We present a very simple electronic implementation of the tent map, one of the best-known discrete dynamical systems. This is achieved by using integrated circuits and passive elements only. The experimental behavior of the tent map electronic circuit is compared with its numerical simulation counterpart. We find that the electronic circuit presents fixed points, periodicity, period doubling, chaos and intermittency that match with high accuracy the corresponding theoretical values.

Europhysics Letters 87 (2009) 28003 celuletas7.tex PACS 89.75.Da -Systems obeying scaling laws PACS 05.45.Tp -Time series analysis PACS 05.40.-a -Fluctuation phenomena, random processes, noise, and Brownian motion In 2005, Nagler and Claussen (Phys. Rev. E 71, 067103 (2005)) investigated the time series of the elementary cellular automata (ECA) for possible (multi)fractal behavior. They eliminated the polynomial background at b through the direct fitting of the polynomial coefficients a and b. We here reconsider their work eliminating the polynomial trend by means of the multifractal-based detrended fluctuation analysis (MF-DFA) in which the wavelet multiresolution property is employed to filter out the trend in a more speedy way than the direct polynomial fitting and also with respect to the wavelet transform modulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelet transform is used to calculate the trend as a local feature that enters the so-called details signal. We illustrate our result for three representative ECA rules: 90, 105, and 150. We confirm their multifractal behavior and provide our results for the scaling parameters.

This paper carries out the image encryption with a revised and modified cryptosystem based on a rule-90 cellular automaton. For this purpose, we used an appropriate and convenient matrix approach to implement the main components of the encryption system, two indexed families of permutations and a pseudo-random bit generator. Furthermore, we modify the encryption scheme for improving its security. This makes our encryption proposal resist some common attacks, e.g. chosen plain-text attack, and the encryption and decryption processes are performed in a flexible way. Also, some security aspects of the cryptosystem are evaluated with a series of statistical tests exhibiting good results. It is believed that this proposal fits naturally in the present digital technology and is capable of achieving high levels of performance.

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