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)

The finding of fractal scaling (FS) in behavioral sequences has raised a debate on whether FS is a pervasive property of the cognitive system or is the result of specific processes. Inferences about the origins of properties in time sequences are causal. That is, as opposed to correlational inferences reflecting instantaneous symmetrical relations, causal inferences concern asymmetric relations lagged in time. Here, I integrate Granger-causality with inferences about FS. Four simulations illustrate that causal analyses can isolate distinct FS (...) sources, whereas correlational techniques cannot. I then analyze three simultaneous sequences of responses from a database of word-naming trials. I find that two, or perhaps three, distinct sources account for the presence of FS in these sequences, but FS is not a general property of the system. This suggests that FS arises due to the properties of a limited number of identifiable psychological and/or neural processes. Finally, I reanalyze a previously published dataset of acoustic frequency spectra using the new tools. The causality/criticality combination introduced here offers a new important perspective in the study of cognition. (shrink)

One of the challenges facing AI governance is the need for multiple scales. Universal human rights require a global scale. If someone asks AI if education is harmful to women, the answer should be “no” regardless of their location. But economic democratization requires local control: if AI’s power over an economy is dictated by corporate giants or authoritarian states, it may degrade democracy’s social and environmental foundations. AI democratization, in other words, needs to operate across multiple scales. Nature allows the (...) multiscale flourishing of biological systems through fractal distributions. In this paper, we show that key elements of the fractal scaling found in nature can be applied to the AI democratization process. We begin by looking at fractal trees in nature and applying similar analytics to tree representations of online conversations. We first examine this application in the context of OpenAI’s “Democratic Inputs” projects for globally acceptable policies. We then look at the advantages of independent AI ownership at local micro-levels, reporting on initial outcomes for experiments with AI and related technologies in community-based systems. Finally, we offer a synthesis of the two, micro and macro, in a multifractal model. Just as nature allows multifractal systems to maximize biodiverse flourishing, we propose a combination of community-owned AI at the micro-level, and globally democratized AI policies at the macro-level, for a more egalitarian and sustainable future. (shrink)

A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final (...) formulation of Quantum Gravity. (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)

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)

It has long been appreciated that the brain is oscillatory 1. Early measurements of brain electrophysiology revealed rhythmic synchronization unifying large swaths of the brain. The study of neural oscillation has enveloped cognitive neuroscience and neural systems. The traditional belief that oscillations are epiphenomenal of neuron spiking is being challenged by intracellular oscillations and the theoretical backing that oscillatory activity is fundamental to physics. Subjective experience oscillates at three particular frequency bands in a cognitive triad: perception at 5 Hz, action (...) at 2 Hz, and attention at 0.1 Hz. This triad functions as a means of information flow across scales of magnitude in a biological fractal. The _Homunculus Solution _is proposed in which mental experience occurs at fixed scales of biology. The mind is composed of minds, perceived as "the voices in your head." Each voice has voices inside its head to increasingly microscopic scales, forming an interactive fractal of subjective experience. Normal 0 false false false EN-US X-NONE X-NONE. (shrink)

Fractal structure is a ubiquitous property found in nature and biology, and has been observed in processes at different levels of organization, including rhythmic behavior and musical structure. A temporal process is characterized as fractal when serial long-term correlations and statistical self-similarity (scaling) are present. Previous studies of sensorimotor synchronization using isochronous (non-fractal) stimuli show that participants' errors exhibit persistent structure (positive long-term correlations), while their inter-tap intervals (ITIs) exhibit anti-persistent structure (negative long-term correlations). Auditory-motor synchronization (...) has not been investigated with anti-persistent stimuli. In the current study, we systematically investigated whether the fractal structure of auditory rhythms was reflected in the responses of participants who were asked to coordinate their taps with each event. We asked musicians and non-musicians to tap with 12 different rhythms that ranged from anti-persistent to persistent. The scaling exponents of the ITIs were strongly correlated with the scaling exponents of the stimuli, showing that the long-term structure of the participants' taps scaled with the long-term structure of the stimuli. Surprisingly, the performance of the musicians was not significantly better than that of the non-musicians. Our results imply that humans are able to readily adapt (rather than simply react) to the overall statistical structure of temporally fluctuating stimuli, regardless of musical skill. (shrink)

