Abstract: A new class of fractals which magnified behave like a rectifiable curve and then, magnified further, disclose their inner structure, is defined analytically and investigated.
B I B L I O G R A F I A1. Mandelbrot, B., "The fractal geometry of nature", 1982
2. Mandelbrot, B., "Fractals and scaling in finance", 1997
3. Peitgen, H.-.O.& Jurgens, H.& Saupe, D., "Chaos and fractals, new frontiers of science", 1992
4. Okniński, A., "Chaos in discrete maps, deterministic scattering, and nondifferentiable functions", J. Stat. Phys., vol. 52, 1988, p.577-594
5. Weierstrass, K., "Über kontinuerliche funktionen eines reellen arguments, die für keinen wert des letzteren einen bestimmten differential quotienten besitzen", Mathematische Werke II, 1895
6. Hardy, G.H., "Weierstrass's nondifferentiable function", Trans. Am. Math. Soc., vol. 17, 1916, p.301-325
7. Edgar, G.A. (Eds.), Classics on fractals, 1993
8. Berry, M.V.& Lewis, Z.V., "On the Weierstrass-Mandelbrot fractal function", Proc. R. Soc. London, A, vol. 370, 1980, p.459-484
9. Hunt, B.R., "The Hausdorff dimension of graphs of Weierstrass functions", Proc. Am. Math. Soc., vol. 126, 1988, p.791-800
10. Berry, M.V., "Quantum fractals in boxes", J. Phys. A: Math. Gen., vol. 29, 1996, p.6617-6629
11. Wójcik, D.& Białynicki-Birula, I.& Życzkowski, K., "Time evolution of quantum fractals", Phys. Rev. Lett., vol. 85, 24, 2000, p.5022-5025
12. Wójcik D, Życzkowski K. Fractality of certain quantum states. arXiv:math-ph/0107030
13. Feynman, R.P.& Hibbs, A.R., "Quantum mechanics and path integrals", 1965
14. Abbott, L.F.& Wise, M.B., "Dimension of a quantum-mechanical path", Am. J. Phys., vol. 49, 1981, p.37-39
15. Ord, G.N., "Fractal space-time: a geometric analogue of relativistic quantum mechanics", J. Phys. A: Math. Gen., vol. 16, 1983, p.1869-1884
16. Cannata, F.& Ferrari, L., "Dimension of relativistic quantum mechanical paths", Am. J. Phys., vol. 56, 1988, p.721-725
17. Nottale, L., "Fractals and the quantum theory of space-time", Int. J. Mod. Phys. A, vol. 4, 1989, p.5047-5117
18. Nottale, L., "Fractal space-time and microphysics", 1993
19. Ansoldi, S.& Aurilia, A.& Spalluci, E., "Hausdorff dimension of a quantum string", Phys. Rev. D, vol. 56, 1997, p.2352-2361
20. Ansoldi, S.& Aurilia, A.& Spalluci, E., "Loop quantum mechanics and the fractal structure of quantum space-time", Chaos, Solitons & Fractals, vol. 10, 1999, p.197-212
21. El Naschie, M.S., "Jones invariant, Cantorian geometry and quantum space-time", Chaos, Solitons & Fractals, vol. 10, 1999, p.1241-1250
22. Ord, G.N., "Fractals and the quantum classical boundary", Chaos, Solitons & Fractals, vol. 10, 1999, p.1281-1294
23. Wheeler, J.A., "Geometrodynamics", 1962
24. Belov, A.S., "A study of certain trigonometric series", Math. Notes, vol. 13, 1973, p.291-298, (translated from Russian, Mat Zametki 1973
13:481-92)
25. Erdélyi, A., "Asymptotic expansions", 1987 
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