Is emergence connected to nature's transition between fractal regimes at different size scales?

Is emergence connected to nature's transition between fractal regimes at different size scales?

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A fractal algorithm like Mandelbrot is self-similar in all size scales. This is not the case in nature. A tree is fractal in the sense that each branch is similar to the tree as a whole. But that is only true at a certain range of scales, about 0.1 - 10 meter. The forest does not look like one tree, nor does the texture at millimeter scale or the cellular structure at microscopic scale. At those scales the tree may or not be fractal, but at least it is not fractal in the same way as on the 1 meter size. Nature breaks the fractal regime after only a couple or so self-similar scales.

Are these transitions between fractal regimes studied by biology?

Are there any ideas around about how different fractal regimes might be connected with emergent phenomena? At very small scales there exists no tree, but only elementary quantum particles/waves. Macromolecules and cells and the tree and the forest each emerge as a phenomena on different size scales. I wonder if this emergence is matched by the different fractal regimes at those scales?

The Major Transitions of Life from a Network Perspective

Many attempts have been made to understand the origin of life and biological complexity both at the experimental and theoretical levels but neither is fully explained. In an influential work, Maynard Smith and Szathmáry (1995) argued that the majority of the increase in complexity is not gradual, but it is associated with a few so-called major transitions along the way of the evolution of life. For each major transition, they identified specific mechanisms that could account for the change in complexity related to information transmission across generations. In this work, I propose that the sudden and unexpected improvement in the functionality of an organism that followed a major transition was enabled by a phase transition in the network structure associated with that function. The increase in complexity following a major transition is therefore directly linked to the emergence of a novel structure𠄿unction relation which altered the course of evolution. As a consequence, emergent phenomena arising from these network phase transitions can serve as a common organizing principle for understanding the major transitions. As specific examples, I analyze the emergence of life, the emergence of the genetic apparatus, the rise of the eukaryotic cells, the evolution of movement and mechanosensitivity, and the emergence of consciousness. Finally, I discuss the implications of network associated phase transitions to issues that bear relevance to the history, the immediate present and perhaps the future, of life.

1. Introduction

Despite many decades of 'war on cancer' and success in treatment of several cancers, the war is far from being victorious. Finding specific cancer genes was the major direction of the attack for many decades. However, a sharp increase in the complexity and variability of genetic signatures of activated/mutated genes recently observed even in the same cancers at different malignant stages has considerably slowed the advancement in this direction [1]. Thus, stronger than ever, there is a need for new conceptual paradigms about the nature of cancer.

When talking about the nature of cancer, it is plausible to consider two different views: cancer is a deterministic switch (not excluding high heterogeneity typical for cancer [2]) no matter how it is induced, (biochemically, physically, or genetically) or cancer is a chaotic imbalance of biochemical reactions, a sort of side effect of cellular complexity, which was overseen by evolution. In this work we show some evidence that the picture seems to be more complicated. To show it, we study emergence of possible fractal geometry on the cell surface at different stages of progression towards cancer. Fractal [3, 4] is one of the intriguing patterns in nature observed as 'self-similar' irregular curves or shapes that repeat their pattern when zoomed in or out. As was found, fractal patterns are formed under far-from-equilibrium conditions [5], or emerge from chaos [6]. Examples of fractal patterns range from the large-scale structure of the Universe [7] to the geometry of some biological tissues [8].

The idea of a possible connection between cancer and fractals has been suggested in a number of works [9–11]. It was proposed that imbalance of various biochemical reactions, which is typically associated with cancer, could result in chaos, and the subsequent appearance of fractal geometry. It was shown that tumor vasculature and antiangiogenesis demonstrated explicit fractal behavior [10, 12]. Cancer-specific fractal behavior of tumors at the macroscale was recently found when analyzing the tumor perimeters [8, 13]. Similar analysis at the micro- and submicron scales done in both neoplastic and normal cells demonstrated that fractal dimensions can be different for cancer and normal cells [14–18]. In particular, the analysis of fractal dimension of the adhesion maps imaged with atomic force microscopy (AFM) showed a strong segregation between malignant and normal human cervical epithelial cells [18]. However, nobody has systematically studied how accurate the approximation of the cell surface as fractal was in those works (fractal dimension can be assigned to any surface, not necessary true fractals). In other words, the study of the emergence of fractal geometry in itself on the cell surface has not been studied.

Here we investigate the emergence of fractal geometry on the surface of human cervical epithelial cells during their progression towards cancer: from normal, through immortal (premalignant), to cancerous stages. In addition, we carefully recorded the number of population doubling for all cells starting from their extraction from tissue (all cells were primary cells extracted from human normal or tumour tissues premalignant cells were immortalized normal cells). This is done to monitor progression towards malignancy within each cell group. The cervical cell model was chosen because of the existence of a well-developed model for cell progression towards cancer, and due to a practical need: the improvement in early detection of cancer, which is based on the imaging of individual cells, can substantially decrease morbidity and mortality [19–21].

While cancer development in vivo can be different from the development in vitro, the use of the cell model allows us to control the cell phenotype, which is impractical when doing measurements in vivo. Here we assume that the properties of 'normality', immortality, and malignancy can be well-defined in both in vitro and in vivo (though this assumption may seem to be well adopted these days, it has yet to be proven in the future). To exclude a coincidental result, we use six different cell strains and twelve cell lines.

