Projections of patterns and mode interactions

References

• M.A. Armstrong, Groups and Symmetry, Springer-Verlag, 1988. New York.
   Google Scholar
• P. Borckmans, G. Dewel, A. De Wit, E. Dulos, J. Boissonade, F. Gauffre, and P. De Kepper, Diffusive instabilities and chemical reactions, Int. J. Bifurcation Chaos 12 (2002), pp. 2307–2332.
   Web of Science ®Google Scholar
• V. Castets, E. Dulos, J. Boissonade, and P. De Kepper, Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern, Phys. Rev. Lett. 64–24 (1990), pp. 2953–2956.
   Web of Science ®Google Scholar
• S.B.S.D. Castro, Mode Interactions with Symmetry, PhD thesis, University of Warwick, 1993.
   Google Scholar
• S.B.S.D. Castro, Mode interactions with spherical symmetry, Int. J. Bifurcation Chaos 4–04 (1994), pp. 885–904.
   Web of Science ®Google Scholar
• S.B.S.D. Castro, Mode interactions with symmetry, Dyn. Stab. Syst. 10–1 (1995), pp. 13–31.
   Google Scholar
• G. Cicogna, Symmetry breakdown from bifurcations, Lett. al Nuovo Cimento 31 (1981), pp. 600–602.
   Google Scholar
• P. De Kepper, V. Castets, E. Dulos, and J. Boissonade, Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction, Phys. D Nonlinear Phenom. 49 (1991), pp. 161–169.
   Google Scholar
• P. De Kepper, E. Dulos, J. Boissonade, A. De Wit, G. Dewel, and P. Borckmans, Reaction–diffusion patterns in confined chemical systems, J. Stat. Phys. 101 (2000), pp. 495–508.
   Web of Science ®Google Scholar
• B. Dionne and M. Golubitsky, Planforms in two and three dimensions, Z. Angew. Math. Phys. 43 (1992), pp. 36–62.
   Web of Science ®Google Scholar
• E. Dulos, P. Davies, B. Rudovics, and P. De Kepper, From quasi-2D to 3D Turing patterns in ramped systems, Phys. D Nonlinear Phenom. 98 (1996), pp. 53–66.
   Google Scholar
• M. Golubitsky and I. Stewart, The Symmetry Perspective, Birkhauser Verlag, 2002. Base!, Boston, Berlin.
   Google Scholar
• M. Golubitsky, I.N. Stewart, and D. Schaeffer, Singularities and Groups in Bifurcation Theory, Volume II, Springer-Verlag, 2012. New York, Berlin, Heidelberg.
   Google Scholar
• M.G.M. Gomes, Black-eye patterns: A representation of three-dimensional symmetries in thin domains, Phys. Rev. E 60 (1999), pp. 3741–3747.
   Google Scholar
• H.G. Gunaratne, Q. Ouyang, and H.L. Swinney, Pattern formation in the presence of symmetries, Phys. Rev. E 50 (1994), pp. 2802–2806.
   Google Scholar
• T. Hahn (ed.), International Tables for Crystallography, 5th ed., International Union of Crystallography, 2006. Dordrecht, the Netherlands.
   Google Scholar
• I.S. Labouriau and E.M. Pinho, Symmetries of projected wallpaper patterns, Math. Proc. Camb. Phil. Soc. 141 (2006), pp. 421–441.
   Web of Science ®Google Scholar
• W. Miller, Symmetry Groups and their Applications, Academic Press, 1972. New York, San Francisco, London.
   Google Scholar
• J.F. Oliveira, S.B.S.D. Castro, and I.S. Labouriau, Hexagonal projected symmetries, Acta Crystallogr. Sect. A 71 (2015), pp. 549–558.
   Google Scholar
• Q. Ouyang and H.L. Swinney, Onset and beyond Turing pattern formation, in Chemical Waves and Patterns. Understanding Chemical Reactivity, vol 10, R. Kapral and K. Showalter, eds., Springer, Dordrecht, 1995, pp. 269–295.
   Google Scholar
• E.M. Pinho and I.S. Labouriau, On the projection of functions invariant under the action of a crystallographic group, J. Pure Appl. Algebra 218 (2014), pp. 37–51.
   Web of Science ®Google Scholar
• M. Senechal, Quasicrystals and Geometry, Cambridge University Press, 1996. Cambridge.
   Google Scholar
• I. Szalai, J. Horváth, and P. De Kepper, Contribution to an effective design method for stationary reaction-diffusion patterns, Chaos Interdiscip. J. Nonlinear Sci. 25 (2015), pp. 064311 1–13.
   Web of Science ®Google Scholar
• A.M. Turing, The chemical basis of morphogenesis, Phil. Trans. R. Soc. London. Ser. B, 237 (1952), pp. 37–72.
   Web of Science ®Google Scholar
• A. Vanderbauwhede, Local Bifurcation and Symmetry, Habilitation thesis, Rijksuniversiteit Gent, 1980. (also Res. Notes Math. 75. Pitman, Boston (1982)).
   Google Scholar
• A.T. Winfree, The Geometry of Biological Time, Springer-Verlag, 2001. New York.
   Google Scholar
• C. Zhou, H. Guo, and Q. Ouyang, Experimental study of the dimensionality of lack-eye patterns, Phys. Rev. E 65 (2002), pp. 03618 1–5.
   Google Scholar