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1. M. Li and P.M.B. Vitanyi, An Introduction to Kolmogorov Complexity and Its Applications (Springer-Verlag, New York, 1993). Page v in preface.

2. A.N. Kolmogorov, ``Three Approaches to the Quantitative Definition of Information," Problems of Information Transmission 1 (1965) pp. 1-11; G.J. Chaitin, ``On the Length of Programs for Computing Finite Binary Sequences: Statistical Considerations," Journal of the ACM 16 (1969) pp. 145-159; and R.J. Solomonoff, ``A Formal Theory of Inductive Inference, Part 1," Information and Control 7 (1964) pp. 1-22.

3. See Li and Vitanyi [1] for the best overview. See J. Schmidhuber, ``Discovering neural nets with low Kolmogorov complexity and high generalization capability", Neural Networks (1997, in press), for a machine learning application. A short version of this text has appeared in A. Prieditis and S. Russell, editors, Machine Learning: Proceedings of the Twelfth International Conference, pages 488-496, Morgan Kaufmann Publishers, San Francisco, CA, 1995.

4. See Kolmogorov [2]; Chaitin [2]; and Solomonoff [2].

5. See Kolmogorov [2]; Chaitin [2]; and Solomonoff [2].

6. B. Mandelbrot, The Fractal Geometry of Nature (San Francisco: Freeman, 1982).

8. See Kolmogorov [2]; Chaitin [2]; and Solomonoff [2]; L.A. Levin, ``Laws of Information (Nongrowth) and Aspects of the Foundation of Probability Theory," Problems of Information Transmission 10, No. 3, 206-210 (1974); C.S. Wallace and D.M. Boulton, ``An Information Theoretic Measure for Classification," Computer Journal 11, No. 2, 185-194 (1968); and J. Rissanen, ``Modeling by Shortest Data Description," Automatica 14 (1978) pp. 465-471.

9. J.H. Langlois and L.A. Roggman,  Attractive Faces Are Only Average,  Psychological Science 1 (1990) pp. 115-121.

10. D.I. Perrett, K.A. May and S. Yoshikawa, ``Facial Shape and Judgments of Female Attractiveness," Nature 368 (1994) pp. 239- 242.

11. P.J. Benson and D.I. Perrett, ``Extracting Prototypical Facial Images from Exemplars," Perception 22 (1993) pp. 257-262.

12. Lyonel Feininger, translated by J. Schmidhuber.

13. See Mandelbrot [6]; and H.-O. Peitgen and P.H. Richter, The Beauty of Fractals: Images of Complex Dynamical Systems (Springer-Verlag, New York, 1986).

14. K. Culik and J. Kari, ``Parallel Pattern Generation with One-Way Communications," in J. Karhumaki, H. Maurer and G. Rozenberg, eds., Results and Trends in Theoretical Computer Science (Springer-Verlag, New York, 1994) pp. 85-96.

15. For work on face animation, see I.A. Essa, T. Darrell and A. Pentland, ``Modeling and Interactive Animation of Facial Expressions Using Vision," Technical Report, MIT Media Lab Perceptual Computing Section TR 256, 1994. See also Mengxiang Li, ``Minimum Description Length Based 2-D Shape Description," in IEEE 4th Int. Conference on Computer Vision (May 1992) pp. 512-517.

16. C.E. Shannon, ``A Mathematical Theory Of Communication (Parts 1 and 2)", Bell System Technical Journal 27 (1948) pp. 379-423.

17. F. Nake, Ästhetik als Informationsverarbeitung (Springer-Verlag, Berlin, 1974).

18. See Kolmogorov [2]; Wallace and Boulton [8]; and Chaitin [2].

Manuscript received 2 January 1995.

Related work: J. Schmidhuber. Facial beauty and fractal geometry. Note IDSIA-28-98, IDSIA, June 1998 (ca. 0.6 M, including 5 color figures). Postscript (1.29M, ca. 4.96 M gunzipped).

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