  We study Turing pattern formation in a system undergoing radial growth in two
dimensions. The Lengyel-Epstein two variable model is implemented in COMSOL
Multiphysics and solved on domains growing at different speeds while sweeping
other parameters to examine a wide range of Turing pattern morphologies. By
altering the configuration of the finite element mesh, we examine patterning in
several simulation growth modes. The observed pattern morphologies match
previously observed trends for Turing pattern growth modes. Fast growth leads
to pattern formation parallel to the growing boundary, intermediate growth
leads to pattern formation perpendicular to the growing boundary, and slow
growth leads to pattern growth from the interior. Exponential growth leads to
the expected fast-growth mode of pattern formation parallel to the moving
boundary. Simulations to replicate interior growth using logistic illumination
do not show simple pattern trends due to the effects of partial pattern
suppression from the illumination.
