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Recurrent sets. (English) Zbl 0495.51017

MSC:
51M25 Length, area and volume in real or complex geometry
28A75 Length, area, volume, other geometric measure theory
68Q45 Formal languages and automata
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[1] Blumenthal, L.M; Menger, K, Studies in geometry, (1970), Freeman San Francisco · Zbl 0204.53401
[2] Davis, C; Knuth, D; Davis, C; Knuth, D, Number representations and dragon curves I, II, J. recreational math., J. recreational math., 3, 133-149, (1970)
[3] de Bruijn, N.G, Algebraic theory of Penrose’s non-periodic tilings of the plane, (), 39-66, (= Indag. Math. 43) · Zbl 0457.05022
[4] Furstenberg, H, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. systems theory, 1, 1-49, (1967) · Zbl 0146.28502
[5] Giles, J, Construction of replicating superfigures, J. combinatorial theory ser. A, Superfigures replicating with polar symmetry, J. combinatorial theory ser. A, 26, 335-337, (1979) · Zbl 0414.05017
[6] Golomb, S.W, Replicating figures in the plane, Math. gaz., 48, 403-412, (1964) · Zbl 0125.38504
[7] Hilbert, D, Über die stetige abbildung einer linie auf ein flächenstück, Math. ann., 38, 459-460, (1891) · JFM 23.0422.01
[8] Julia, G, Mémoire sur l’itération des functions rationnelles, J. math., 1, 47-245, (1918) · JFM 46.0520.06
[9] Kiesswetter, K, Ein einfaches beispiel für eine funktion welche überall stetig und nicht differenzierbar ist, Math. phys. semesterber, 13, 216-221, (1966) · Zbl 0143.07304
[10] Mandelbrot, B.B, Fractals form, chance and dimension, (1977), Freeman San Francisco · Zbl 0376.28020
[11] Mandelbrot, B.B, The fractal dimension of percolation, polymers and almost everything else, ()
[12] France, M.Mendès, Principe de la symétrie perturbée, () · Zbl 0451.10019
[13] France, M.Mendès; Tenenbaum, G, Dimension des courbes planes, papiers pliés et suites de rudin-shapiró, Bull. soc. math. France, 109, 207-215, (1981) · Zbl 0468.10033
[14] Milne, S.C, Peano curves and smoothness of functions, Advances in math., 35, 129-157, (1980) · Zbl 0449.26015
[15] Parry, W, Intrinsic Markov chains, Trans. amer. math. soc., 112, 55-66, (1964) · Zbl 0127.35301
[16] Peano, G, Sur une courbe, qui remplit une aire plane, Math. ann., 36, 157-160, (1890) · JFM 22.0405.01
[17] Penrose, R, Pentaplexity, Math. intell., 2, 32-37, (1979) · Zbl 0426.52005
[18] Robbin, J.W, Topological conjugacy and structural stability for discrete dynamical systems, Bull. amer. math. soc., 78, 923-952, (1972) · Zbl 0256.58008
[19] Rozenberg, G; Saloma, A, The mathematical theory of L-systems, (1980), Academic Press New York
[20] \scK. Ruohonen, Personál communication.
[21] Seneta, E, Non-negative matrices, (1973), Allen & Unwin London · Zbl 0278.15011
[22] Szilard, A.L; Quinton, R.E, An interpretation for DOL systems by computer graphics, The science terrapin, 4, 8-13, (1979)
[23] von Koch, H, Une méthode géométrique élémentaire pour l’étude de certaines questions de la théorie des courbes planes, Acta math., 30, 145-174, (1906) · JFM 37.0413.02
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