This article describes how the term fractal dimension (FD) plays a vital role in fractal geometry. It is a degree that distinguishes the complexity and the irregularity of fractals, denoting the amount of space filled up. There are many procedures to evaluate the dimension for fractal surfaces,...

This article explores paradoxical dynamics embedded in the fabric of existence. The logic of Spencer-Brown, as extended by Francisco Varela, is placed within the historical context of cybernetics. Varela's concept of reentry provides a bridge to fractal geometry through recursive iteration on...

In this contribution, particle size distributions (PSD) of soil samples are analyzed by fractal methods. Different scaling domains, characterizing different ranges of particle sizes, are identified. Numerical models based on cellular automata are presented with the aim to understand the basic...

This article proposes the concept of Symmetric Product Measures (SPM) for addressing the geometric characterization of the distribution of the intersections of the stable and unstable manifolds in (hyperbolic) dynamical systems. Prototypical examples of SPM associated with multiplicative...

Fractal geometry plays an important role in the contemporary science. In some sense, objects with integer dimension are partial cases of the more general realm of entities having a ragged shape and fractional dimension. Fractals of a broad class are described by deterministic iterated function...

Digital design technologies play a significant role in assisting the designer through conceptual architectural design. Computer supported design systems can generate various images at the early design phase and can contribute to seeking alternative architectural forms. Currently, different...

This paper demonstrates a novel local search approach based on an adaptive (time variant) search space index improving the exploration ability as well as diversity in multi-objective Particle Swarm Optimization. The novel strategy searches for the neighbourhood particles in a range which...