The first phyllotaxis pattern formation model was proposed in 1868 by Schwendener, and consists of stacking one disk at a time on the surface of a cylinder. As simple as it is, this model exhibits plenty of geometric and dynamical richness, which are best revealed by systematic computer simulations. It helps explain the predominance of Fibonacci phyllotaxis, where the number of helixes (parastichies) in the two transverse families are successive Fibonacci numbers. It also helped us the mechanisms of formation of a type of pattern never mentioned in the literature, that we called Quasi Symmetric. In these patterns, often characterized by rapid parameter changes, the two parastichies numbers tend to be close to one another. Now go and count parastichies on a strawberry….