Simulation steps

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Simulation steps of the moving reference model of the foraminiferal shell growth (after Tyszka 2006, modified)

Moving reference model: FORAMINIFERA

Model steps2.gif

  • A – The first spherical chamber (proloculus) is defined and simulated. This chamber has an aperture defined by a single point (black dot) on the shell (sphere) surface.

  • B – Then the reference growth axis (see the local reference line on the figure) is constructed based on the center of the 1st chamber and its aperture defined before. The reference growth axis describes current direction of growth of the shell and direction of the growth vector (TF). Its length is given by a parameter TF. The range and direction of this displacement is determined by "growth vector". The growth vector is used to calculate displacement of a center of the new chamber with respect to the aperture of the previous chamber.

  • C - In this step, the direction of the growth vector is deflected (deviated) by the Δφ angle with respect to the reference growth axis.

  • D - Then the “growth vector” is rotated by β angle as another parameter defined in the model. This way the center of the new (second) chamber is defined, therefore, the second chamber can be simulated. This new chamber can be isometric or allometric (based on 3 parameters, i.e. chamber scaling ratios, including kx - chamber width ratio, ky - chamber height ratio, kz - chamber depth ratio. If all chamber scaling ratios equal each other, i.e., kx = ky = kz, this new chamber is isometric to the previous one.

  • E – Then an aperture of the new (second) chamber is calculated according to the local minimization principle. The distance between the apertures of the two successive chambers must be as short as possible. The apertures cannot be enclosed within any other already existing chamber. (Topa & Tyszka 2002).

  • F – Constructing a new local reference line with a new growth vector. Its length is given again by the parameter TF. This new reference line is defined by the last two apertures. This step corresponds to B (see above). The next steps follow C->D->E->F steps. Iterations of these stages approximate ontogenetic growth of multilocular foraminiferal shells.

after: Tyszka & Topa 2005; Tyszka 2006