From one of the most influential scientists of our time, a dazzling exploration of the hidden laws that govern the life cycle of everything from plants and animals to the cities we live in. The former head of the Sante Fe Institute, visionary physicist Geoffrey West is a pioneer in the field of complexity science, the science of emergent systems and networks. The term "complexity" can be misleading, however, because what makes West's discoveries so beautiful is that he has found (...) an underlying simplicity that unites the seemingly complex and diverse phenomena of living systems, including our bodies, our cities and our businesses. Fascinated by issues of aging and mortality, West applied the rigor of a physicist to the biological question of why we live as long as we do and no longer. The result was astonishing, and changed science, creating a new understanding of energy use and metabolism: West found that despite the riotous diversity in the sizes of mammals, they are all, to a large degree, scaled versions of each other. If you know the size of a mammal, you can use scaling laws to learn everything from how much food it eats per day, what its heart-rate is, how long it will take to mature, its lifespan, and so on. Furthermore, the efficiency of the mammal's circulatory systems scales up precisely based on weight: if you compare a mouse, a human and an elephant on a logarithmic graph, you find with every doubling of average weight, a species gets 25% more efficient--and lives 25% longer. This speaks to everything from how long we can expect to live to how many hours of sleep we need. Fundamentally, he has proven, the issue has to do with the fractal geometry of the networks that supply energy and remove waste from the organism's body. (shrink)

Theterm, fractal, coined by Benoit B. Mandelbrot, describes a shape or pattern within a greater pattern of which it is a scaling piece identical to the greater pattern and in which are reproduced an infinite number of parts or fragments which are also identical to it, thus, identical to the whole at all scales. In this paper, the author describes Hindu cosmology as it is replicated in the elements of the Bharata Natyam, drawing the analogy to fractal (...) patterning. (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)

Habitat fragmentation produces isolated patches characterized by increased edge effects from an originally continuous habitat. The shapes of these patches often show a high degree of irregularity: their shapes deviate significantly from regular geometrical shapes such as rectangular and elliptical ones. In fractal theory, the geometry of patches created by a common landscape transformation process should be statistically similar, i.e. their fractal dimensions and their form factors should be equal. In this paper, we analyze 49 woodlot fragments (Pinus (...) sylvestris L.) in the Belgian Kempen region to study the direct relationship between a transformation process and the concomitant patch geometry. Although the fractal dimension of the woodlots is scattered (i.e. they are not statistically similar), the perimeter-area relation of the fragments is characterized by a single, ‘dimension-like’ exponent. This exponent suggests a certain shape homogeneity among the patches, which is confirmed by the absence of hierarchical levels associated with sharp increases of the fractal dimension at scale transitions. The interaction of different natural (soil factor, vegetation type) and anthropogenic (afforestation, urbanization) processes during patch development is assumed to have generated this feature. Comparison of the area and perimeter fractal dimension with an ecological index for habitat quality, the interior-to-edge ratio, shows that the fractal dimension is suitable for predicting interior habitat presence, which is more likely for patches with smooth perimeters and compact areas. The ratio of the area to the perimeter fractal dimension confirms this observation, with high values for high interior-to-edge ratios, characteristic for regularly shaped patches. (shrink)

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)

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)

This NATO Advanced Study Institute centered on large-scale molecular systems: Quantum mechanics, although providing a general framework for the description of matter, is not easily applicable to many concrete systems of interest; classical statistical methods, on the other hand, allow only a partial picture of the behaviour of large systems. The aim of the ASI was to present both aspects of the subject matter and to foster interaction between the scientists working in these important areas of theoretical physics and theoretical (...) chemistry. The quantum-mechanical part was mostly based on the operator-algebraic formulation of quantum mechanics and comprised quantum statistics of infinite systems with special em phasis on macroscopic observables, equilibrium conditions, irreversibility on the one hand, symmetry breaking for molecules in the radiation field and macroscopic quantum phenomena in the theory of superconductivity (BCS-theory) on the other hand. In addition, phase-space methods for many-body systems were also presented. Statistical physics was the main topic in the other lectures of the School; much emphasis was put on the statistical features of macros copic ("large") systems, the lectures dealt with mass and energy transport im polymers, in gels and in microemulsions, with aggregation and growth phenomena, with relaxation in complex, correlated systems, with conduction and optical properties of polymers, and with the means of describing disordered systems, above all fractals and related hierarchical models. (shrink)

