STIT tessellations -- a mathematical model for structures generated by sequential division
There are many geometric structures which are formed by division of areas or volumes. Examples are road systems, cracks in drying soil, craquelée effect on coated surfaces,
biological cell walls. There are already many suggestions to model such structures, where most of these models can only be dealt with by simulation studies.
An exception is the so-called STIT tessellation, which was introduced by Nagel and Weiss (2005), and which allows for theoretical investigations which reveal essential properties and relations for its parameters. Therefore, the STIT model has the potential to become a reference model for fractures which can be adapted to real data.
In the talk, the STIT tessellation is presented and some important features are explained and illustrated. It will also be compared to the two well established models of Poisson-Voronoi and Poisson line/plane tessellations.