List of Illustrations
1 Chapter 1Figure 1.1 Living diatoms as observed under LM, brightfield. (a) Two living cel...Figure 1.2 Live centric (a, b) and pennate (c–h) diatoms. (a, b) Pleurosira laev...Figure 1.3 Specific diatom morphology gleaned from images with whole and partial...Figure 1.4 Cleaned diatoms in valve (g, h–j, m–r, u, v) and girdle views (a–f, k...Figure 1.5 (a) SEM of a single cleaned partially open frustule, two overlapping ...Figure 1.6 A cross-section at the center of Coscinodiscus sp. cell collected and...
2 Chapter 2Figure 2.1 A drawing composed by JLP that is reminiscent of one of Mezzanotte’s...Figure 2.2 Shape perception of Arachnoidiscus ehrenbergii from image ProvBay5_1...Figure 2.3 Diatom valve face symmetries. (a) Arachnoidiscus ehrenbergii-rotatio...Figure 2.4 Double translational symmetry at two scales exhibited in a Paralia s...Figure 2.5 Three stages of valve formation (as defined in [2.125]) in Biddulphi...Figure 2.6 ProvBay5_12lx450, Arachnoidiscus ehrenbergii. (a) Original scanning ...Figure 2.7 Tilt-corrected final entropy vs. number of rotations for all images,...Figure 2.8 Typical entropy vs. symmetry plot. The example is image ProvBay5_12l...Figure 2.9 Number of rotations vs. tilt-corrected final entropies for Cyclotell...Figure 2.10 Histogram and overlain probability density function for all tilt-co...Figure 2.11 Histogram and overlain cumulative density function for all tilt-cor...Figure 2.12 For all images, average symmetry per taxon ranging from Triceratium...Figure 2.13 Average taxon symmetry for all external centric diatom valves rangi...Figure 2.14 Vertical valve formation comparison: average external and forming v...Figure 2.15 Symmetry values for Asteromphalus, Arachnoidiscus, and Aulacodiscus...Figure 2.16 Cyclotella meneghiniana symmetry for normal and abnormal valves.Figure 2.17 Cyclotella meneghiniana symmetry values for normal forming and exte...Figure 2.18 Asterolampra marylandica (SanDBay02_03dx1100) as a sequence of 24 c...Figure 2.19 Plots of symmetry vs. 24-valve formation simulation steps from annu...Figure 2.20 Valve formation steps for eight taxa as a probability density funct...Figure 2.21 Valve formation steps for eight taxa as a cumulative density functi...Figure 2.22 Valve formation steps for eight taxa as a skew-right normal prior p...Figure 2.23 Valve formation simulation comparison of symmetry and chaotic insta...Figure 2.24 Valve formation simulation comparison of symmetry and random instab...Figure 2.25 Average sequence of 24 simulated valve formation steps of symmetry ...
3 Chapter 3Figure 3.1 Pascal’s triangle, which shows the development of the sizes of diato...Figure 3.2 An early illustration of a diatom chain with a sketch of the size se...Figure 3.3 In the left half of the figure, diatoms of the chain L0 R1 L2 R1 are...Figure 3.4 The string L0 R1 L2 R1 is in the left branch first mirrored and then...Figure 3.5 Bar chart of the size indices from the 7th generation (128 diatoms) ...Figure 3.6 Elementary step in the development of a substring A of any generatio...Figure 3.7 The Pascal triangle illustrates the development of a substring W. W ...Figure 3.8 Dragon curve of the 13-th generation. It contains 213 - 1 = 8,192 an...Figure 3.9 Eunotia chain at the bottom of a Petri dish of a culture. Looking at...Figure 3.10 Bar chart of differences in lengths of adjacent diatoms within the ...Figure 3.11 Interpretation of the observed sequence of differences (Figure 3.10...Figure 3.12 Eunotia chain at the bottom of a Petri dish of a culture. A chain w...Figure 3.13 Probability Pk(t) that the k-th division has occurred at the time tk...