Different summarized shape indices, like mean shape index (MSI) and area weighted mean shape index (AWMSI) can change over multiple size scales. This variation is important to describe scale heterogeneity of landscapes, but the exact mathematical form of the dependence is rarely known. In this paper, the use of fractal geometry (by the perimeter and area Hausdorff dimensions) made us able to describe the scale dependence of these indices. Moreover, we showed how fractal dimensions can be deducted from (...) existing MSI and AWMSI data. In this way, the equality of a multiscale tabulated MSI and AWMSI dataset and two scale-invariant fractal dimensions has been demonstrated. (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)

Human neural and behavioral activities have been reported to exhibit fractal dynamics known as 1/f noise, which is more aptly named 1/f scaling. Some argue that 1/f scaling is a general and pervasive property of the dynamical substrate from which cognitive functions are formed. Others argue that it is an idiosyncratic property of domain‐specific processes. An experiment was conducted to investigate whether 1/f scaling pervades the intrinsic fluctuations of a spoken word. Ten participants each repeated the (...) word bucket over 1,000 times, and fluctuations in acoustic measurements across repetitions generally followed the 1/f scaling relation, including numerous parallel yet distinct series of 1/f fluctuations. On the basis of work showing that 1/f scaling is a universal earmark of metastability, it is proposed that the observed pervasiveness of 1/f fluctuations in speech reflects the fact that cognitive functions are formed as metastable patterns of activity in brain, body, and environment. (shrink)

We have demonstrated, using the Cantor dust method, that the statistical distribution of appearance and disappearance of rodents species (Arvicolid rodent radiation in Europe) follows power laws strengthening the evidence for a fractal structure set. Self-similar laws have been used as model for the description of a huge number of biological systems. With Nottale we have shown that log-periodic behaviors of acceleration or deceleration can be applied to branching macroevolution, to the time sequences of major evolutionary leaps (global life (...) tree, sauropod and theropod dinosaurs postural structures, North American fossil equids, rodents, primates and echinoderms clades and human ontogeny). The Scale-Relativity Theory has others biological applications from linear with fractal behavior to non-linear and from classical mechanics to quantum mechanics. (shrink)

It is difficult to watch wild animals while they move, so often biologists analyse characteristics of animal movement paths. One common path characteristic used is tortuousity, measured using the fractal dimension (D). The typical method for estimating fractal D, the divider method, is biased and imprecise. The bias occurs because the path length is truncated. I present a method for minimising the truncation error. The imprecision occurs because sometimes the divider steps land inside the bends of curves, and (...) sometimes they miss the curves. I present three methods for minimising this variation and test the methods with simulated correlated random walks. The traditional divider method significantly overestimates fractal D when paths are short and the range of spatial scales is narrow. The best method to overcome these problems consists of walking the dividers forwards and backwards along the path, and then estimating the path length remaining at the end of the last divider step. (shrink)

This paper shows how the republican model of Cicero has been transmitted fragmentarily, through the Italian civic humanist tradition (Maquiavelo), the English republican humanism of XVI, XVII and XVIII centuries, and the republicanism of the American patriots, ("neo-republicanism"). The proposals of Pettit and Brugger are analyzed, and a great variety of positions that some consider "republican" are summarily reckoned. Finally, it is maintained that the classic republican model is present in a very fragmented way in contemporary political theories, for these (...) theories are incapable to accept some strong anthropological, ethical and metaphysical theses. Cicero's model of republicanism appears to us like in a large scale copy or replica, precisely in the political and legal reality of the contemporary world, in its practices and institutions, and in the political function of its theoretical reflections. (shrink)

We present a model for genome evolution, comprising biologically plausible events such as transpositions inside the genome and insertions of exogenous sequences. This model attempts to formulate a minimal proposition accounting for key statistical properties of genomes, avoiding, as far as possible, unsupportable hypotheses for the remote evolutionary past. The statistical properties that are observed in genomic sequences and are reproduced by the proposed model are: (i) deviations from randomness at different length scales, measured by suitable algorithms, (ii) a special (...) form of size distribution (power law distribution) characterising different levels of genome organisation in the non‐coding, and (iii) extensive resemblance in the alternation of coding and non‐coding regions at several length scales (self‐similarity) in long genomic sequences of higher eukaryotes. BioEssays 23:647–656, 2001. © 2001 John Wiley & Sons, Inc. (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)

