An Overview of Fractal Geometry Applied to Urban Planning

Free Will as Defined by the Constrained Disorder Principle: a Restricted, Mandatory, Personalized, Regulated Process for Decision-Making

The concept of free will has challenged physicists, biologists, philosophers, and other professionals for decades. The constrained disorder principle (CDP) is a fundamental law that defines systems according to their inherent variability. It provides mechanisms for adapting to dynamic environments. This work examines the CDP's perspective of free will concerning various free will theories. Per the CDP, systems lack intentions, and the "freedom" to select and act is built into their design. The "freedom" is embedded within the response range determined by the boundaries of the systems' variability. This built-in and self-generating mechanism enables systems to cope with perturbations. According to the CDP, neither dualism nor an unknown metaphysical apparatus dictates choices. Brain variability facilitates cognitive adaptation to complex, unpredictable situations across various environments. Human behaviors and decisions reflect an underlying physical variability in the brain and other organs for dealing with unpredictable noises. Choices are not predetermined but reflect the ongoing adaptation processes to dynamic prssu½res. Malfunctions and disease states are characterized by inappropriate variability, reflecting an inability to respond adequately to perturbations. Incorporating CDP-based interventions can overcome malfunctions and disease states and improve decision processes. CDP-based second-generation artificial intelligence platforms improve interventions and are being evaluated to augment personal development, wellness, and health.

Box dimension of the border of Kingdom of Saudi Arabia

Fractal dimension unlike topological dimension is (usually) a non-integer number which measures complexity, roughness, or irregularity of an object with respect to the space in which the set lies. It is used to characterize highly irregular objects in nature containing statistical self-similarity such as mountains, snowflakes, clouds, coastlines, borders etc. In this article, box dimension (a version of fractal dimension) of the border of Kingdom of Saudi Arabia (KSA) is computed using a multicore parallel processing algorithm based on the classical box-counting method. A power law relation is obtained from numerical simulations which relates the length of the border with the scale size and provides a very close estimate of the actual length of the KSA border within the scaling regions and scaling effects on the length of KSA border are considered. The algorithm presented in the article is shown to be highly scalable and efficient and the speedup of the algorithm is computed using Amdahl's and Gustafson's laws. For simulations, a high performance parallel computer is employed using Python codes and QGIS software.