Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions have universal aesthetic appeal. Perceptual and aesthetic responses to visual complexity have been more varied with findings suggesting both linear (Forsythe (...) et al., 2011) and curvilinear (Berlyne, 1970) relationships. Individual differences have been found to account for many of the differences we see in aesthetic responses but some, such as culture, have received little attention within the fractal and complexity research fields. This 2-study paper aims to test preference responses to fractal dimension and visual complexity, using a large cohort (N=443) of participants from around the world to allow universality claims to be tested. It explores the extent to which age, culture and gender can predict our preferences for fractally complex patterns. Following exploratory analysis that found strong correlations between fractal dimension and visual complexity, a series of linear mixed-effect models were implemented to explore if each of the individual variables could predict preference. The first tested a linear complexity model (likelihood of selecting the more complex image from the pair of images) and the second a mid-range fractal dimension model (likelihood of selecting an image within mid-range). Results show that individual differences can reliably predict preferences for complexity across culture, gender and age. However, in fitting with current findings the mid-range models show greater consistency in preference not mediated by gender, age or culture. This paper supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying preference but also highlights the fragility of universal claims by demonstrating individual differences in preference for the interrelated concept of visual complexity. This highlights a current stalemate in the field of empirical aesthetics. (shrink)

It has been claimed that quantum mechanics, unlike classical mechanics, allows for free will. In this paper I articulate that claim and explain how a complex physical system possessing fractal-like self similarity could exhibitboth self consciousness and self determination. I use complexity theory to show how quantum mechanical indeterminacies at the neural level could “percolate up” to the levels of scale within the brain at which sensory-motor information transformations occur. Finally, I explain how macro level indeterminacy could be (...) coupled with self determination to provide a physical system with the capacity for radically free willing. (shrink)

The Hoffmann reflex (H-wave) is produced by alpha-motoneuron activation in the spinal cord. A feature of this electromyography response is that it exhibits fluctuations in amplitude even during repetitive stimulation with the same intensity of current. We herein explore the hypothesis that physical training induces plastic changes in the motor system. Such changes are evaluated with the fractal dimension (FD) analysis of the H-wave amplitude-fluctuations (H-wave FD) and the cross-covariance (CCV) between the bilateral H-wave amplitudes. The aim of this (...) study was to compare the H-wave FD as well as the CCV before and after track training in sedentary individuals and athletes. The training modality in all subjects consisted of running three times per week (for 13 weeks) in a concrete road of 5 km. Given the different physical condition of sedentary vs. athletes, the running time between sedentary and athletes was different. After training, the FD was significantly increased in sedentary individuals but significantly reduced in athletes, although there were no changes in spinal excitability in either group of subjects. Moreover, the CCV between bilateral H-waves exhibited a significant increase in athletes but not in sedentary individuals. These differential changes in the FD and CCV indicate that the plastic changes in the complexity of the H-wave amplitude fluctuations as well as the synaptic inputs to the Ia-motoneuron systems of both legs were correlated to the previous fitness history of the subjects. Furthermore, these findings demonstrate that the FD and CCV can be employed as indexes to study plastic changes in the human motor system. (shrink)

Classical fractal dimensions have recently been effectivized by characterizing them in terms of real-valued functions called gales, and imposing computability and complexity constraints on these gales. This paper surveys these developments and their applications in algorithmic information theory and computational complexity theory.

Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging and analyzing (...) at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex 'value spaces', with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic. (shrink)