As a result of this work, we show evidence that the simple fractal geometry on the cell surface (and conceivably, chaos) is reached only at a particular stage when premalignant (immortal) cells are transformed into cancerous. Before and after that, the cells demonstrate a substantial deviation from simple fractal (cannot be treated as fractals). Specifically, we observed a strong correlation between multi-fractality, a parameter we introduced to characterize the deviation from fractal, and the stage of progression to cancer. Multi-fractality is zero (simple or ideal fractal) at the stage of when immortal cells turn into cancerous (between immortal cells of large number of divisions and cancer cells of small number of divisions). The multi-fractality of cancer cells deviates from zero with the increase of the number of divisions of cancer cells. We can speculate that these results vote in favour of the switch to cancer as a chaotic imbalance of biochemical reaction shaping the cell surface. However, further malignant development recovers the balance (though different from the one of normal cells), and votes in favour of deterministic cancer development (at least the part responsible for formation of the cell surface).


Life in the Antarctic makes a key contribution to our knowledge of the global biosphere due to its uniqueness and connectivity to adjacent ecosystems. The observed impacts and projected risks of rapid climate change for Antarctic biotas (Rogers et al., 2020 ) are a function of the severity of the hazards, the exposure and vulnerability of the biotas to stresses (Convey & Peck, 2019 ), and their capacity to adapt or escape. Research strategies are needed to assess further the uniqueness and resilience of Antarctic biotas to inform decision-makers and conservationists on regional and global priorities (Meredith et al., 2019 ).

The findings in this synthesis focus on studies published since 2010, building upon research carried out since the beginning of the 20th century. This research included basic biological approaches (e.g. taxonomy), targeted studies on key species such as Antarctic krill Euphausia superba (Miller & Hampton, 1989 ), and ecological studies of biogeochemical cycles, including fluxes of energy to apex predators and physiological adaptations. For a broad coverage of historical results see e.g. Laws ( 1984 ), Smith ( 1990 ), Hempel ( 1994 ), and Knox ( 2006 ). Notable research into Antarctic life sciences during the past century includes the demonstration of how life, particularly fishes, evolved and adapted physiologically to the ice-cold environment (di Prisco, Maresca & Tota, 1991 ). Since then, the rapid development of biomolecular methods has enabled a variety of advances. New research platforms (e.g. research stations, ships) and novel instrumentation (e.g. satellites, landers, autonomous underwater vehicles, robotic floats and automated observatories) have allowed much-improved investigations of biological developments and environmental changes. While numerical and conceptual models often originated in more-accessible ecosystems, specific analytical tools have also been developed to obtain deeper insights into Antarctic-specific ecological processes. Highly focused studies of Antarctic biotas and their environments have been conducted under international initiatives, such as the Ecology of the Antarctic Sea Ice Zone (EASIZ), Evolution and Biodiversity in the Antarctic (EBA) and additional research initiatives of the Scientific Committee on Antarctic Research (SCAR) and the Scientific Committee on Oceanic Research (SCOR).

In 2010, SCAR launched the Scientific Research Programme ‘Antarctic Thresholds – Ecosystem Resilience and Adaptation’ (AnT-ERA) to facilitate biological process-focused research in marine, freshwater and terrestrial ecosystems facing various stressors. Since then, a vast array of results ranging from molecular to ecosystem levels has been generated. Examples, are assembled in the Antarctic Climate Change and the Environment report and its regular updates to Antarctic Treaty Meetings (Turner et al., 2014 ).

This synthesis aimed to identify the most important climate-dependent findings from the past decade on biological processes in Antarctic ecosystems. These findings are synoptically synthesised into scientific messages, with associated levels of confidence. Where appropriate the findings are assembled independently for the marine, limnetic or terrestrial ecosystem from which they originate, to identify similarities and contrasts across these ecosystems. Results were considered to be ‘most important’ if they (i) were novel and could be clustered into messages with considerable relevance for the scientific community, research and funding strategies, projects and textbooks, or (ii) have relevance for stakeholders, such as: the Intergovernmental Panel on Climate Change (IPCC), the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES), the United Nations Decade of Ocean Science for Sustainable Development, the Antarctic Treaty System with its nature conservation initiatives, the Commission for Environmental Protection (CEP) and the Commission on the Conservation of Antarctic Living Resources (CCAMLR). Stakeholders also include science managers, politicians, journalists, and the general public. Some of the findings reflect questions raised by the 1st Scientific Antarctic Committee on Antarctic Research Antarctic and Southern Ocean Science Horizon Scan, the implementation of which has recently been assessed (Kennicutt et al., 2019 ).


The importance of segregation in the brain is supported by numerous studies (Sporns & Betzel, 2016 Wig, 2017). However, there is a lack of general mechanisms explaining the emergence of brain modularity. In the present study, we propose an explicit mechanism of reshaping local neighborhoods through topological reinforcement that might act as a fundamental principle contributing to the emergence of modules in brain networks. In addition, our work shows that a Hebbian rule acting on an activity-based model may actually be instantiating the same underlying rewiring pattern responsible for the modules creation, that is, the topological reinforcement.

