This paper applies machine learning and the mathematics of chaos to the task of designing indoor rock-climbing routes. Chaotic variation has been used to great advantage on music and dance, but the challenges here are quite different, beginning with the representation. We present a formalized system for transcribing rock climbing problems, then describe a variation generator that is designed to...

In this paper, the design of a fully-digital chaos-based random bit generator (RBG) is reported. The proposed generator exploits a chaotic system whose map is implemented in the time domain where the state variables of the system are represented by the phase of digital ring oscillators. This results in an extremely robust and e cient entropy source which can be implemented as a digital standard...

Chaos and fractals are novel fields of physics and mathematics showing up a new way of universe viewpoint and creating many ideas to solve several present problems. In this paper, a novel algorithm based on the chaotic sequence generator with the highest ability to adapt and reach the global optima is proposed. The adaptive ability of proposal algorithm is flexible in 2 steps. The first one is ...

In the last decade, a very interesting relationship between cryptography and chaos theory was developed. As a result of this close relationship, several chaos-based cryptosystems, especially using autonomous chaotic dynamical systems, have been put forward. However, this chapter presents a novel Chaotic Random Bit Generator (CRBG), which is based on the Poincaré map of a non-autonomous dynamica...

We report the experimental observation of a "devil's staircase" in a time-dependent system considered as a paradigm for the transition to large-scale chaos in the universality class of Hamiltonian systems. A test electron beam is used to observe its non-self-consistent interaction with externally excited wave(s) in a traveling wave tube (TWT). A trochoidal energy analyzer records the beam energ...

Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits (T ) of a dynamical system scales as a function of computer precision (ε) and the correlation dimension (d) of the chaotic attractor: T ∼ ε. In this work, we are concerned with increasing the average p...

This paper applies machine learning and the mathematics of chaos to the task of designing indoor rock-climbing routes. Chaotic variation has been used to great advantage on music and dance, but the challenges here are quite different, beginning with the representation. We present a formalized system for transcribing rock climbing problems, then describe a variation generator that is designed to...

A 1-dimensional generalization of the well known Logistic Map is proposed. The proposed family of maps is referred to as the B-Exponential Map. The dynamics of this map are analyzed and found to have interesting properties. In particular, the B-Exponential Map exhibits robust chaos for all real values of the parameter B e 4. We then propose a pseudo-random number generator based on the B-Expone...