4 Chapter 4Figure 4.1-4.6 Amphitetras antediluviana, mature valves, S.E.M. Figure 4.1 Comp...Figure 4.7-4.12 Amphitetras antediluviana, forming valves, S.E.M. Figure 4.7 Ea...Figure 4.13-4.18 Amphitetras antediluviana, forming ocelli, S.E.M. Figure 4.13 ...Figure 4.19-.24 Amphitetras antediluviana, forming cribra, S.E.M. Figure 4.19 E...Figure 4.25-4.30 Amphitetras antediluviana, S.E.M. Figure 4.25 Detail of nearly...
5 Chapter 5Figure 5.1 (a and b) Concentric pattern of areolae on the valve of Aulacodiscus ...Figure 5.2 Figure 5.2 (a) An artificially generated concentric pattern where all...Figure 5.3 The repeating stages of the formation of the rows of a concentric pat...Figure 5.4 Natural (b) and artificial (a, c) unidirectional spiral patterns. (a,...Figure 5.5 Natural (b) and artificial (a, c) bidirectional spiral pattern. (a) T...
6 Chapter 6Figure 6.1 A flow chart illustrating the methodology for assigning the most like...Figure 6.2 Diagram showing the frustule structure of (a) a centric frustule and ...Figure 6.3 Diagram illustrating two types of 2D lattices, the hexagonal and rect...Figure 6.4 A segmented micrograph of the external view of a single valve of Rope...Figure 6.5 Two SEMs of the internal view of a single valve of Pleurosigma sp. (a...Figure 6.6 SEM of the external view of a single valve of Roperia tesselata (1,02...Figure 6.7 SEM of the internal view of a single valve of Asteromphalus hookeri (...Figure 6.8 SEM of an internal view of a single valve of Roperia tesselata in upr...Figure 6.9 (a) A segmented SEM of the internal view of a single valve of Asterom...Figure 6.10 A segmented SEM of the internal view of a single valve of Asterompha...Figure 6.11 A threshold of the same micrograph of the internal view of a single ...Figure 6.12 A segmented selected part of the SEM of an internal view of a single...Figure 6.13 A segmented micrograph of a zoom in the internal view of a single va...Figure 6.14 (a) A thresholded micrograph of the internal view of a single valve ...Figure 6.15 A selected circle of an SEM of the internal view of a single valve o...Figure 6.16 (a) SEM of the external view at the center of a single valve of Thal...Figure 6.17 (a) A thresholded SEM of a zoom-in of the internal view of a single ...Figure 6.18 (a) A segmented SEM of the external view of a single immature valve ...Figure 6.19 (a) A segmented SEM micrograph of a zoom-in external view of Asterol...Figure 6.20 (a) A segmented SEM micrograph of the external view of Roperia tesse...Figure 6.21 (a) A segmented SEM micrograph of a selected 2D pore group at the ex...Figure 6.22 (a) A segmented SEM micrograph of the internal view of Haslea sp. (1...Figure 6.23 A segmented SEM of a zoom-in of a Gyrosigma fasciola valve (276 × 17...Figure 6.24 (a) A segmented SEM of a zoom-in of a valve of Gyrosigma balticum, a...Figure 6.25 (a) The areolae chambers appearing from a crack in the valve of Aste...Figure 6.26 An artificial honeycomb-like structure and its correpsonding 2D FFT ...Figure 6.27 A zoom-in of the external view of a single slightly immature valve o...Figure 6.28 (a) SEM of an external view of the central area of a single valve of...Figure 6.29 (a) SEM of the external view of a single valve of Cocconeis sp. illu...
7 Chapter 7Figure 7.1 Ensemble surface features—examples: (a) smooth, but not flat; (b) fla...Figure 7.2 Actinoptychus senarius modeled valve formation sequence steps 1 throu...Figure 7.3 Arachnoidiscus ehrenbergii modeled valve formation sequence steps 1 t...Figure 7.4 Cyclotella meneghiniana modeled valve formation sequence steps 1 thro...Figure 7.5 Single-linkage cluster analysis using Hamming distance for non-zero v...Figure 7.6 Contribution percentage of ensemble surface measures Jacobian, Hessia...Figure 7.7 Jacobian, Hessian, and Laplacian from z-terms and Christoffel symbols...Figure 7.8 Contribution of the u and v parameters of the z-term of the Jacobian,...Figure 7.9 All Christoffel symbols for the three contravariant indices: top, k =...Figure 7.10 Plot of all Christoffel symbols shows change in contribution for