Our universe, science reveals, began in utter simplicity, then evolved into burgeoning complexity. Starting with subatomic particles, dissimilar entities formed associations—binding, bonding, growing, branching, catalyzing, cooperating—as “self” joined “other” following universal laws with names such as gravity, chemical attraction, and natural selection. Ultimately life arose in a world of dynamic organic chemistry, and complexity exploded with wondrous new potential. Fast forward to human evolution, and a tension that had existed for billions of years now played out in an (...) unprecedented arena of conscious calculation and cultural diversity. Cooperation interleaving with competition; intimacy oscillating with integrity—we dwell in a world where yin meets yang in human affairs on many levels. In The Fractal Self, John Culliney and David Jones uncover surprising intersections between science and philosophy. Connecting evidence from evolutionary science with early insights of Daoist and Buddhist thinkers, among others, they maintain that sagely behavior, envisioned in these ancient traditions, represents a pinnacle of human achievement emerging out of our evolutionary heritage. They identify an archetype, “the fractal self,” a person in any walk of life who cultivates a cooperative spirit. A fractal self is a sage in training, who joins others in common cause, leads from within, and achieves personal satisfaction in coordinating smooth performance of the group, team, or institution in which he or she is embedded. Fractal selves commonly operate with dedication and compassionate practice in the service of human society or in conserving our planet. But the competitive side of human nature is susceptible to greed and aggression. Self-aggrandizement, dictatorial power, and ego-driven enforcement of will are the goals of those following a self-serving path—individuals the authors identify as antisages. Terrorist leaders are an especially murderous breed, but aggrandizers can be found throughout business, religion, educational institutions, and governments. Humanity has reached an existential tipping point: will the horizon already in view expand with cooperative progress toward godlike emergent opportunities or contract in the thrall of corrupt oligarchs and tribal animosities? We have brought ourselves to a chaotic edge between immense promise and existential danger and are even now making our greatest choice. (shrink)

The 21st century is the time of complexity. We delineate it and its importance as necessary to solve ‘wicked problems.’ Inherently transdisciplinary, trans-scale, and interconnected to living systems, the solution to Heliophysics’ identity crisis and to unlock the next generation of scientific discovery may be to embrace complexity. With the right foresight, direction, and incentive over the next ten years, Heliophysics can become a beacon for how all of society thinks about and does complexity science.

We examine two connectionist networks—a fractal learning neural network (FLNN) and a Simple Recurrent Network (SRN)—that are trained to process center-embedded symbol sequences. Previous work provides evidence that connectionist networks trained on infinite-state languages tend to form fractal encodings. Most such work focuses on simple counting recursion cases (e.g., anbn), which are not comparable to the complex recursive patterns seen in natural language syntax. Here, we consider exponential state growth cases (including mirror recursion), describe a new training scheme (...) that seems to facilitate learning, and note that the connectionist learning of these cases has a continuous metamorphosis property that looks very different from what is achievable with symbolic encodings. We identify a property—ragged progressive generalization—which helps make this difference clearer. We suggest two conclusions. First, the fractal analysis of these more complex learning cases reveals the possibility of comparing connectionist networks and symbolic models of grammatical structure in a principled way—this helps remove the black box character of connectionist networks and indicates how the theory they support is different from symbolic approaches. Second, the findings indicate the value of future, linked mathematical and empirical work on these models—something that is more possible now than it was 10 years ago. (shrink)

Natural forms, often characterized by irregularity and roughness, have a unique complexity that exhibit self-similarity across different spatial scales or levels of magnification. Our visual system is remarkably efficient in the processing of natural scenes and tuned to the multi-scale, fractal-like properties they possess. The fractal-like scaling characteristics are ubiquitous in many physical and biological domains, with recent research also highlighting their importance in aesthetic perception, particularly in the visual and, to some extent, auditory modalities. Given the (...) multitude of fractal-like scaling manifestations, we explore potential commonalities in the way they might affect aesthetic preference within and across different physical and sensory domains. We use a range of visual and tactile stimuli to explore the equivalence of fractal-scaling effects on aesthetic preferences within and across visual and tactile modalities. Our results suggest that, despite some superficial differences, the underlying dimensional structure mediating the preference across the two domains is remarkably similar. The qualitative nature of this dimensional structure as well as suggestions for future research are discussed. (shrink)

Successful applications of hierarchical complexity to the behaviors of organisms, animals and humans, and social entities evidence the scaling properties of self-similarity, thus the bounded fractal characteristics of orders of hierarchical complexity. The theory specifies an identical sequence of discrete-state transition steps required from each stage of performance to the next. It repeats at all scales. Tasks nested within the step sequence evidence self-similarity with the orders of complexity. This model introduces questions about noise categories when (...) system tasks are fully accounted for, dependent, self-similar, and measurable. Ubiquitous transition steps are inherent dynamics of evolution. (shrink)

This article explores an understanding of organizational management developed from the metaphorical application of complexity science to the field of organizational development. It focuses on the insights that fractality triggers in relation to an alternative way of examining and appreciating organizational hierarchy, and the subsequent implications to liberating creativity, ingenuity and potentiality of individuals working within the organization. Sites where such a fractal-hierarchy mindset appears to be evident are discussed, and the effects on productivity noted.

