The plant hormone auxin plays a central role in growth and morphogenesis. In the shoot apical meristem, the auxin flux is polarized through its interplay with PIN proteins. Concentration based mathematical models of the auxin flux permit to explain some aspects of phyllotaxis , where auxin accumulation points act as auxin sinks and correspond to primordia. Simulations show that these models can reproduce geometrically regular patterns like spirals in sunflowers or Fibonacci numbers. We propose a mathematical study of a related non-linear o.d.e. using Markov chain theory. We will next consider a concurrent model which is based on the so-called flux hypothesis, and show that it can explain the self-organization of plant vascular systems.