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)

Fractals are built from patterns generated from immense complexity within the resonant frequencies that connect and tune the universe. Play of such frequencies would result in the exchange of energy and coupling of informational systems at various levels and scales. The present essay serves as a small ride into life’s association with such phenomenon. At a fundamental level communication happens via process called ‘resonance’, and this in turn manifests at a physical level as self-replicating and self-resonating patterns called ‘fractals.’ This (...) could be the reason why at a physical level every structure carries this fractal imprint nature, making it the cosmic signature. The fractal patterns popping out in the natural world surrounding us could be thought of as frozen energy or resonant life patterns. Thus, we hypothesize life could have emerged or appeared as a ‘fracto-resonant’ phenomenon, resulting from the play of interference between material and non-material aspects. In this regard, we propose frequencies or vibrations to be more fundamental to life and call for scientific studies that aim at understanding the effect of various frequencies and vibrations on life forms and consciousness. (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)

Field propagation on fractal structures can generate a large scale symmetric space-time geometry. The significance of this fact and the nature of the resulting space-time are discussed.“Each contained all the others, but in this totality each was confused and comingled with all the others without order and system.”—Haïm Vital, 1543–1620 (Kabbalist of Safed); English translation taken from “Sabbatai Sevi” by G. Scholem (Routledge and Kegan Paul, London, 1973), p. 36.

This authored monograph introduces a genuinely theoretical approach to biology. Starting point is the investigation of empirical biological scaling including their variability, which is found in the literature, e.g. allometric relationships, fractals, etc. The book then analyzes two different aspects of biological time: first, a supplementary temporal dimension to accommodate proper biological rhythms; secondly, the concepts of protension and retention as a means of local organization of time in living organisms. Moreover, the book investigates the role of symmetry in (...) biology, in view of its ubiquitous importance in physics. In relation with the notion of extended critical transitions, the book proposes that organisms and their evolution can be characterized by continued symmetry changes, which accounts for the irreducibility of their historicity and variability. The authors also introduce the concept of anti-entropy as a measure for the potential of variability, being equally understood as alterations in symmetry. By this, the book provides a mathematical account of Gould's analysis of phenotypic complexity with respect to biological evolution. The target audience primarily comprises researchers interested in new theoretical approaches to biology, from physical, biological or philosophical backgrounds, but the book may also be beneficial for graduate students who want to enter this field. (shrink)

Contemporary architecture is increasingly grounded in science and mathematics. Architectural discourse has shifted radically from the sometimes disorienting Derridean deconstruction, to engaging scientific terms such as fractals, chaos, complexity, nonlinearity, and evolving systems. That's where the architectural action is -- at least for cutting-edge architects and thinkers -- and every practicing architect and student needs to become conversant with these terms and know what they mean. Unfortunately, the vast majority of architecture faculty are unprepared to explain them to students, not (...) having had a scientific education themselves. Here is an architecture book by an architect/scientist, just in time to help architects in the new millennium. Alexander discusses many of the scientific terms arising in cutting-edge architecture, and explains them to those who don't have scientific training or advanced mathematical knowledge. We find discussions of the evolution of forms; the importance of process in design; iteration; genetic algorithms; sequences of transformations; different levels of scale (i.e. fractals); etc. They are explained here by an architect who is also a scientist, because he wants to change the way architects think and build. Alexander is not merely popularizing other scientists' results and making them accessible to architects: he is in fact presenting new and original scientific work that ties many of these concepts together in a way that will be useful to architects. (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.

Resumen: Este artículo sostiene que la regla en el mundo social es el cambio, en todas las escalas de tiempo, sin ciclos ni periodicidades. Por consiguiente, el tema que emerge inmediatamente es la irregularidad del mundo. Si esto es cierto, deben ser posibles unas ciencias sociales irregulares. El mejor antecedente para una idea semejante se encuentra en la comprensión del propio Mandelbrot acerca de los fractales y multifractales. Las ciencias sociales tratan radicalmente, de fenómenos irrepetibles, singulares. Estos han sido llamados (...) como eventos raros. De esta suerte, una nueva epistemología emerge y es posible. Al final se muestra que existen nexos fuertes entre las ciencias sociales con la biología y la ecología. Pero en ese punto, el texto termina abierto.: This paper claims that change is the rule in the social world, in all scales of time, without cycles or periodic dynamics. Hereafter, the topic that immediately arises is the irregularity of the world. If this is true, then irregular social sciences are to be possible. The best antecedent of such an idea is to be found in Mandelbrot’s own understanding of fractals and multifractals. Thus, the social sciences radically deal with phenomena that are in no way repeated, for they are singular. Such events have been called as rare events. In thus tenure, a brand-new epistemology arises and is possible. At the end, some connections between the social sciences and biology and ecology are depicted. That, however, is where this text ends and remains open. (shrink)