The interconnections between self and surroundings in Daoist thought have been explored in the past in a variety of contexts. This paper, however, explores the Daoist version of the relational self from the general perspective of chaos theory and, more specifically, examines the role of the self in creating emergent form and dynamism in nature and society. The fractal self and world merge through the disciplined effort of the sage until the effort becomes effortless. Both self and world are (...) transformed and become one through the emergent moment. This moment represents a new opportunity for subsequent patterns, or attractors, to emerge. We suggest that the self folds itself into the world, creating and being created by a new attractor, or pattern, in the organization of nature, which we argue is Dao. Our current investigation addresses the following aspects of chaos theory and its relation to Daoism: (1) the Daoist notion of wuwei as perfect congruence; (2) yin and yang at the edge of chaos; (3) the emergent nature of the myriad things; and (4) a Daoist warning against fractal disconnections in the world. Finally, we conclude that the self has the potential to become the world. To approach this amplified condition, the self must dedicate itself to and risk open engagement with events across the complexity of nature. Through openly engaging the world, the self is transformed, leaving the world forever changed. (shrink)

Feminists have long been aware that the notion of women is problematic and using it uncritically without further qualifications leads to exclusions. In the article, I argue that the source of these problems lies in the understanding of concepts as static and clearly defined. I deploy Hegel’s idea of syllogism to define dynamic concepts, which I term ‘fractal concepts’ because of their complexity and constant development. In such structures the balance between the universal, the particular and the individual (...) is maintained and, consequently, every woman is essential for the definition of such a non-essentialist notion of women. I propose that an epistemological interpretation of the Hegelian idea of recognition can be used to describe the development of fractal concepts in the confrontation of different perspectives. It also explains the obstruction of this process by the desire for domination and control, which results in the appropriation of group identities by their privileged members. I situate the logical and political framework developed in the paper in the context of feminist controversies around the concept of woman and argue that it provides us with a comprehensive account of intersectionality as well as an explicative solution to the regress problem. (shrink)

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss (...) some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology. (shrink)

Digital companies exhibit discontinuous growth in the process of shifting from their existing core business to a newer and less familiar business. This pattern of growth often ends in failure mainly because companies invest most of their resources in maintaining the value network of their existing core business, which ultimately results in a “lock-in” effect. The fractal theory assumes that there are similarities among fractals within companies. These similarities may reduce the threats posed by the value network lock-in effect (...) and increase the chances of successful discontinuous growth. In this study, we applied fractal theory to consider the following questions: in what aspects does the successful discontinuous growth of digital companies exhibit fractal characteristics? What strategy does digital companies use to ensure these fractal characteristics? We adopted an exploratory single-case study method and chose ByteDance as the case company to analyze its successful shift from Toutiao to Douyin. Our results show that a necessary condition for the successful discontinuous growth of digital companies is that similarities exist between the existing core business and the new business and entrepreneurial bricolage is a strategy used by digital companies to ensure the existence of fractal characteristics of similarities. We discuss the theoretical contributions and practical implications of this finding. (shrink)

