Parameter dependence of stochastic layers in a quasicrystalline web

Stochastic web maps with approximate quasicrystalline symmetry possess an infinite number of inequivalent fixed points embedded in stochastic layers of varying thickness. In this investigation exploratory steps are taken toward a systematic numerical determination of the widths of the stochastic layers as a function of the web map's control parameter. The study concentrates on a particular stochastic layer in the approximately fivefold symmetric web. Computer graphics and a simple stretching-and-folding criterion provide a coarse view, which is supplemented at finer scales by Greene's residue method. The exact reflection symmetries of invariant sets, as well as a five-dimensional representation of the map, are exploited to improve numerical precision. As the control parameter varies, one finds not only variations expected from island chain structures, but also larger-scale oscillations whose origin is not understood.