is measurable via entropy, and this information is related to symmetry. Uncanny symmetry may be measured at multiple scales, and entropy as the measurement of this information is related to morphogenesis. Quantified centric diatom uncanny symmetry will be used to characterize behavior of symmetry changes for a variety of taxa. The relationship of uncanny symmetry to stability changes during centric diatom valve formation will be quantified using concepts from dynamical systems analysis. From here on out, we use the term symmetry to mean uncanny symmetry.
2.2 Methods
2.2.1 Centric Diatom Images Used for Analysis
Taxa were selected from a catalog of scanning electron micrographs (SEMs) in the library of one of the authors (M.A.T.). SEMs of centric diatom genera represented by selected species were used to quantify and analyze uncanny symmetry of diatom valve shape. Taxa selected for use represented circular, eccentric, and polygonal valve shapes that span the range of shapes of centric diatoms. A number of criteria were used to select images for analysis. Images were taken so that the view was determined to be perpendicular to the valve, where the valve appeared to be flat or at 0°. The whole valve had to be unbroken or in a state where breakage was qualitatively deemed to not impair the ability to discern the surface and/or shape boundary. The entire valve outline was unobstructed by debris, or if debris was present, it was qualitatively deemed to not detract from discerning the surface and/or shape boundary. Individuals were chosen to represent closely related species, and multiple species were selected from each genus when feasible.
Taxa whose images were chosen for study are given in Table 2.1. These 15 centric diatom genera represent a wide variety of genera, species, shapes, and valve patterns found in centric diatoms. Within each genus, species exhibit distinct features that are associated with the silica deposition process as evidenced by the morphology on the valve face. Morphological valve features are a record of silica deposition during valve formation and part of the morphogenetic process. The shape and position of valve features are indicators of symmetry of the valve surface.
Table 2.1 List of species considered and thumbnail, masked image examples for all of the individual diatom taxa we analyzed, all scaled to the same apparent diameter, along with individual number of rotations. Actual diameters vary with the life cycle. All thumbnails are external valves. All SEMs by Mary Ann Tiffany.
| Genus species | Thumbnail images | Rotations |
|---|---|---|
| 1. Actinoptychus | ||
| 1.1. Actinoptychus senarius |
|
3 |
| 1.2. Actinoptychus splendens |
|
14 |
| 2. Amphitetras antediluviana |
|
4 |
| 3. Arachnoidiscus | ||
| 3.1. Arachnoidiscus ehrenbergii |
|
14-31 |
| 3.2. Arachnoidiscus ornatus |
|
17-24 |
| 4. Asterolampra | ||
| 4.1. Asterolampra grevillei |
|
13 |
| 4.2. Asterolampra marylandica |
|
7 |
| 5. Asteromphalus | ||
| 5.1. Asteromphalus heptactis |
|
7 |
| 5.2. Asteromphalus imbricatus |
|
9 |
| 5.3. Asteromphalus shadboltianus |
|
7 |
| 5.4. Asteromphalus vanheurckii |
|
10-11 |
| 6. Aulacodiscus | ||
| 6.1. Aulacodiscus africanus |
|
4-5 |
| 6.2. Aulacodiscus kittonii |
|
4 |
| 6.3. Aulacodiscus oregonus |
|
8-13 |
| 6.4. Aulacodiscus petersii |
|
3 |
| 6.5. Aulacodiscus rogersii |
|
|