Prevailing theories of consciousness may be characterized as either a physicalist view of mind with material building blocks that grow in complexity unto an emergent conscious experience, or as a dualistic model in which mind-body interaction is taken as the interface of conscious intent and unconscious bodily processing. Roger Penrose supports a model of consciousness that goes beyond dualism by adding a third domain [19]. The Three World model describes interconnected yet independent aspects of consciousness: Physical, Mental & Platonic. (...) These three worlds are grounded in the three axioms of quantum mechanics: measurement, superposition and entanglement. The Mental World corresponds to the superposition principle in which all possible future realities are superposed as potentials before a choice is made. The superposition is analogous to the choices we make everyday. In the Physical World, the measurement principles states that the quantum system must collapse the superposed possibilities into a single actuality. The most peculiar phenomenon in quantum mechanics is entanglement. Quantum systems may be entangled in a timeless and spaceless way such that they will still be connected despite separation in space or time. The Platonic World is akin to entanglement, because mathematics and conceptual forms are unchanging regardless of space or time. Finally, a new model called Fractal Trialism is proposed which describes how there is a nested trialism within each of the three worlds in order to elaborate their interconnectedness. This model describes digital computers, quantum computers and shared experience. Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}. (shrink)

Primal emergence -- Out of the dreamtime -- The quickening of chemistry -- Ecology emergent -- Intimate ark : sex and emergence -- Social order in nature : between conflict and cooperation -- Self within world -- From self to sage -- From self to no-self to all-self -- Anti-sage : from cult to empire -- Into Indra's net.

The book you hold in your hands is the outcome of the "ISCS 2013: Interdisciplinary Symposium on Complex Systems" held at the historical capital of Bohemia as a continuation of our series of symposia in the science of complex systems. Prague, one of the most beautiful European cities, has its own beautiful genius loci. Here, a great number of important discoveries were made and many important scientists spent fruitful and creative years to leave unforgettable traces. The perhaps most significant period (...) was the time of Rudolf II who was a great supporter of the art and the science and attracted a great number of prominent minds to Prague. This trend would continue. Tycho Brahe, Niels Henrik Abel, Johannes Kepler, Bernard Bolzano, August Cauchy Christian Doppler, Ernst Mach, Albert Einstein and many others followed developing fundamental mathematical and physical theories or expanding them. Thus in the beginning of the 17th century, Kepler formulated here the first two of his three laws of planetary motion on the basis of Tycho Brahe’s observations. In the 19th century, nowhere differentiable continuous functions (of a fractal character) were constructed here by Bolzano along with a treatise on infinite sets, titled “Paradoxes of Infinity” (1851). Weierstrass would later publish a similar function in 1872. In 1842, Doppler as a professor of mathematics at the Technical University of Prague here first lectured about a physical effect to bear his name later. And the epoch-making physicist Albert Einstein – while being a chaired professor of theoretical physics at the German University of Prague – arrived at the decisive steps of his later finished theory of general relativity during the years 1911–1912. In Prague, also many famous philosophers and writers accomplished their works; for instance, playwright arel ape coined the word "robot" in Prague (“robot” comes from the Czech word “robota” which means “forced labor”). (shrink)

A summary of topics and theoretical approaches to dynamical systems and psychology. Includes chapters on physical systems, self-organization, state space and dimensionality, networks, neurodynamics, fractals and how such concepts help to explain cognition and the mind.

Les choses ne sont pas que des choses. Peut-être quelque chose d'essentiel échappe-t-il encore à la méthodologie philosophique appliquée aux théories des formes complexes aujourd'hui. Comment le simple et le complexe, deux catégories apparemment contraires, sont-elles dès les prémices de l'univers, nouées de façon inséparable? Tel est le problème onto-cosmologique que vise à résoudre l'homme sur terre, pour autant qu'il est exposé à l'avènement du posthumanisme persistant et au surgissement du transhumanisme subsistant. La nature n'est plus seulement moulée dans une (...) série des formes chaotiques, mais elle est aussi façonnée par une concaténation des systèmes catastrophiques. Il existe donc des choses imprévues que personne n'a jamais vues et des pensées fractales que personne n'a jamais eues dans le monde. (shrink)

Using fractal analyses to study events allows us to capture the scale-independence of those events, that is, no matter at which level we study a phenomenon, we should get roughly the same results because events exhibit similar structure across scales. This is demonstrably true in mathematical fractals but is less assured in behavioral fractals. The current research directly tests the scale-independence hypothesis in the behavioral domain by exploring the fractal structure of aggression, a social phenomenon comprising events that (...) span temporal scales from minutes of face-to-face arguments to centuries of international armed conflicts. Using publicly available data, we examined the temporal fractal structure of four scales of aggression: wars, riots, violent crimes, and body movement during arguments. Our results lend mixed support to the scale-independence hypothesis and provide insight into the self-organization of human interactions. (shrink)

