×

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
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Blumenthal, L. M.; Menger, K., Studies in Geometry (1970), Freeman: Freeman San Francisco · Zbl 0204.53401
[2] Davis, C.; Knuth, D., Number representations and dragon curves I, II, J. Recreational Math., 3, 133-149 (1970) · Zbl 1473.11066
[3] de Bruijn, N. G., Algebraic theory of Penrose’s non-periodic tilings of the plane, (Kon. Nederl. Akad. Wetensch. Proc. Ser. A, 84 (1981)), 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] Superfigures replicating with polar symmetry. 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)
[8] Julia, G., Mémoire sur l’itération des functions rationnelles, J. Math., 1, 47-245 (1918)
[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: Freeman San Francisco · Zbl 0376.28020
[11] Mandelbrot, B. B., The fractal dimension of percolation, polymers and almost everything else, (Landmand, U., Statistical Mechanics and Statistical Methods in Theory and Application (1977), Plenum: Plenum New York)
[12] France, M. Mendès, Principe de la symétrie perturbée, (Bertin, Marie José, Seminar Delange-Pisot-Poitou (1981), Birkhauser-Verlag: Birkhauser-Verlag Basel) · 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)
[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: Academic Press New York · Zbl 0508.68031
[20] K. Ruohonen; K. Ruohonen
[21] Seneta, E., Non-negative Matrices (1973), Allen & Unwin: 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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.