A physiological function can be described as a cycle based on a cusp bifurcation set in catastrophe theory. This cycle involves four phases that are successively developed along a functional potential, which is used to perform a given physiological act. The work we present is firstly based on a detailed study of the global function of vision, which covers a vast field extending from the molecular to cerebral scale. We then present other examples of generalised functions by expanding the frame (...) of reference, from the scale of an organ to the scale of a whole organism with predation function, and to the scale of a social group with crisis management. We observed that the criteria remain the same, whether the function is considered on the scale of a cell membrane or a group of individuals organised into a cohort. Moreover, a so-called generalised function can be broken down into simpler sub-functions, each phase of the initial function containing the physiological act of each sub-function. It seems thus that a fractal extension may characterise the four-cusp spiral. This spiral is increasingly large as the types of sub-functions are multiplied. In functions relative to sociological science, such as crisis management, which are not natural but built and designed by humans, close attention must be paid to following the rules of these generalised biological functions. (shrink)

B a c k g r o u n d. Considering a scientific truth as a process is connected with the understanding a concrete truth as unity of absolute and relative moments of such process. Beginning by Hegel, truth was regarded as linear process with final point of its development. It was absolute truth, as return of absolute idea to itself in absolute spirit by Hegel. It was the third world by Popper as the world of objective truth. Ukrainian philosopher (...) Pavlo Kopnin opened development of truth for future, eliminating from it the final point in his materialistic interpretation of the truth as a process. However, such process was still regarded as linear process. It was natural for the stage of linear science. As I have already wrote (Dobronravova, 2017), modern stage of nonlinear science actualizes the considering of a scientific truth as nonlinear process. In situation of many variants of nonlinear dynamics the understanding of concrete truth needs to be updated. Such updating is the goal of the article. M e t h o d s. Dialectic method in addition to scientific realism is the most natural approach to research the modern nonlinear science. Methodologic conception of genetic constructivism by V. Stepin is foundation to consider the relations between theoretical and empirical levels of nonlinear knowledge. Criticism of correspondent conception of truth in internal realism by H.Putnam is initiative position in looking for right epistemolology of nonlinear science. Concrete truth as nonlinear process means the description of real nonlinear dynamics with knowledge about a choice, made by a self-organizing system between alternatives in bifurcation point. Nonlinear theories reconstruct few options of further development for nonlinear system. To explain a real situation in certain moment of such development means to describe the real choices by system in points of branching the possibilities. It means that nonlinear science becomes historical one that describes irreversible change of events. Methodologically it means the restriction for claim to repeat the results of empirical checking the predictions of theory, because of choice by chance in bifurcation points. This claim can work for nonlinear medium if different options can be realized in it simultaneously (like Benar's cells in layer of heated liquid or different parties in democratic societies). Otherwise things are going in the situations of historical kind, where the irreversible choice between alternatives has place (like historical choice between right-hand and left-hand traffic in different countries). Repetitions in empirical checking the predicted variants are not possible in principle because of random nature of choice in bifurcation points. R e s u l t s. Non-linear physical theories are descriptive, just like biological, geological and geographic theories. So arrogant condemnation of such theories by physicists and philosophers of science who took physics as a sample in many previous years founded on misunderstanding the specificity of different kinds of theories and their objects. Logical structure of explanation and prediction are not the same in non-linear theories. Non-linear theory can predict a set of possibilities but not the realization of certain one in certain moment. Concrete truth can be justified if human intervention provides the realization of special condition to choose selected variant. C o n c l u s i o n s. We have to understand that such task is more complicated, if we take into account the quantitative way to solve the nonlinear equations. The chain of iterations in approximate solution of such equations can rather give computer simulation of non-linear dynamics. Exact prediction with iteration formula of each next step of unfolding non-linear dynamics, does not guarantee the long scale prediction of complex nonlinear system state. It does not mean that knowledge we got about nonlinear phenomena are not useful for human practice. Thus, the change of dimension in fractal structures of "noise" in cardiograms lets to admit the first signs of heart illness and to cure heart in time. Meteorologists can warn pilots about oncoming storm, defining speed of rising flows in atmosphere by fractal dimension of pictures on the screen of radar. Those are the predictions in nonlinear science. Are they the proofs of concrete truth? Perhaps, yes, they are if we recall old formulation about practice as criteria of truth. (shrink)

