Abstract
The internal structure of the iterations of Koch curve and Sierpiński gasket—the known fractals [4]—is described in terms of multi-hypergraphical membrane systems related to membrane structures [13] and whose membranes are hyperedges of multi-hypergraphs used to define gluing patterns for the components of the iterations of the considered fractals.
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References
Bruni, R., Gadducci, F., Lluch Lafuente, A.: An algebra of hierarchical graphs. In: Wirsing, M., Hofmann, M., Rauschmayer, A. (eds.) TGC 2010, LNCS, vol. 6084, pp. 205–221. Springer, Heidelberg (2010)
Cherkasova, L.A., Kotov, V.E.: Structured nets. In: Gruska, J., Chytil, M. (eds.) Mathematical Foundations of Computer Science. LNCS, vol. 118, pp. 242–251. Springer, Heidelberg (1981)
Edalat, A.: Domains for computation in mathematics, physics and exact real arithmetic. The Bulletin of Symbolic Logic 3, 401–452 (1997)
Falconer, K.: Fractal Geometry. Mathematical Foundations and Applications. Wiley, Hoboken (2003)
Gallo, G., Longo, G., Pallottino, S., Nguyen, S.: Directed hypergraphs and applications. Discrete Appl. Math. 42, 177–201 (1993)
Harel, D.: On Visual Formalisms. Comm. ACM 31, 514–530 (1988)
Hasuo, I., Jacobs, B., Niqui, M.: Coalgebraic representation theory of fractals. Electron. Notes Theor. Comput. Sci. 265, 351–368 (2010)
Hutchinson, J.E.: Fractals and self-similarity. Indiana Univ. Math. J. 30, 713–747 (1981)
Leinster, T.: A general theory of self-similarity. Adv. Math. 226, 2935–3017 (2011)
Narici, L., Beckenstein, E.: The Hahn–Banach theorem: the life and times. Topology Appl. 77, 193–211 (1997)
Obtułowicz, A.: Multigraphical membrane systems revisited. In: Csuhaj-Varjú, E., Gheorghe, M., Rozenberg, G., Salomaa, A., Vaszil, G. (eds.) CMC 2012. LNCS, vol. 7762, pp. 311–322. Springer, Heidelberg (2013)
Orlarey, Y., Fober, D., Letz, S., Bilton, M.: Lambda calculus and music calculi. In: International Computer Music Conference ICMA 1994 (1994)
Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)
Riddle, L.: Classic iterated function systems, Koch curve, Sierpiński gasket, http://ecademy.agnesscott.edu/~lriddle/ifs/kcurve/kcurve.htm , http://ecademy.agnesscott.edu/~lriddle/ifs/siertri/siertri.htm
Rozenkrantz, D.J., Hunt III, H.B.: The complexity of processing hierarchical specifications. SIAM J. Comput. 22, 627–649 (1993)
Stefanescu, G.: The algebra of flownomials, Report, Technical University Munich (1994)
Vallée, N., Monsuez, B.: A formal model of system components using fractal hypergraphs. In: Proc. of the Int. Multiconference of Engineers and Computer Scientists, IMECS 2010, Hong Kong, vol. II (2010)
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Obtułowicz, A. (2014). In Search of a Structure of Fractals by Using Membranes as Hyperedges. In: Alhazov, A., Cojocaru, S., Gheorghe, M., Rogozhin, Y., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. CMC 2013. Lecture Notes in Computer Science, vol 8340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54239-8_21
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