Given accumulated evidence that global network properties can systematically affect the composition of local network structures, such as motifs (Fretter et al., 2012 Reichardt et al., 2011 Vazquez et al., 2004), we propose a complementary bottom-up approach that is acting locally in order to shape global features. Our proposed mechanism is in line with empirical data where “homophily” appears as an essential feature of brain connectivity. At the micro scale, it has been shown that the probability of finding a connection between a pair of neurons is proportional to their number of shared neighbors (Perin, Berger, & Markram, 2011) whereas at the macro scale, the strength of connections between brain regions tends to be the higher the more similar their connectivity profiles are (Goulas, Schaefer, & Margulies, 2015).

Our results show that topological reinforcement reliably and robustly produces modular network architectures over time, accompanied by the small-world property. Additionally, the final modular organization of the networks seems to correspond to groups of nodes in the initial networks that have higher than average connection density. As such, our rewiring mechanism acts as an amplification of these “proto-modules,” similarly to a previously reported effect in weak modular weighted networks evolving under a Hebbian rule based on chaotic maps synchronization (Yuan & Zhou, 2011).

We extended the framework of topological reinforcement by introducing a plausible biological implementation. Our dynamical model choice, the SER model, offers the advantage of capturing essential characteristics of stylized neuronal activity while being more tractable than detailed typical models. This minimalistic excitable network model has a rich history across disciplines and in particular in neuroscience (Anderson & May, 1992 Bak, Chen, & Tang, 1990 Drossel & Schwabl, 1992 Furtado & Copelli, 2006 Kinouchi & Copelli, 2006), where it can capture nontrivial statistical features of brain activity patterns (Haimovici, Tagliazucchi, Balenzuela, & Chialvo, 2013 Messé, Hütt, König, & Hilgetag, 2015). This model has also been used to study the impact of network topology, such as modules, hubs, and cycles, on network activity patterns (Garcia, Lesne, Hilgetag, & Hütt, 2014 Messé et al., 2015 Müller-Linow et al., 2008). A relative-threshold variant (requiring a certain percentage of a node’s neighbors to be active, in order to activate the node) was explored in Hütt, Jain, Hilgetag, and Lesne (2012) and Fretter, Lesne, Hilgetag, and Hütt (2017). The deterministic limit of the model (p → 1, f → 0) has been analyzed in Garcia, Lesne, Hütt, and Hilgetag (2012) and in much detail in (Messé et al., 2018).

In the biological implementation, the topological reinforcement rule was reformulated by using functional connectivity (FC) as a surrogate of TO. These results were consistent with TR, indicating that the biological implementation acted indirectly at the topological level. In other words, the FC served as a proxy of TO, and therefore Hebbian reinforcement led indirectly and ultimately to the topological reinforcement of a modular network organization. The explanation for this finding is based on the fact that, for suitable dynamical regimes and structural architectures, FC is positively correlated with TO in excitable networks (Messé et al., 2018), which is intuitive if one considers that common inputs may promote correlations. Thus, we propose the topological reinforcement principle as an underlying common ground, bridging an activity-based Hebbian model and a purely topological generative model.

Our results are in line with recent theoretical work on the contribution of specific network motifs to higher-order network organization, in which the reinforcement of connections between neurons receiving common inputs led to the formation of self-connected assemblies (Ravid Tannenbaum & Burak, 2016). Hence, our Hebbian plasticity scenario exploited the correspondence between TO and FC as it could be observed with the exploration of different SER parameter constellations. These parameters promote different relations between TO and FC, and we found that such a dependence systematically predicted the emergence (or not) of modular networks.

Previous computational studies have shown that evolutionary algorithms of network connectivity optimizing, for example, functional complexity (defined as balance between segregation and integration) can lead to modular network formation (Sporns, Tononi, & Edelman, 2000). Such findings point to the relevance of modularity as a crucial organization principle underlying complex functional brain processes. Nevertheless, these models do not provide a biologically interpretable and implementable mechanism, since the explicit global optimization function (functional complexity) cannot be directly interpreted as a biological mechanism shaping brain connectivity.

In the sense of biological plausibility, activity-based plasticity models (e.g., based on Hebbian plasticity) constitute a more directly interpretable approach. Previous studies have used a variety of neural activity models ranging from abstract representations, such as chaotic maps (van den Berg & van Leeuwen, 2004) and phase oscillators (Gleiser & Zanette, 2006), to more physiologically realistic models, such as neural masses (Stam, Hillebrand, Wang, & Van Mieghem, 2010) and spiking neuron (Kwok, Jurica, Raffone, & van Leeuwen, 2006) models. In general, Hebbian reinforcement led to the formation of modular architectures, consistent with our results for the excitable model. Interestingly, as a practical biological example beyond the pure theoretical realm, this type of plasticity-guided modular emergence has recently been studied also in real neural activity in zebrafish larvae (Triplett, Avitan, & Goodhill, 2018), pointing to the relevance of the current results. The open question for this type of models concerns the specific underlying topological changes that they promote, since these studies focus on the implementation of the phenomenon (based on the activity) and not on the algorithmic level (the topological dimension) and both levels interact in nontrivial ways. Indeed, some of these models even showed that final topological features (e.g., number of modules) might purely depend on properties of the dynamical model (Yuan & Zhou, 2011). In other words, they did not provide insights about a general mechanism specifying which topological changes might be necessary for the emergence of modular structure. Compared with this group of models, our model is different in that the topological reinforcement principle is agnostic with respect to the specific dynamical regime, and it explicitly addresses the topological changes that take place in the network.

