Fractal geometry, Turing machines and divide-and-conquer recurrences

S. Dube

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (1994)

  • Volume: 28, Issue: 3-4, page 405-423
  • ISSN: 0988-3754

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Dube, S.. "Fractal geometry, Turing machines and divide-and-conquer recurrences." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 28.3-4 (1994): 405-423. <http://eudml.org/doc/92487>.

@article{Dube1994,
author = {Dube, S.},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {iterated function systems; fractal geometry},
language = {eng},
number = {3-4},
pages = {405-423},
publisher = {EDP-Sciences},
title = {Fractal geometry, Turing machines and divide-and-conquer recurrences},
url = {http://eudml.org/doc/92487},
volume = {28},
year = {1994},
}

TY - JOUR
AU - Dube, S.
TI - Fractal geometry, Turing machines and divide-and-conquer recurrences
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 1994
PB - EDP-Sciences
VL - 28
IS - 3-4
SP - 405
EP - 423
LA - eng
KW - iterated function systems; fractal geometry
UR - http://eudml.org/doc/92487
ER -

References

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  1. 1. M. F. BARNSLEY, Fractals Everywhere, Academic Press, 1988. Zbl0691.58001MR1231795
  2. 2. J. L. BENTLEY, D. HAKEN and J. B. SAXE, A General Method for Solving Divide-and-Conquer Recurrences, SIGACT News, 1980, 12, pp. 36-44. Zbl0451.68038
  3. 3. L. BLUM, M. SHUB and S. SMALE, On a Theory of Computation and Complexity over the Real Numbers: NP Completeness, recursive functions and universal machines, Bulletin of American Mathematical Society, 1989, 21, pp. 1-46. Zbl0681.03020MR974426
  4. 4. T. H. CORMEN, C. E. LEISERSON and R. L. RIVEST, Introduction to Algorithms, MIT Press, 1990. Zbl1158.68538MR1066870
  5. 5. K. CULIK II and S. DUBE, Affine Automata and Related Techniques for Generation of Complex Images, Theoretical Computer Science, 1993, 116, pp. 373-398. Zbl0779.68062MR1231951
  6. 6. K. CULIK II and S. DUBE, Encoding Images as Words and Languages, International Journal of Algebra and Computation, 1993, 3, No. 2, pp. 211-236. Zbl0777.68056MR1233222
  7. 7. S. DUBE, Undecidable Problems in Fractal Geometry, Technical Report 93-71, Dept. of Math. and Comp. Sci., University of New England at Armidale, Australia. Zbl0816.58024MR1307741
  8. 8. S. DUBE, Using Fractal Geometry for Solving Divide-and-Conquer Recurrences, to appear in Journal of Aust. Math. Soc., Applied Math., Preliminary version in Proc. of ISAAC'93, Hong Kong. Lecture Notes in Computer Science, Springer-Verlag, 762, pp. 191-200. Zbl0852.68101MR1359178
  9. 9. K. J. FALCONER, Digital Sun Dials, Paradoxical Sets and Vitushkin's Conjecture, Math Intelligencer, 1987, 9, pp. 24-27. Zbl0609.28005
  10. 10. J. GLEICK, Chaos-Making a New Science, Penguin Books, 1988. Zbl0706.58002MR1010647
  11. 11. J. E. HOPCROFT and J. D. ULLMAN, Introduction to Automata Theory, Languages and Computation, Addison-Wesley, 1979. Zbl0426.68001MR645539
  12. 12. J. HUTCHINSON, Fractals and Self-similarity, Indiana University Journal of Mathematics, 1981, 30, pp. 713-747. Zbl0598.28011MR625600
  13. 13. B. MANDELBROT, The Fractal Geometry of Nature, W. H. Freeman and Co., San Francisco, 1982. Zbl0504.28001MR665254
  14. 14. R. PENROSE, The Emperor's New Mind, Oxford University Press, Oxford, 1990. Zbl0795.00009

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