In the paper, the class of discrete linear systems is enlarged with the inclusion of discrete-time fractional linear systems. These are systems described by fractional difference equations and fractional frequency responses. It is shown how io compute the impulse response and transfer function. Fractal signals are introduced as output of special linear systems: fractional differaccumulators, sy...

We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases. Stochasti...

This article presents the language LinF for L-System specification. L-Systems are formal string rewriting systems introduced in 1968 by the botanist Aristid Lindenmayer that are used to model fractal images. LinF allows the definition of three-dimensional fractals and stochastic fractals. Together with the LinF definition this paper presents the implementation of cFLC, an OpenGL-based system th...

Fractal scaling relations are found in repeated measurements of voluntary human behavior (e.g., time estimation, visual search, word naming). These fractal scaling relations suggest that the variation in the observed behavior is scale-free with small-scale and large-scale variations sharing the same structure. Researchers have proposed a conceptual control parameter that may account for reliabl...

Fractal AI is a theory for general artificial intelligence. It allows to derive new mathematical tools that constitute the foundations for a new kind of stochastic calculus, by modelling information using cellular automaton-like structures instead of smooth functions. In the repository included we are presenting a new Agent, derived from the first principles of the theory, which is capable of s...

The space time that is used in relativistic Quantum Mechanics and Quantum Field Theory is the Minkowski space time. Yet, as pointed out by several scholars this classical space time is incompatible with the Heisenberg Uncertainity Principle: We cannot go down to arbitrarily small space time intervals, let alone space time points. Infact this classical space time is at best an approximation, and...

The optimal reactive power dispatch (ORPD) is a very important problem aspect of power system planning and is a highly nonlinear, non-convex optimization problem because consist of both continuous and discrete control variables. Since the power system has inherent uncertainty, hereby, this paper presents both of the deterministic and stochastic models for ORPD problem in multi objective and sin...

Fractal stochastic point processes FSPPs provide good mathematical models for long term correlations present in auditory nerve bers in a number of species Sim ulations and analytical results for FSPPs concur with experimental data over long times Refractoriness modi ed Poisson point processes in contrast model only the short term characteristics of these data FSPPs incorporating refractoriness ...

Stochastic differential equations in R with random coefficients are considered where one continuous driving process admits a generalized quadratic variation process. The latter and the other driving processes are assumed to possess sample paths in the fractional Sobolev space W β 2 for some β > 1/2. The stochastic integrals are determined as anticipating forward integrals. A pathwise solution p...

Fractal Image Compression is a lossy compression technique that has been developed in the early 1990s. Fractal image compression explores the self-similarity property of a natural image and utilizes the partitioned iterated function system (PIFS) to encode it. The fractal image compression problem had three major requirements: speeding up the compression algorithm, improving image quality and i...