An alternative modeling approach is provided by generative models, where typically a given probability function governs the insertion of links and/or nodes during simulations (Betzel & Bassett, 2017). Recent work has shown that including homophily as a factor to determine connection probability (and after proper data-driven parameter tuning) makes it possible to account for a great deal of functional (Vértes et al., 2012) as well as structural (Betzel et al., 2016) topological features of real large-scale brain networks. Although these studies provide a valuable basis for confirming the importance of TO as an essential feature and reducing the dimensionality of brain connectivity to a few model parameters (Betzel & Bassett, 2017), disentangling the mechanistic nature of the phenomena (e.g., modularity emergence) turns out to be nontrivial, since information about the final state might be explicitly built-in in the generative model. But even more crucially, how the generative function is actually implemented in real systems is out of the scope of this kind of modeling approach. As a complement to this group of models, our contribution offers a concrete scenario in which a generative mechanism can actually be implemented in a biologically more realistic fashion.

In summary, as expected for any modeling approach, a trade-off exists between generative and activity-based models. Phenomenological descriptions and mechanistic explanations complement each other and a gap remains for explaining how they link to each other. Our contribution represents an attempt to address this gap: first, by providing an explicit topological mechanism of module formation (generative mechanism) second, by trying to reconcile such an abstract level of analysis with the biological implementation, by means of an activity-based formulation of the model.

The present results are subject to several methodological considerations. For example, our study did not take into account a geometrical embedding and rather focused on the pure topological contribution of the topological reinforcement. Although we recognize that the brain is a spatially embedded system and that physical constraints, such as wiring-cost, play a fundamental role shaping brain connectivity (Henderson & Robinson, 2013), previous studies have shown that, in addition to them, topological aspects are essential to describe real connectomes (Betzel et al., 2016 Kaiser & Hilgetag, 2006). Thus, we aimed at isolating the topological effect and avoiding the situation in which geometric constraints, such as the distance-dependent probability of connection used in previous studies (Jarman, Trengove, Steur, Tyukin, & van Leeuwen, 2014), introduce already by themselves a clustered connectivity, thus potentially overriding the changes based on the topology itself. Specifically for the case of our model, an initial spatially constrained, distance-dependent connectivity could also create “proto-modules” on which the connectivity would develop.

For sufficiently long simulations, a stationary behavior is observed. However, because of their relative simplicity, the rules tend to disconnect the evolving networks (see Supporting Information Figure S5, Damicelli et al., 2019). This consequence can also be found in previous studies with this type of models, where other modeling choices were made, such as discarding runs with disconnections or explicitly using network size and density that avoid such a scenario (Rubinov, Sporns, van Leeuwen, & Breakspear, 2009 van den Berg & van Leeuwen, 2004). From a practical point of view, we chose a number of rewiring steps that avoids such scenario. We recognize an interesting line for future work taking into account possible counteracting mechanisms that might balance out disconnections and add realism to the model.

Other interesting potential variations of the presented model for future work could include networks with weighted edges where the plasticity rule acts regulating the weights, as well as model settings simulating developmental pruning processes, where the total network density decays over time.

Regarding the plausible biological implementation, we chose a simple abstract model for computational tractability. It would be interesting to compare our framework with more biologically realistic dynamical models, such as networks of spiking neurons.

Electronic supplementary material is available online at

Published by the Royal Society under the terms of the Creative Commons Attribution License, which permits unrestricted use, provided the original author and source are credited.


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Synthesis and characterization of compounds 1 H, 13 C NMR, and HRMS spectra dynamic light scattering and fluorimetric scattering additional data on quantification of kinetics and evolution of particle size by iSCAT characterization of a biphasic reaction between 4 and 2 by ensemble methods contrast to mass calibration (PDF)

Micelles observed at the onset of the nucleation stage of the biphasic reaction between 1.25 mM 1 and 1 equiv 2 (MP4)

Micelles observed in the biphasic reaction between 1.25 mM 1 and 1 equiv 2 near completion point. (MP4)

Micelles observed in the biphasic reaction between 0.5 mM 1 and 5 equiv 2 after 1 hour (MP4)

Vesicles observed in the biphasic reaction between 2.5 mM 4 and 1 equiv 2 after 20 min (MP4)

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The creative part of the Universe are its languages of pure information, Ss-eeds and minds that p. more The creative part of the Universe are its languages of pure information, Ss-eeds and minds that project between scales information without loss of entropy through processes of reproduction.

