Frontiers of Computing Systems Research pp 197-238 | Cite as

# Clouds, Computers and Complexity

Chapter

## Abstract

Modern computers are complex. But is it meaningful to say that a computer is complex when compared to a system as intricate as the brain? Is a miniature version of a computer more complex, more intricate—or just smaller? How can we begin to conceive of ever more complex systems if we lack the ability to describe them? Clearly, we need to add new terminology to our descriptive lexicon of complexity.

## Keywords

Fractal Dimension Simulated Annealing Algorithm Fractal Theory Wire Length Interconnection Complexity
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## References

- [1]B. B. Mandelbrot,
*The Fractal Geometry of Nature*, W. H. Freeman and Co., San Francisco, CA (1982).zbMATHGoogle Scholar - [2]M. Barnsley,
*Fractals Everywhere*, Academic Press, Inc., San Diego, CA (1988).zbMATHGoogle Scholar - [3]J. Feder,
*Fractals*, Plenum Press, New York, NY (1988).zbMATHGoogle Scholar - [4]
*Fractals’ Physical Origin and Properties*, Proceedings of the special seminar on fractals, held October 9–15, 1988, Erice, Sicily, Italy. L. Pietronero (Ed.), Plenum Press, New York, NY (1989).Google Scholar - [5]P. Bak, Chao Tang, and K. Wiesenfeld,
*Self-organized criticality*, Phys. Rev A, vol. 38(1), pp. 364–374 (1988).MathSciNetzbMATHCrossRefGoogle Scholar - [6]P. Bak and Kan Chen,
*Self-organized criticality*, Scientific American, pp. 47–53, January 1991.Google Scholar - [7]A. Bruce and D. Wallace,
*Critical point phenomena: universal physics at large length scales*, in*The New Physics*, Cambridge University Press, Cambridge, England, Ch. 8, pp. 236–267 (1989).Google Scholar - [8]J. H. Kaufman, O. R. Melroy, and G. M. Dimino,
*Information-theoretic study of pattern formation: rate of entropy production of random fractals*, Phys. Rev. A, vol. 39(3), pp. 1420–1428 (1989).MathSciNetCrossRefGoogle Scholar - [9]Proc. IEEE, Special issue on neural networks, I: Theory and Modeling, vol. 78(9), September (1990).Google Scholar
- [10]Proc. IEEE, Special issue on neural networks, II: Analysis, Techniques, and Applications, vol. 78(10), October (1990)Google Scholar
- [11]J. A. Anderson and E. Rosenfeld (Eds.),
*Neurocomputing: Foundations of Research*, MIT Press, Cambridge, MA (1988).Google Scholar - [12]S. Lovejoy,
*Area-perimeter relation for rain and cloud areas*, Science, vol. 216(9), pp. 185–187 (1982).CrossRefGoogle Scholar - [13]D. K. Ferry,
*Interconnection lengths and VLSI*, IEEE Circuits and Devices Magazine, pp. 39–42, July 1985.Google Scholar - [14]H. B. Bakoglu,
*Circuits, Interconnections, and Packaging for VLSI*, Ch. 9, pp. 416–421, Addison-Wesley Publishing Co., Reading, MA (1990).Google Scholar - [15]D. K. Ferry, L. A. Akers, and E. W. Greeneich,
*Ultra Large Scale Integrated Microelectronics*, Ch. 5., pp. 214–216, Prentice-Hall, En-glewood Cliffs, NJ (1988).Google Scholar - [16]B. S. Landman and R. L. Russo,
*On a pin versus block relationship for partitions of logic graphs*, IEEE Trans. Computers, vol. C-20(12), pp. 1469–1479 (1971).CrossRefGoogle Scholar - [17]W. E. Donath,
*Placement and average interconnection lengths of computer logic*, IEEE Trans. Circuits and Systems, vol. CAS-26(4), pp. 272–277 (1979).CrossRefGoogle Scholar - [18]J. E. Cotter and P. Christie,