The biosemiotic complexity of acoustic communities in the primary forests of Ulu Temburong and Yasunì was investigated with continuous 24-h recordings, using the acoustic signature and multiscale approach of ecoacoustic events and their emergent fractal dimensions. The 3D recordings used for the analysis were collected in undisturbed primary equatorial forests under the scope of the project, Fragments of Extinction, which produces 3D sound portraits with the highest definition possible using current technologies – a perfect dataset on which to (...) perform a multiscale qualitative analysis. The ecoacoustic events detected by a combination of the Acoustic Complexity Indices, ACIft, ACIft evenness, and ACItf evenness, and its fractal dimension were developed according to a biosemiotics approach in which the ecofield theory states that EE functions like a species-specific carrier of meaning. EEs, extracted according to 10 levels of temporal resolution, from 1 to 360 s, confirm the hypothesis that these acoustic communities have an internal complexity that responds to a fractal structure. Yasunì was richer in EEs, with a higher coefficient of variation of hourly fractal dimension. This methodology opens up promising new perspectives in the acoustic assessment of habitat quality and monitoring landscape modification. It also confirms the great potential of the biosemiotics approach in converting acoustic frequencies into ecoacoustic events through encoding procedures that mimic potential species-specific interpretations of the sonic environment. (shrink)

Unlike previous studies that consider the Chicago Board of Options Exchange implied volatility index, we examine long memory and fractality in the universe of nine CBOE volatility indices. Using daily data from October 5, 2007, to October 5, 2020, covering calm and crisis periods, we find evidence of long memory and fractality in all indices and a change in the degree of volatility persistence, which points to inefficiency. The long memory of the SKEW index is strong before the onset of (...) three crisis periods, but eases afterwards. The findings provide new insights that matter to investment decisions and trading strategies. (shrink)

This research proposes a modified metaheuristic optimization algorithm, named as improved stochastic fractal search, which is formed based on the integration of the quasiopposition-based learning and chaotic local search schemes into the original SFS algorithm for solving the optimal capacitor placement in radial distribution networks. The test problem involves the determination of the optimal number, location, and size of fixed and switched capacitors at different loading conditions so that the network total yearly cost is minimized with simultaneous fulfillment of (...) operating constraints. Also, the hourly on/off scheduling plans of switched shunt capacitors considering a modified cost objective function are obtained. The proposed ISFS algorithm has been tested on two IEEE 69-bus and 119-bus RDNs and a practical 152-bus RDN. For clarifying the effectiveness and validation of the ISFS, the simulated results have been compared with those of other previously utilized solution approaches in the literature as well as the original SFS. From result comparison, the proposed ISFS outperforms other previous approaches regarding solution quality and statistical performance for the compared cases, especially in the complex and large-scale networks. Notably, compared with the original SFS, the proposed ISFS shows a significantly better performance in all the tested cases. (shrink)

Fractal art graphics are the product of the fusion of mathematics and art, relying on the computing power of a computer to iteratively calculate mathematical formulas and present the results in a graphical rendering. The selection of the initial value of the first iteration has a greater impact on the final calculation result. If the initial value of the iteration is not selected properly, the iteration will not converge or will converge to the wrong result, which will affect the (...) accuracy of the fractal art graphic design. Aiming at this problem, this paper proposes an improved optimization method for selecting the initial value of the Gauss-Newton iteration method. Through the area division method of the system composed of the sensor array, the effective initial value of iterative calculation is selected in the corresponding area for subsequent iterative calculation. Using the special skeleton structure of Newton’s iterative graphics, such as infinitely finely inlaid chain-like, scattered-point-like composition, combined with the use of graphic secondary design methods, we conduct fractal art graphics design research with special texture effects. On this basis, the Newton iterative graphics are processed by dithering and MATLAB-based mathematical morphology to obtain graphics and then processed with the help of weaving CAD to directly form fractal art graphics with special texture effects. Design experiments with the help of electronic Jacquard machines proved that it is feasible to transform special texture effects based on Newton's iterative graphic design into Jacquard fractal art graphics. (shrink)

Where Medicine Went Wrong explores how the idea of an average value has been misapplied to medical phenomena, distorted understanding and lead to flawed medical ...