All languages are creative, reflexive mind mirrors of information about the immanent program of existence and extinction of spacetime and its Universal syntax, common to all languages including mathematics.
All sciences have subjective errors, as huminds use to measure reality their own clocks of space and time and deny vital, organic properties to the Universe
The mind is a still linguistic sentient mapping of the Universe, which acts as a mirror, reducing reality into a smaller scale of space-time and then projecting its image into a ßodywave or territory of order of the physical, biological or social 'mind-point' that 'holds a world in itself'.
The game of mind mirrors thus can be studied objectively through the analysis of the common syntax and semantics of its languages.
Why the laws of the Universe are so simple? In brief: because all is made of 2 ST-ates, Space=still form, information and time=motion, change, which Relativity taught us cannot be distinguished from each other. So we write the mother of all equation: S<=>T. The papers you are going to read are the seed for an encyclopedia of what we shall call ‘ST¡ence’, a more objective analysis of reality than present ‘science’, which is based in the use of anthropomorphic concepts of Space and Time and hyperbolic theories of the human role in the Universe, we summon up in a single word, ‘egocy: ego=idiocy’. While scientists recognize since the Quantum & Relativity r=evolution in Natural Sciences and the attempts to introduce biological concepts in social ones that the main handicap for the advance of stience are the ‘disguised’ a priori postulates born of ‘egocy’, because the Universe, as we know it, is an infinite ‘fractal’ of mental, biased points of view, any attempt to dislodge humanity from its ‘perceived’ central position is counter-intuitive. And so it returns invariably disguised of pretentious ‘new postulates’ that are ‘more of the same’. However ‘st¡ence’ is defined by its objectivity. It would be the same for an alien species while science will be specific of each thinking organism. Can then stience be imposed against the ‘happiness of ego-trips’, ‘wishful thinking’ and ‘reductionist models’ that fit our perceived view? Unlikely because e-motions code our program of survival and defend the ego. For that reason among billions of human beings, a truly stientific=objective view is so rare. The partial precedents of this work in fact can be reduced to a few people, Lao-Tse, Aristotle, Leonardo, Leibniz, Darwin, Einstein, Butler & Spengler in economic and social sciences, none of which was clearly understood, as they left no disciples that evolved further their work.
What are those postulates of disguised anthropomorphism? The most important are our perception of time and space in human terms. We use a single ‘dimension-measure-clock of time’, whose unit, the second corresponds to the human synchronous ‘quantum’ of time-change-motion, (a step of our limbs, a beat of our heart, a glimpse of our Eye & thought). And we use the 3 perpendicular coordinates of our force of perception of space, light with its orthogonal magnetic, electric and c-speed.
Then we equalize all the other clocks and quanta of time to ours, declared ‘lineal, infinite’ and we ‘compress’ all other scales of space into our light-space dimensions. And create with this reduced understanding of the synchronicity & simultaneity of time and space structures grand theories of the Universe, at best biased, often so much that they are ‘not even wrong’.
Yet even if Einstein recognized that ‘Leibniz is right, there are ∞ time clocks in the Universe with different speeds, but if so we have to start physics from scratch’, nobody has done it till those texts, which have zero stats, following the tradition of its forebears.
The second disguised anthropomorphic postulate is ‘language’. We DON’T perceive reality but a part of the total information through mental languages, based in those reduced visual dimensions of space and single ‘time motion’. And so in the next abstract level of language we reduced geometry to the 3 orthogonal ‘Euclidean dimensions of space’, defining ‘points without parts, straight lines and planes without breath’, which do not exist in reality. While as we reduced time causality to a single lineal clock, we developed Aristotelian A->B logic. Both are reductions of the real ‘points’ of the Universe, which have a volume of energy and information, absorbed through a relative infinite number of ‘parallel lines’ that flux into the point (Non-Euclidean points) and grow in size as we come closer to them, revealing inner ‘spacetime scales’. So the geometry of the Universe is more complex. So it is its causality, since there are multiple time clocks of different speeds and sizes, which cause reality, from those ‘∆’ scales. So you are caused by the ∆-¡ cellular scale, your 3 ∆º physiological networks that create you as a whole, and the outer ∆+1 world. While in your own scale, you are made of the 3 topological parts as everything in the Universe: a limb-field of lineal, flat, tubular form – the shortest distance of maximal motion an spherical particle-head, the geometry that stores maximal information and a hyperbolic, hour-glass ßody-wave that connects both, the more complex geometry, sum of the other 2 that can reproduce them.
So just with a closer view of what is the real, ‘extended’ nature of time – infinite clocks – space, infinite scales – geometry (fractal, non-Euclidean) and time (pentalogic with 3 scales and 3 adjacent synchronous parts in each scale, in the human case the second that synchronizes limbs, bodies and heads in physical matter if we adopt the realist Broglie’s view, the field, wave and particle synchronized by its internal clocks), we start to describe a different Universe.
This universe is ‘background independent’, as we are made of topologic, vital spaces whose inner and outer motion are regulated by multiple clocks, whose synchronicities maintain the whole system in a relative, dynamic stability.
The obvious conclusion then, as Lao-Tse, Leibniz and Einstein wanted is a Universe of relational space-time: we are topological, vital spaces, performing cyclical time actions, and so is everything else in the Universe.
But anthropomorphic dogmas again limit this view of reality, since we DON’T perceive directly time=motion and space=form, but the languages that describe its properties, either verbal languages with its Universal grammar that describe spacetime systems with: Names=space forms <= > verbs=time motions or recently since Galileo, mathematical, digital languages that describe those scales of spacetime with social, scalar numbers, algebraic operands fit to study the different type of time-motions and geometric points.
As a result of this interposed perception of space and time with languages of verbal times and spatial names, or scalar numbers, temporal operands and spatial points, the overwhelming majority of humans believe in anthropomorphic ‘creationist’ theories, according to which ‘God and man’ are the only beings that share those 2 languages and God (and often man) creates with the languages. So in all Abrahamic religions god created naming things in Hebrew or Arab while in modern science physicists believe equations create reality, so when they write an equation of black hole evaporation or supersymmetric particles, regardless of the null evidence, they think its must happen. And because Hubble found an equation, V=HoD, eerily similar to ‘God’, we believe in big bang theory. Each of those creationist models are obviously challenged by Stience who reasons that space and time are the a priori substances of reality and the mirror languages that reduce those properties to fit a mental space, simplifications created by the properties of space and time.

