This report firstly examines how Morphogenesis can be interpreted through the use of computer modelling, concentrating on reaction-diffusion equations and how they can be used to simulate real-world animal skin patterns. The report then focuses on the work done by Greg Turk in his 1991 paper ”Generating Textures on Arbitrary Surfaces Using Reaction-Diffusion” [19]. The work accomplished in Turk...

SFI WORKING PAPER: 2000-08-046 SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at ...

In a static environment, optional participation and a local agglomeration of cooperators are found to be beneficial for the occurrence and maintenance of cooperation. In the optional public goods game, the rock-scissors-paper cycles of different strategies yield oscillatory cooperation but not stable cooperation. In this paper, by incorporating population density and individual mobility into th...

We present a comprehensive study of pattern formation in single-field relaxational systems with field-dependent coefficients. A modulated mean-field theory leads to a form amenable to analysis via the geometric architecture developed in our earlier work for systems that exhibit phase transitions between global steady states [Phys. Rev. E 69, 011102 (2004)]. We demonstrate that the phase diagram...

The pattern formation of asynchronous cellular automata with mass conservation is explored. A cellular automaton rule causing a specified kind of pattern was manually designed, and the mechanism of pattern formation was found similar to real chemical process. In addition, a methodology to automatically search for pattern-forming cellular automata is proposed, and its performance is validated. T...

We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many contexts (coarsening and branching in micromagnetics and superconductors). The main ingredient in the proof of our inequalities is a geometric construction which wa...

We study a tissue interaction model on skin pattern formation proposed by Cruywagen and Murray [J. Nonlin. Sci., 2 (1992), 217–240]. We prove rigorously that the model has travelling wave solutions for all sufficiently large wave speeds, which were found numerically by Cruywagen, Maini, and Murray [J. Math. Biol., 33 (1994), 193– 210]. Our results also confirm the asymptotic expansions obtained...

Systems of Lane-Emden equations arise in the modelling of several physical phenomena, such as pattern formation, population evolution and chemical reactions. In this paper we construct Noether and partial Noether operators corresponding to a Lagrangian and a partial Lagrangian for a coupled Lane-Emden system. Then the first integrals with respect to Noether and partial Noether operators are obt...

We review our recent experimental results on control of the modulational instability, pattern formation, and solitons in a nonlinear discrete dissipative feedback system. We show that the discreetness and bandgap effects can provide efficient control of the nonlinear instability modes of the system. Furthermore, we explore the possibilities for excitation of dissipative discrete solitons in suc...

This paper presents a solution to the problem of pattern formation on a grid, for a group of identical autonomous robotic agents, that have very limited communication capabilities. The chief method of communication between the agents is by moving and observing their positions on the grid. The proposed algorithm is a sequence of several coordinated “bee dances” on the grid, through which the age...