The used steps to construct the animated diagrams were as follows:

1. Get bivariate raw data (x,y).
2. Grid the x,y data and determine bivariate frequency distributions.
3. Construct contour maps of coccolith frequencies per grid cell.
4. Extract pre-selected contour lines (two coccoliths per grid-cell).
5. Construct bivariate time-frequency diagram in 3D (addition of time).
6. Construct animated scenes from suites of rotated views.

Raw data:

The original measurements of diameters and element measurements are electronically deposited at the Supplemental Database of Journal of Paleontology (follow the links for raw data). For each sample, there exists an ASCII text file, with the bivariate measurements for each coccolith given as X (diameter, in µm) and Y (number of elements), separated by a comma.

Inter- and intrasample morphological variability was analyzed by gridding the 'diameter versus number of elements' space of each sample into rectangular cells 1 µm long and two elements wide, and counting the frequency (subsequently designated as F) of specimens per grid-cell. This was done using FORTRAN program Grid.f, which was written by the author. The results are bivariate frequency distributions for every sample with X, Y, and F representing categories of 1 µm coccolith diameter, two elements in the distal shield and coccolith density per grid-cell. These frequency distributions formed the basis for the construction of the contour plots illustrated in Knappertsbusch (2000). Follow the links under 'Raw Data' and then coutour plots. The values for the graphs of bivariate frequency distributions per sample are supplied with the present study and can be downloaded as text files (download bivariate frequency distributions).

Contour plots proved to be most practical to document the intra- and inter-sample changes by observation of the position of modes of the morphotypes. These were constructed by importing the matrices of bivariate frequency distributions that were obtained with Grid.f to SURFACE III vers. 2.6plus software from the Kansas Geological Survey. SURFACE III is in the shareware domain and is available from the Technical Information Services page. Surface III draws contour lines from X, Y, Z data at user-defined intervals and exports these in the form of Cartesian coordinates. In the present case a contour interval of two coccoliths per grid-cell was found to be most practical to map the frequency modes of morphotypes. The Cartesian coordinates (x,y) for all contour lines that were constructed per sample can be downloaded as text files (download contour lines).

For visualization of the evolutionary pattern of C. leptoporus, contour lines were exported as Cartesian coordinates using the 'export/contours to ArcInfo' tool in Surface III. In a next step the coordinates of those contours indicating the density of F>2 coccoliths per grid-cell were chosen in every sample. This was done with a conventional spreadsheet and data plotting program (e.g., Cricket Graph) where individual contours could be plotted separately and then selected by repeated plot-and-cut operations. Next, the obtained X,Y couples of the selected contour lines were assigned the geological age of the particular sample. This resulted in X,Y,Z triplets in ASCII format, Z indicating the sample age in millions of years. The values were then organized in text blocks per sample and per morphotype ready for viewing with the 3D graphical display tool Rotater 3.0 from Craig Cloeden. Rotater spins spatial data in 3D in real time and is freely available for Macintosh computers and for Windows computers. Numerical codes were used to assign each morphotype a different color in Rotater. The data for C. leptoporus prepared in this way can be downloaded and watched with Rotater 3.0 (download C. leptoporus data for watching with Rotater). Rotater 3.0 must be installed first).

The last step was to compile an animated scene of the evolution of C. leptoporus viewed with Rotater. This was performed using suites of bitmap pictures every 4.7 degree of rotation around the time-axis (= Z) in mono and stereo (red-green) mode. The pictures were then imported into GifBuilder 0.5 for Macintosh. GifBuilder is freeware and available at the CNET freeware/shareware site (direct ftp download is possible at ftp://ftp.cmp.com/pub/filemine/gifbuilder-0.5.sit.hqx).