Materials and methods

Introduction to spectral analysis

Spectral analysis aims to detect periodic variation in a signal, such as the time series of step lengths or turning angles from a movement trajectory of an animal. For spectral analysis, the time series of movement parameters is transformed from the time domain into the frequency domain (frequency = 1/period of the signal). The signal is decomposed by the Fourier transform into sine and cosine terms (i.e. representing various frequencies) and then partitioned into all frequencies contributing to the variation in the original time series (Boggess & Narcowich 2009 ). The partitioning allows to pinpoint the most relevant frequencies and hence periods, however, no information is provided about when in time these frequencies occur. Moreover, an important assumption of the Fourier transform is a stationary signal, that is, the mean and variance of the signal do not change over the sampling period. This often does not hold for movement time series, where behaviour changes along a trajectory. The wavelet transform can overcome these limitations (Daubechies 1990 ).

Wavelet analysis

The wavelet transform can detect and localize different forms of changes in time series, by scaling and shifting a single mother wavelet function across the time series and quantify the correspondence between them as a wavelet coefficient. Because the wavelet transform uses a finite oscillatory function, it can resolve the temporal location, that is, pinpoint where in the movement signal the correspondence between the signal and the mother wavelet is high, resulting in high values for the associated wavelet coefficients. This is a major distinction to spectral analysis that does not contain information about temporal location. Furthermore, by scaling (i.e. dilating and contracting) the mother wavelet, the wavelet transform allows to zoom into smaller and larger scale variation across the time series and hence to look at variation in the signal at different scales.

The two main types of wavelet transform are the CWT and the DWT. CWT calculates the coefficients at every possible scale, whereas in DWT the shifting and scaling of the mother wavelet function is based on powers of 2 and therefore the signal is partitioned into dyadic blocks. Nevertheless, it is considered to be just as accurate as the CWT (Mallat 1999 Khorrami & Moavenian 2010 ). The scaling process of DWT can be also represented as a decomposition tree, where the original movement time series S is passed through low-pass and high-pass filters, yielding approximation (A) and detail (D) sub-bands. In its basic form, the decomposition is done based on only the lower resolution component (i.e. approximations) and the high-frequency component is not analysed further. However, the power of DWT can be significantly increased by a level by level transformation of both the low- and high-frequency components (Gokhale & Khanduja 2010 ). By retaining the length of the approximation and the detail sub-bands the same as the original signal, this will allow an analysis best matched to the signal (Appendix S1, Supporting Information).

Approximation sub-bands that contain the low-frequency components of the signal maintain the general structure of the movement signal. Conversely, the detail sub-bands contain the higher frequencies, enabling to capture the details of variation in the signal. As an example, the approximation sub-bands should retain periodicity due to migration back and forth between breeding and overwintering sites, whereas detail sub-bands should retain daily movement variation between foraging and resting sites.

Prospective Engineering Applications of Dynamic Transfer Processes Possessing the Self-Organized Fractal Interfaces

General formulation of practically applicable fundamental approach for development of engineering applications in systems with dynamically appearing and disappearing fractal structures is proposed. The approach is illustrated on the low-temperature pyrolysis of butane/propane mixture being pumped via the liquid tin and bismuth alloy preserved at the temperature 200 ± 20°C in the U-shaped test glass. Other prospective engineering applications of the approach are proposed on the base of analysis of selected experiments described in literature.

1. Introduction

It is well known from such classical books as [1] that fractals appear in a big variety of natural phenomena. Important emphasis on analysis involving fractals is put to their self-organized character in such works as [2, 3]. Despite the fact that initially the self-organized dynamics in open systems were considered without special attention to the fractals [4], we would like to note that such basic theory as scale relativity [5] considers the space as a fractal. In the theory [5] the geodesics of elementary particles, which form substances, are considered as having fractal dimensions, which are changing with the scales. Nottale notes in the chapter 2 of his work [5] that the fractal dimension of paths for particles analyzed by Feynman in the quantum scale equals 2.

What might be found regarding the geodesics of elementary particles in the bigger scales?

The obvious answer to this question is the note that there should be a possibility for interaction with motion of energy along these geodesics, as its fractal characteristics may coincide with the fractal characteristics of the self-organized dynamic systems in the bigger scales. In such a case the feedback of this interaction may be found on the both macroscale of a dynamic system with the fractals, and in the quantum scale of elementary particles and structures, which are formed by the particles in this scale.

