Apex | Creating Phyllotactic Patterns from Seed to Flower

The Stack-and-Drag Model creates phyllotactic patterns from seed to flower. What does that mean?
On a cylindrical surface, spheres are stacked one by one. The stacking direction is upwards from two initial, touching spheres, representing cotyledons. New spheres become smaller according to an S-graph. After the last stem unit (which ordinal number is preset), spheres close the surface in a transition vertical/horizontal: the apical hemisphere. (The number of spheres fitting on this top is not preset.)
We distinguish unit growth (green) and unit translations or receptacle growth (blue for longitudinal and red for radial). The 'green graph', which shows the ratio r(unit) / r(stem), affects phyllotaxis dramatically. The blue and red graphs define axial and radial translations, and they are not of topological importance.
Besides the unit growth curve, pattern determining parameters are:
exp(ansion) - makes spheres compressible to repulsive,
sens(itivity) - decelerates ('smoothens') the structure, or accelerates it (makes it 'nervous'),
canal(ization) - acts apon Buvat's 'anneau initial'.
S-curve parameters are: hlife (halflife), base (minimum radius), and const (gradient).

Apex is not a physiologic simulator. With this piece of software, one is able to create metastructures, which relate with familiar plant forms - but do not imitate them. Structures and the shape of units can easily be edited.
While Fibonacci numbers are the normal output, Apex does not necessarily produce them, nor the 'Golden Angle'. Sometimes, just like in Nature, deviations like the double-Fibonacci series, the Lucas series, or a lower accessory sequence may arise.


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