Toward Ultimate Computing. Brain/Mind/Computer. Origin and Evolution of Life. From Brain to Cytoskeleton. Cytoskeleton/Cytocomputer. Protein Conformational Dynamics. Anesthesia: Another Side of Consciousness. Models of Cytoskeletal Computing. Viruses/Ambiguous Life Forms. NanoTechnology. The Future of Consciousness. Bibliography. Appendices. Index.

Ultimate Computing: Biomolecular Consciousness and NanoTechnology

Effects of phase space discretization on the long-time behavior of dynamical systems

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Informal remarks on the orbit structure of discrete approximations to chaotic maps

The iterates of the logistic map, ${x}_{n+1}$=${\mathrm{rx}}_{n}$(1-${x}_{n}$), exhibit chaotic behavior for many values of r\ensuremath{\in}[3.57,4.0]. However, if we treat x as an m-state discrete variable, as is done in any digital computer calculation, then the iterates of x invariably form short limit cycles of length \ensuremath{\approxeq} \ensuremath{\surd}m for chaotic values of r. Although this result questions the validity of digital computer simulations of chaos, we nevertheless find that the statistical properties of the continuous equation, such as the invariant probability distribution and the Lyapunov exponent, are preserved in these cycles. We also find that the transition between periodic and chaotic behavior is still well defined in the discretized map.

Simulating chaotic behavior with finite-state machines

After surveying several earlier definitions of "chaos" , this paper is devoted to presenting the recently introduced notion of distributional chaosto a non-specialist audience. It is shown that the theory of distributional chaos avoids various shortcomings of the earlier theories and that it allows one not only to distinguish between chaotic and non-chaotic behavior, but also to measure the actual extent of any existing chaotic behavior. The whole is illustrated with numerous examples.

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W.F Darsow

Papers

The simulation of random processes on digital computers: Unavoidable order