  We explain some pde2path setups for pattern formation in 1D, 2D and 3D. A
focus is on new pde2path functions for branch switching at steady bifurcation
points of higher multiplicity, typically due to discrete symmetries, but we
also review general concepts of pattern formation and their handling in
pde2path, including localized patterns and homoclinic snaking, again in 1D, 2D
and 3D, based on the demo sh (Swift-Hohenberg equation). Next, the demos
schnakpat (a Schnakenberg reaction-diffusion system) and chemtax (a quasilinear
RD system with cross-diffusion from chemotaxis) simplify and unify previous
results in a simple and concise way, CH (Cahn-Hilliard) deals with mass
constraints, hexex deals with (multiple) branch points of higher degeneracy in
a scalar problem on a hexagonal domain, and shgc illustrates some global
coupling. The demos acS, actor, schnakS and schnaktor (the Allen-Cahn and
Schnakenberg models on spheres and tori) consider pattern formation on curved
surfaces, cpol considers a problem of cell polarization described by
bulk-surface coupling, and bruosc (Brusselator) explains how to augment
autonomous systems by a time periodic forcing. Along the way we also comment on
the choice of meshes and mesh adaptation, on time integration, and we give some
examples of branch point continuation and Hopf point continuation to
approximate stability boundaries.