*The analytical form of the length distri-bution function for computer interconnections*, IEEE Trans. Circuit and Systems, vol. CAS-38(3), pp. 317–320 (1991).CrossRefGoogle Scholar - [19]W. E. Donath,
*Wire length distribution for placements of computer logic*, IBM. J. Res. Dev., vol. 25(3), pp. 152–155 (1981).CrossRefGoogle Scholar - [20]R. W. Keyes,
*The wire-limited logic chip*, IEEE J. Solid-State Circuits, vol. SC-17(6), pp. 1232–1233 (1982).CrossRefGoogle Scholar - [21]The Author is indebted to Francesco Palmieri, Dept. Electrical and Systems Engineering, University of Connecticut, for providing this derivation.Google Scholar
- [22]D. F. Wong, H. W. Leong, and C. L. Liu,
*Simulated Annealing for VLSI*, Kluwer Academic Publishers, Norwell, MA (1988).zbMATHCrossRefGoogle Scholar - [23]P. J. M. van Laarhoven and E. H. L. Aarts,
*Simulated Annealing: Theory and Applications*, D. Reidel Publishing Co., Dordrecht, Holland (1988).Google Scholar - [24]S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi,
*Optimization by simulated annealing*, Science, vol. 220, pp. 671–680 (1983).MathSciNetzbMATHCrossRefGoogle Scholar - [25]W. E. Donath,
*Statistical properties of the placement of a logic graph*, SIAM J. App. Math., vol. 16(2), pp. 439–457 (1968).MathSciNetzbMATHCrossRefGoogle Scholar - [26]R. W. Keyes,
*The Physics of VLSI Systems*, Ch. 8, pp. 178–182, Addison-Wesley Publishing Co., Wokingham, England (1987).Google Scholar - [27]R. C. Tolman,
*The Principles of Statistical Mechanics*, Ch X, Dover Publications, Inc., New York, NY (1978). First published in 1938 by Oxford University Press.Google Scholar - [28]A. P. French and E. F. Taylor,
*An Introduction to Quantum Physics*, Ch. 13, W. W. Norton and Co., Inc., New York, NY (1978).Google Scholar - [29]F. W. Sears and G. L. Salinger,
*Thermodynamics, Kinetic Theory, and Statistical Thermodynamics*, (Fifth Ed.) Ch. 11, Addison-Wesley Publishing Co., Reading, MA (1980).Google Scholar - [30]To the Author’s knowledge this is the first time this expression has been published. It may be easily verified by following the procedure outlined in [29].Google Scholar
- [31]N. Metropolis, A. W. Rosenbluth, A. H. Teller, M. N. Rosenbluth, and E. Teller,
*Equation of state calculations by fast computing machines*, J. Chem. Phys., vol. 21(6), pp. 1087–1092 (1953).CrossRefGoogle Scholar - [32]P. Christie and S. B. Styer,
*A fractal description of computer interconnection distributions*, in Proc. SPIE vol. 1390,*Microelectronic Interconnects and Packaging: System Integration*, pp. 359–367 (1990).Google Scholar - [33]S. Wang,
*Fundamentals of Semiconductor Theory and Device Physics*, Ch. 6, pp. 250–255, Prentice-Hall, Inc., Englewood Cliffs, NJ (1989).Google Scholar - [34]B. B. Mandelbrot, Y. Gefen, A. Aharony, and J. Peyrière,
*Fractals: their transfer matrices and their eigen-dimension al sequences*, J. Phys. A, vol. 18, pp. 335–354 (1985).MathSciNetCrossRefGoogle Scholar - [35]A. Aharony, Y. Gefen, A. Kapitulnik, and M. Murat,
*Fractal eigendi-mensionalities for percolation clusters*, Phys. Rev. B, vol. 31(7), pp. 4721–4724(1985).CrossRefGoogle Scholar

## Copyright information

© Plenum Press, New York 1991