Such a possibility is really close to the engineering applications on both scales. Exploration of this hypothetical possibility on several engineering examples is an objective of this paper.

2. Approaches to the Systems with Hypothetical Interactions between the Self-Organized Structures on Different Scales

Recent achievements in the experimental researches of the systems, which produce dynamically created and self-organized fractals, allow consideration of such systems as a basis for prospective development of new energy sources. The basic approach for this is in organizing possibilities for energy transfer along the fractal geodesics, which span along several scales, among which one is considered as transmitting energy and the other one as receiving it. If the transmitting scale is the quantum microscale, the structures on this scale may undergo changes, which can be classified as their transmutation or nuclear reactions providing with energy of motion for the self-organized structures in the bigger scale. If the self-organization on this bigger scale involves motion of electric charges, the possibility for direct generation of electricity becomes most prospective possibility regarding the approach for creation of new energy sources. In such a case there is no need for the generation of heat from nuclear reactions, then for electricity generation from the heat using steam turbines, and so forth.

The necessary note regarding this ideal possibility should be in careful separation of two stages of the whole process. The first stage is an intentional creation of the self-organized fractal structures in some construction in an engineering scale. These structures have their main task to enter into an interaction with the motion along the fractal geodesics of elementary particles, which form some fuel substance. This interaction has to have disturbing character on the geodesics resulting in a decay or transmutation of the fuel substance. The second stage of the process is to obtain a feedback of this disturbing action to the bigger scale possessing moving and charged structures, which are applicable for extraction of energy coming from the nuclear transmutation in microscale.

These two interconnected tasks have to be joined in the same construction in the bigger scale using the self-organized fractal processes.

We describe two currently available engineering approaches to accomplish these tasks in the following two subsections.

2.1. Retroactive Force Loop Proposed by Nottale

The first approach is to apply the proposal for hydraulic macroscale experiment described by Nottale and Lehner [6]. This approach has its partial support in our own experiments with the low-temperature pyrolysis of gaseous hydrocarbons to be described in the third section of this paper. It assumes the creation of so-called macroquantum oscillating wave packet in the engineering macroscale, which has to obtain its form being dynamically tuned according to the theory [5] to elucidate the fractal character of space and existence in it of so-called generalized quantum potentials [7] appearing opposite to the potentials driving some transfer processes. Such processes in our engineering system may be the processes of dynamically changing heat and mass transfers, which are created by change of global gradients of corresponding physical potentials in the system. For example, with reference to the heat transfer considered in [7] as diffusion, the diffusion driving potential:

Corresponding generalized quantum potential:

Here, the constant is equal to

for the quantum scale. It may take other values for the other scales. The is the Plank constant and is a mass of the system. The constant is the heat conductivity for a temperature . is the quantum-like force of the generalized quantum potential.

The proposal for physical experiment in [6] includes an example of one-dimensional system with the harmonic oscillations represented by the standard equation

. The oscillations should be iteratively governed by the retroactive force loop to approach the form of macroquantum wave packet with its energy written as:

Accordingly to the simulations in [6], once the oscillations approach the form governed by the predicted quantum-like force, the macroquantum wave packet becomes more stable with regard to the simulated external perturbations.

From our point of view, such a situation may also bring some side effects to the oscillations in lower scales. We hypothesize in our work [8] that, due to an existence of the dynamically changing global gradients, the atomic and molecular ensembles on micro- and mesoscales may have a special character of harmonic oscillations with slightly deviated potentials between their interacting parts because of link with the oscillations in bigger scales.

Because of this possibility, a wide class of engineering systems utilizing pyrolysis and gasification, which have possibilities for the self-organized oscillations on the fractal geometries spanned on several scales [9], may be applied for research of this link and corresponding energy transfer between the oscillations in different scales.

Main recommendation for engineering applications regarding this possibility is to provide these systems with an intentional modulation of basic energy transfer processes in reactors to direct their internal self-organization towards appearance of the macroquantum wave packets having connection with the same packets and oscillations in lower scales. Such a connection may bring lower activation energies for the reactions of thermochemical decomposition in these reactors.

Obvious note regarding totally different time scales of the presumably connected oscillations in the different spatial scales brings us to the conclusion about existence of some kind of a fractal transformation governing the energy transfer between the scales. This energy transfer may be considered analogous to the self-organized appearance of electromagnetic waves in resonator from background electromagnetic fluctuations in it. A wide spectrum of these fluctuations creates oscillations, whose frequency is determined by the spatial and construction parameters of the applied resonator.

This is, however, only an analogy. The energy transfer along the dynamic fractal spanned on several scales might be much more complicated than this. To describe the second approach of the section, one may discuss the disturbing side effects of this energy transfer towards microscales on some known experimental examples of so-called low-energy nuclear reactions (LENR), many of which are accompanied by the transmutation of involved substances.

