed on nutrients in the water. Despite Charnia's fern-like appearance, it is not a photosynthetic plant or alga because the nature of the fossil beds where specimens have been found implies that it originally lived in deep water, well below the photic zone where photosynthesis can occur.