Exploring Ancient Architectural Designs with Cellular Automata\ud

The paper discusses the utilization of three-dimensional cellular automata employing the two-dimensional totalistic cellular automata to simulate how simple rules could emerge a highly complex architectural designs of some Indonesian heritages. A detailed discussion is brought to see the simple rules applied in Borobudur Temple, the largest ancient Buddhist temple in the country with very complex detailed designs within. The simulation confirms some previous findings related to measurement of the temple as well as some other ancient buildings in Indonesia. This happens to open further exploitation of the explanatory power presented by cellular automata for complex architectural designs built by civilization not having any supporting sophisticated tools, even standard measurement systems

1/fα1/f^\alpha spectra in elementary cellular automata and fractal signals

We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays $1/f$ spectra though considered as trivial, and on the other hand that various automata classified as chaotic/complex display no $1/f$ spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce $1/f^{\alpha}$ spectra. From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics and computer sciences, there are various candidates to show spectra similar to our results.Comment: 4 pages (3 figs included

Cellular automata and self-organized criticality

Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized criticality, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range of length and time scales.Comment: 23 pages, 12 figures (most in color); uses sprocl.tex; chapter submitted for "Some new directions in science on computers," G. Bhanot, S. Chen, and P. Seiden, ed

Complexity, parallel computation and statistical physics

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to simulate it. Depth provides an objective, irreducible measure of history applicable to systems of the kind studied in statistical physics. It is argued that physical complexity cannot occur in the absence of substantial depth and that depth is a useful proxy for physical complexity. The ideas are illustrated for a variety of systems in statistical physics.Comment: 21 pages, 7 figure