Mark Matthews
Understanding the link between differential growth and form is necessary for understanding the morphogenesis of living organisms. This thesis describes two tools for simulating the growth of surfaces in three dimensions. These tools make it possible to explore the link between differential growth and form, and link growth to pattern formation traditionally considered outside of growth. Surface growth is controlled by diffusible morphogens which can be interactively placed, or predefined. The morphogens can diffuse, decay and interact. Two different techniques, a mass-spring system and finite element analysis, are used to simulate the physics of the surface. A number of test cases are presented. The first example is a model of sea urchin development. Secondly the dorsal petal lobes and leaves of the Antirrhinum majus (snapdragon) are examined. Finally, an oscillating genetic network is used to control the growth of a surface, creating some novel forms.
Mark Matthews. Physically Based Simulation of Growing Surfaces. M.Sc. thesis, University of Calgary, December 2002.