A cellular automata modelling of dendritic crystal growth based on Moore and von Neumann neighbourhood

An important step in understanding crystal growth patterns involves simulation of the growth processes using mathematical models. In this paper some commonly used models in this area are reviewed, and a new simulation model of dendritic crystal growth based on the Moore and von Neumann neighbourhoods in cellular automata models are introduced. Simulation examples are employed to find ap- propriate parameter configurations to generate dendritic crystal growth patterns. Based on these new modelling results the relationship between tip growth speed and the parameters of the model are investigated

DNA Sequence Evolution through Integral Value Transformations

In deciphering the DNA structures, evolutions and functions, Cellular Automata (CA) do have a significant role. DNA can be thought of as a one-dimensional multi-state CA, more precisely four states of CA namely A, T, C, and G which can be taken as numerals 0, 1, 2 and 3. Earlier, G.Ch. Sirakoulis et al reported the DNA structure, evolution and function through quaternary logic one dimensional CA and the authors have found the simulation results of DNA evolutions with the help of only four linear CA rules. The DNA sequences which are produced through the CA evolutions, however, are seen by our research team not to exist in the established databases of various genomes although the initial seed (initial global state of CA) was taken from the database. This problem motivated us to study the DNA evolutions from a more fundamental point of view. Parallel to the CA paradigm we have devised an enriched set of discrete transformations which have been named as Integral Value Transformations (IVT). Interestingly, on applying the IVT systematically, we have been able to show that each of the DNA sequences at various discrete time instances in IVT evolutions can be directly mapped to a specific DNA sequence existing in the database. This has been possible through our efforts of getting quantitative mathematical parameters of the DNA sequences involving Fractals. Thus we have at our disposal some transformational mechanism between one DNA to another

Phenomenology of retained refractoriness: On semi-memristive discrete media

We study two-dimensional cellular automata, each cell takes three states: resting, excited and refractory. A resting cell excites if number of excited neighbours lies in a certain interval (excitation interval). An excited cell become refractory independently on states of its neighbours. A refractory cell returns to a resting state only if the number of excited neighbours belong to recovery interval. The model is an excitable cellular automaton abstraction of a spatially extended semi-memristive medium where a cell's resting state symbolises low-resistance and refractory state high-resistance. The medium is semi-memristive because only transition from high- to low-resistance is controlled by density of local excitation. We present phenomenological classification of the automata behaviour for all possible excitation intervals and recovery intervals. We describe eleven classes of cellular automata with retained refractoriness based on criteria of space-filling ratio, morphological and generative diversity, and types of travelling localisations

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