This paper applies a proposed modified stochastic fractal search algorithm (MSFS) for dealing with all constraints of optimal reactive power dispatch (ORPD) and finding optimal solutions for three different cases including power loss optimization, voltage deviation optimization, and L-index optimization. The proposed MSFS method is newly constructed in the paper by modifying three new solution update mechanisms on standard stochastic fractal search algorithm (SSFS). The first modification is to keep only one formula and abandon one formula in the (...) diffusion process while the second modification and the third modification are used in the first update and the second update. In two updates of SSFS, solutions with low quality are updated with high probability while other solutions with high quality do not get chances to be updated. This manner results in the fact that some promising solutions around the high quality solutions can be missed. In order to tackle this restriction, the second modification of MSFS is to newly update the worst solutions in the first update and the best solutions in the second update. In the third modification, all existing formulas of SSFS in the two updates are abandoned and the same new proposed technique is used for updating such solutions in two updates. Compared to SSFS, the three modifications can bring advantages to MSFS such as using smaller number of produced solutions per iteration, spending shorter execution time, finding better optimal solutions, and owning more stable search ability. Furthermore, the proposed method also sees its effectiveness and robustness over SSFS by testing on IEEE 30-bus system and IEEE 118-bus system with three different single objectives for each system. The proposed method can find less minimum, average, and maximum for all the cases in addition to faster search speed. Besides, the proposed method is also compared to other methods such as PSO-based method group, GA-based method group, DE-based method group, and other recent methods. Result comparisons also indicate that the proposed method can be more efficient than almost all these methods with respect to less minimum and smaller values of control parameters. As a result, evaluation of the performance of the proposed method is that it should be used for seeking solutions of ORPD problem. (shrink)

According to Peirce, the value of the idea of freedom arises only to oppose the idea of necessity. Freedom emerges as a working value, a primary esthetic principle, in response to that which is perceived as fixed, determined, necessary, absolute. The idea of Freedom materializes, assumes a million appearances, wears its ten million masks......Freedom as the Freedom-to-Focus is a Peircean esthetic process that becomes realized through the three stages of Fragment/Fractal, Fact, Form. This triadic process corresponds to the semiotic (...) functions of Icon, Index, Symbol. Freedom's course is nonlineal, self-corrective, dynamic, open: Freedom is the occasion for Chaos, and Chaos is the locus of Form. (shrink)

Excessive use of social media is a developing concern in the twenty-first century. This issue needs to be addressed before it has any more significant consequences than what we are currently experiencing. As a preventive technique, advertisements and awareness-raising campaigns about the detrimental impact of digital technologies are used. The application of novel mathematical techniques and terminologies in this field of study will have significant potential to enhance healthy living by preventing certain ailments. This is the most compelling justification for (...) conducting a new study with the most up-to-date techniques at our disposal. This study investigates clear and concise transmission in order to generate a deterministic mathematical model of social media addiction S M A using the fractal-fractional derivative operator. Also, the analysis of the S M A model in terms of the invariant domain, the existence of a positive invariant solution, and equilibria assumptions are stated in a detailed manner. Besides that, the basic reproduction number ℝ 0 < 1 is computed, demonstrating that the proposed methodology is more efficacious. The Atangana-Baleanu FF differential operators are recently defined in FF differential operators that are applied to characterize the S M A model’s mathematical algorithm. We investigated the numerical behaviour of the S M A in three ways: changing the fractional-order α as well as the fractal-dimension ℘ ; changing α while keeping ℘ constant; and changing ℘ while keeping α constant. Our examined visualizations and simulation studies using MATLAB for the numerical modelling of the aforementioned system showed that the novel developed Atangana-Baleanu FF differential operators produce remarkable results when compared to the classical frame. (shrink)