In Older Adults (OAs), Electroencephalogram (EEG) slowing in frontal lobes and a diminished muscle atonia during Rapid Eye Movement sleep (REM) have each been effective tracers of Mild Cognitive Impairment (MCI), but this relationship remains to be explored by non-linear analysis. Likewise, data provided by EEG, EMG (Electromyogram) and EOG (Electrooculogram)—the three required sleep indicators—during the transition from REM to Non-REM (NREM) sleep have not been related jointly to MCI. Therefore, the main aim of the study was to explore, with (...) results for Detrended Fluctuation Analysis (DFA) and multichannel DFA (mDFA), the Color of Noise (CN) at the NREM to REM transition in OAs with MCI vs. subjects with good performances. The comparisons for the transition from NREM to REM were made for each group at each cerebral area, taking bilateral derivations to evaluate interhemispheric coupling and anteroposterior and posterior networks. In addition, stationarity analysis was carried out to explore if the three markers distinguished between the groups. Neuropsi and the Mini-Mental State Examination (MMSE) were administered, as well as other geriatric tests. One night polysomnography was applied to 6 OAs with MCI (68.1 ± 3) and to 7 subjects without it (CTRL) (64.5 ± 9), and pre-REM and REM epochs were analyzed for each subject. Lower scores for attention, memory and executive funcions and a greater index of arousals during sleep were found for the MCI group. Results confirmed that EOGs constituted significant markers of MCI, increasing the CN for the MCI group in REM sleep. The CN of the EEG from the pre-REM to REM was higher for the MCI group vs. the opposite for the CTRL group at frontotemporal areas. Frontopolar interhemispheric scaling values also followed this trend as well as right anteroposterior networks. EMG Hurst values for both groups were lower than those for EEG and EOG. Stationarity analyses showed differences between stages in frontal areas and right and left EOGs for both groups. These results may demonstrate the breakdown of fractality of areas especially involved in executive functioning and the way weak stationarity analyses may help to distinguish between sleep stages in OAs. (shrink)

Entropy is one of the physical bases for the fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. Using the fractal dimension, we can describe urban growth and form and characterize spatial complexity. A number of fractal models and measurements have been proposed for urban studies. However, the precondition for fractal dimension application is to find scaling relations in cities. In the absence of the scaling property, we can make (...) use of the entropy function and measurements. This paper is devoted to researching how to describe urban growth by using spatial entropy. By analogy with fractal dimension growth models of cities, a pair of entropy increase models can be derived, and a set of entropy-based measurements can be constructed to describe urban growing process and patterns. First, logistic function and Boltzmann equation are utilized to model the entropy increase curves of urban growth. Second, a series of indexes based on spatial entropy are used to characterize urban form. Furthermore, multifractal dimension spectra are generalized to spatial entropy spectra. Conclusions are drawn as follows. Entropy and fractal dimension have both intersection and different spheres of application to urban research. Thus, for a given spatial measurement scale, fractal dimension can often be replaced by spatial entropy for simplicity. The models and measurements presented in this work are significant for integrating entropy and fractal dimension into the same framework of urban spatial analysis and understanding spatial complexity of cities. (shrink)

ISBN 978-5-86007-556-6. (in Russian). -/- In the book we can find the analysis of some closely related problems – of the origin and essence of life, the universal world process and the global evolution. Examination of fractal nature of carriers through the distribution of terrestrial and space objects on the steps of scale staircase, depending on the masses and sizes, shows an appropriate relationship with the masses and sizes of live organisms. One of the conclusions is the complementarity of (...) living and nonliving carriers in universe, and the main difference between a living from nonliving matter is an independent source of ordering inherent in living forms and managing all of its reactions. Tables 9. Fig. 11. Ref. 60 titles. (shrink)

From the theoretical discussions, transdisciplinarity starts to have practical consequences in the development of programs that include consortia of universities, bringing together a large variety of professionnals who set ambitious goals, such as the Human Genome Project in the past decade, and also the Human Brain Project for this decade. We intend to present an approach in the spirit of the new paradigms of knowledge in the Human Brain Project generous program started earlier this year in Europe. A possible transdisciplinary (...) approach on brain functions and structure is to bring a valuable, significant and innovative, unconventional contribution to the theory of multi-scale topics of the HBP project. More precisely, we intend to develop the subproject Mathematical and Theoretical Foundations of Brain Research within the HBP project. Our approach aims at exploring brain function from the perspective of the theories which influenced the last decade researches in Physics and Mathematics, such as the fractal theory, chaos and the dynamics of the nonlinear systems, in order to formulate new theories regarding brain mechanisms. We bring together models and new theories based on a principled approach to nonlinear reality. We wish to develop a new paradigm for assessing brain function, the theory of complex systems, which requires a revolutionary attitude, by rethinking how brain works and it is biologically structured. By this approach, we intend to study not only the corpuscular, but also the wave part of the matter. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Extra Ear:Ear on the Arm BlenderStelarc Click for larger view View full resolutionFigure 1.Blender. Teknikunst—Meat Market, Melbourne 2005. Photograph: Stelarc. Collaborator Nina Sellars stands with the Blender during an installation photograph. Text credit: K. Conden and A. Douglas. Click for larger view View full resolutionFigure 2.Blender (3D Model). Teknikunst—Meat Market, Melbourne 2005. Image: Adam Fiannaca. The installation itself stands at just over 1.6 meters high and is anthropomorphic in (...) scale and structure. Text credit: K. Conden and A. Douglas. Click for larger view View full resolutionFigure 3.Blender. Teknikunst—Meat Market, Melbourne 2005. Photograph: Stelarc. Every few minutes the Blender automatically circulates or "blends" its contents via a system of compressed air pumps and a pneumatic actuator. Text credit: K. Conden and A. Douglas.[End Page 117] Click for larger view View full resolutionFigure 4.Ear Scaffold. Los Angeles, Melbourne 2006. Photographer: Nina Sellars. The preoperative scaffolding that was surgically placed below the skin's surface of performance artist Stelarc. Text credit: R. Ferro. Click for larger view View full resolutionFigure 5.Blender (Biomaterial). Teknikunst—Meat Market, Melbourne 2005. Photograph: Cameron Jones. Both artists, Stelarc and Nina Sellars, undertook liposuction operations specifically for the purpose of this new work and have succeeded in securing the sanitized isolation and, most importantly, the legal ownership of the remnants of the procedures. Text credit: K. Conden and A. Douglas. Click for larger view View full resolutionFigure 6.Hole Hooks Forceps. As a guest at Cornell University's conference "Digital Bodies" in 2001, Stelarc spoke of his desire to implant an ear that could pick up sound. His plans become a reality in the photograph taken during surgery. Text credit: R. Ferro. Click for larger view View full resolutionFigure 7.Extra Ear: Ear on the Arm. Los Angeles, Melbourne 2006. Photographer: Nina Sellars. Stelarc's future plans are to implant Bluetooth technology into the Ear on the Arm in a subsequent surgery so that the ear will pick up sound which will be transmitted via the Internet. Text credit: R. Ferro. Click for larger view View full resolutionFigure 8.Blender (Sterile Hood). Teknikunst—Meat Market, Melbourne 2005. Photograph: Stelarc. The biomaterials are now housed within the Blender's industrial casing, on exhibition at the Meat Market Gallery B in North Melbourne until August 18. Text credit: K. Conden and A. Douglas.[End Page 118]Stelarc- Biographical NotesStelarc is an Australian artist who has performed extensively in Japan, Europe, and the USA—including new music, dance festivals, and experimental theater. He has used medical instruments, prosthetics, robotics, Virtual Reality systems, and the Internet to explore alternate, intimate, and involuntary interfaces with the body. He has performed with a THIRD HAND, a VIRTUAL ARM, a VIRTUAL BODY and a STOMACH SCULPTURE. He has acoustically and visually probed the body—having amplified brainwaves, blood-flow and muscle signals and filmed the inside of his lungs, stomach, and colon, approximately two meters of internal space. He has done twenty-five body SUSPENSIONS with insertions into the skin, in different positions and varying situations in private gallery spaces and in remote locations.For FRACTAL FLESH, as part of Telepolis in 1995, he developed a touch-screen interfaced Muscle Stimulation System, enabling remote access, actuation, and choreography of the body. Performances such as PING BODY and PARASITE (1996, 1997) probe notions of telematic scaling and the engineering of external, extended, and virtual nervous systems for the body using the Internet. In 1998 for Kampnagel, he completed EXOSKELETON—a pneumatically powered six-legged walking machine actuated by arm gestures. During 2000, he completed an EXTENDED ARM—a manipulator with eleven degrees-of-freedom that extends his arm to primate proportions and a MOTION PROSTHESIS—an intelligent, compliant servo-mechanism that enables the performance of precise, repetitive, and accelerated prompting or programming of the arms in real time. In 2002, with the collaboration of the Evolutionary and Adaptive Systems Group, COGs, University of Sussex, and TNTU, the HEXAPOD robot prototype was developed. The six-legged MUSCLE MACHINE was constructed with the assistance of The Nottingham Trent University Engineering team, using fluidic rubber muscle actuators. The PROSTHETIC... (shrink)