This article relates the emergence of a group of faculty researchers utilizing complexity science approaches. The narrative emerges from three projects combining research into complexity, communities, and technologies. Details of how the research was initiated, and the nature and quality of the conversational method, are provided. In addition, theoretical concepts that were consciously applied and others that arose through insights from the data as it was collected are discussed. Although this is like most real narratives, a never-ending story, (...) it concludes with a presentation of some of the ideas that separate complexity-informed research from other paradigms. (shrink)

Climate dynamics and trends have significant environmental and socioeconomic impacts; however, in the Benin Republic, they are generally studied with diverse statistical methods ignoring the nonstationarity, nonlinearity, and self-similarity characteristics contained in precipitation time series. This can lead to erroneous conclusions and an unclear understanding of climatic dynamics. Based on daily precipitation data observed in the six synoptic stations of Benin Republic, in the period from 1951 to 2010, we have proposed determining the local trends of precipitations, investigating precipitation nonlinear (...) dynamics, and assessing climatic shift in the study period by Ensemble Empirical Mode Decomposition and Multifractal Detrended Fluctuation Analysis method. To overcome the detrending issue in the standard MFDFA method, the EEMD algorithm is embedded into the MFDFA. The study period is subdivided into three subperiods: 1951–1970, 1971–1990, and 1991–2010. Intrinsic Mode Functions are obtained according to the climatic region in which the stations are located. Results show that precipitation variation is significantly governed by the five first IMFs, in which oscillation periods vary from 1 to 25 days. The trend curves decrease at all the synoptic stations, and their slope values vary accordingly to the subperiods. Referring to the values of the multifractal spectrum parameters, α 0, and the width of the spectrum w, consistent changes are observed regardless of the subperiods and the concerned stations. The spatial and temporal variability of precipitation indicates that the multifractal properties are good indicators for assessing changes in precipitation dynamics, and the changes in their features could be explained by the global change than by the local climate variation. Despite the observed differences in multifractal spectra properties from the three subperiods, it is not possible to verify the subdivision of 1951–2010 in three subperiods as it is done by previous studies in West Africa. Our findings can be used in the validation of global and regional climate models since a valid model should explain empirically detected scaling properties in observed data. (shrink)

Drinking kills a significant proportion of individuals every year, particularly in low-income communities. An impulsive differential equation system is used to explore the effectiveness of activated charcoal in detoxifying the body after methanol poisoning. Our impression of activated charcoal is shaped by the fractional dynamics of the problem, which leads to speedy and low-cost first aid. The adsorption capacity of activated charcoal is investigated using impulsive differential equations. The ABC fractional operator’s findings paint a more realistic image of first aid (...) in public and primary health centers, which can assist to reduce methanol poisoning deaths. Numerical simulations are provided using generalized Adams–Bashforth–Moulton method. (shrink)

The complex-systems approach to cognitive science seeks to move beyond the formalism of information exchange and to situate cognition within the broader formalism of energy flow. Changes in cognitive performance exhibit a fractal (i.e., power-law) relationship between size and time scale. These fractal fluctuations reflect the flow of energy at all scales governing cognition. Information transfer, as traditionally understood in the cognitive sciences, may be a subset of this multiscale energy flow. The cognitive system exhibits not just a (...) single power-law relationship between fluctuation size and time scale but actually exhibits many power-law relationships, whether over time or space. This change in fractal scaling, that is, multifractality, provides new insights into changes in energy flow through the cognitive system. We survey recent findings demonstrating the role of multifractality in (a) understanding atypical developmental outcomes, and (b) predicting cognitive change. We propose that multifractality provides insights into energy flows driving the emergence of cognitive structure. (shrink)

Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and geometry of symmetry (...) is controlled by numerical parameters, which act in analogy with a biological organism’s DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional (2D) design parameters, affine geometry and shape symmetry for visual or tactile shape sensation and perception-based decision making in populations of experts and non-experts. It will be shown that 2D fractal symmetry, referred to herein as the “symmetry of things in a thing”, results from principles very similar to those of affine projection. Results from experiments on aesthetic and visual preference judgments in response to 2D fractal trees with varying degrees of asymmetry are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (on a scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from “symmetry of things in a thing” significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion. (shrink)