Our purpose in this article is to identify and suggest resolution for two core problematics of grounded theory. First, while grounded theory provides transparency to one part of the conceptualization process, where codes emerge directly from the data, it provides no such systematic or transparent way for gaining insight into the conceptual relationships between discovered codes. Producing a grounded theory depends not only on the definition of conceptual pieces, but the delineation of a relationship between at least two of those (...) pieces. Second, the conceptualization process of grounded theory is done in hierarchical fashion, where individual codes emerge from the data but then are used to generate insight into more general concepts and thematic statements. But various works on grounded theory have failed to provide any systematic way of using data specific levels of scale (the codes) to gain insight into more macro levels of scale (concepts and themes). We offer fractal concept analysis as a means of resolving both of these issues. By using a logic structure generator, fractal concept analysis delineates self-similar conceptual frameworks at various levels of abstraction, yielding a method for linking concepts together within and between levels of scale encountered in the grounded theory coding and categorization process. We conclude that this fractal analytic technique can bolster the aims of grounded theory as a formalized and systematic process for generating theory from empirical data. (shrink)

The design of the bronchial tree has largely been proposed as a model of optimal design from a physical-functional perspective. However, the distributive function of the airway may be more related to a geometrical than a physical problem. The bronchial tree must distribute a three dimensional volume of inspired air on a two dimensional alveolar surface, included in a limited volume. It is thus valid to ask whether an optimal bronchial tree from a physical perspective is also optimum from a (...) geometrical point of view. In this paper we generate a simple geometric model for the branching pattern of the bronchial tree, deducing relationships that permit estimation of the departures from the geometrical optimum of each bifurcation. We also, for comparative purposes, estimate the departures from the physical optimum. From the geometrical assumptions: i) a symmetrical dichotomic fractal design, ii) with minimum volume and iii) maximum dispersion of the terminal points; and several simulations we suggest that the optimality is characterized by a bifurcation angle Θ ∼ 60° and a length reduction scale γ = (1/2)1/3 = 0.7937. We propose distances from the physical and geometrical optimality defined as Euclidean distances from the expected optima. We show how the advanced relationships and the distances can be used to estimate departures from the optimality in bronchographs of four species. We found lower physical and geometrical departures in the distal zone than those of the proximal zones, as well as lower physical than geometrical departures from optimality. (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 interaction-dominant approach to perception and action, originally formulated in the mid-1990s, has matured and gained remarkable momentum as an entailment of the dynamical hypotheses proposed at that time. This framework seeks to explain the fluid and intricate interplay of causality spanning the entire organism by integrating high-dimensional details with low-dimensional constraints across various scales of behavior. Both Chemero (2024) and Wallot et al. (2024) have skillfully explored the theoretical implications and methodological challenges this perspective introduces. We echo Chemero's (2024) (...) and Wallot et al.’s (2024) focus on multifractality, while also underscoring new efforts to model the synergetic relationships and cascading dynamics inherent in this interaction-dominant approach. (shrink)