2.2. Self-Organized Dynamic Transfer Processes Possessing Fractal Geometries as Origin of LENR

Generally saying, the approach to the space in the theory [5] may be considered as an integral approach. Even if main description of a fractal character of the space refers to the concept of geodesics of elementary particles, a main part of the analysis in the theory [5] is devoted to the integral properties of such a space in application to the systems in relatively big scales. There is, however, definite evidence, that the fractal properties of space reveal itself not only in the mass distributions in astrophysical scales, considered in [5], but also in structuring in the quantum microscales, where geodesics of elementary particles form nuclei, atoms, and molecules. Because of uncertainty principle, one may freely assume that the geodesics of elementary particles span in the scales of engineering macrosystems. Due to this, the interaction of such macrosystems with presumably very fast motion of energy along the geodesics looks possible. Analysis of basics of the theory [5] provides with two main conditions for that (1) fractal character of the geodesics, (2) change of the fractal dimension of geodesics with change of the scales.

We would like to note that many dynamic processes on interfaces between gases, liquids, and solids provide with a fractal form of the processes. This form is also dynamically changing during the processes. This change may provide us with an accomplishment of the basic condition (2) leading to disturbing interaction with geodesics of some kind of elementary particles located in the spatial range of our engineering system, which contains fractals being dynamically created and changed.

By our opinion, there are several historically first examples of such engineering systems, which were described in the papers [10–12] with a misleading explanation of origin of LENR taking place in the systems. First of all, these systems are the systems with dynamically developing cracks in the solids doped by hydrogen or deuterium. Such a doping and detection of emission of neutrons and other elementary particles lead to search of possibilities for the hydrogen or deuterium fusion taking place with the help of a crystal lattice of the solids. By our opinion, this search is misleading. Main reason for this is well-known property of both gases to make the experimental solids brittle. Presence of atoms of these gases in a crystal lattice is presence of the defects, which promote development of fractures and cracks possessing a fractal geometry of their surfaces. An interaction between the fractal geodesics of elementary particles constituting substances of the solids and the fractures being dynamically developed in the solids provides with disturbing side effects on the structuring of the substances on a nuclear scale.

This interaction is also an alternative explanation for the transmutation phenomena observed in result of an explosive electrochemical destruction of metal foils in the experiments described in [13, 14]. The main characteristics of the dynamically changing fractal interfaces in this case are not the interface between atoms of gas and solid, but the interface between atoms of gas and liquid, or between the electrons being moved by electromagnetic field and conductor, which form system with varying constraints.

The term constraints here is analogous to the same term in [15, 16], which generalizes results of experiments with relativistic electron beams focused on solid targets. Detailed outputs of the experiments are described in the book [17]. The interaction of a targeted substance with the high-energy focused electronic beam being constrained by the substance creates conditions for its transmutation and even for creations of super heavy nuclei, which are considered in [16] using the concepts of fractal isomers and clusters.

Despite the high energies involved, we may characterize these experiments as possessing the same general character of interaction between the competing agents forming mass transfer as in the case of generation of so-called fractal fingers, which are considered in the book [1] on the case of expunging of highly viscous liquid by the less viscous. The process is characterized as inherently nonequilibrium. It creates the dynamically changing fractal interface between two interacting substances. By our opinion, the dynamic properties of interactions between substances on two different sides of such an interface play the most important role in establishing interaction with the fractal geodesics.

An argument to support this conclusion may be found in the special dependencies of two closely connected phenomena taking place in the collapsing bubbles. The process of a bubble collapse may produce light [18] and neutrons [19]. In the first case the emission of photons from bubbles in water is highly dependent on presence of argon in the bubbles [20]. In the second case the dependence has been moved to another side of the interface—liquid. The latest experiments on generation of neutrons from the bubbles being created by powerful ultrasound [21] make evident critical dependency of this generation from the presence of salts of Fe in water. These experiments of the group researching the so-called piezonuclear reactions in the paper [21] support our conclusion about importance of the self-organized dynamics determined by the interacting substances residing on two sides of a dynamically changing fractal interface. This group recently has conducted experiments [22] using bar of steel subjected to a powerful ultrasound having the same frequency as applied to the salts of Fe in water. The same output as in [21] was detected in the form of bursts of neutrons. Authors of [21, 22] argue that neutrons are emitted in result of piezonuclear reactions, which are caused by extreme pressure and subsequent dislocations of adjacent atoms in the cases of imploding bubbles and violently deforming lattices of solids. Transmutation of substances in the steel also was detected in the latest experiments of the group [22]. The theory [23], which stays behind the experiments, considers the metrics of space time as dependent on energy values being involved into interactions. This is generally close to our own approach. Main difference, however, could be noted with regard to the engineering practice. The hypothesis of inherent fractal structure of space allows search of technically more feasible possibilities to alter its metrics. By this hypothesis the super-high concentrations of energy in pretty small spatial areas are good, but not necessary for initiation of piezonuclear reactions.

By our opinion, the dynamic excitation of relatively big internal fractal structures of steel by ultrasound with subsequent development of fractal cracks accompanied by interaction between the atoms of Fe and atoms of some gas on the fractal interfaces might be responsible for the neutron bursts and transmutation. The same could be noted with regard to the fractal interfaces between gas and liquid in collapsing bubbles.

In addition to the considerations presented above, we would like to note that the discovered in [21, 22] side effects of the interactions between the fractal geodesics of constituents of experimental substances and their fractal interfaces may take place not only at the nuclear scale level. To find out such interactions, which create disturbing actions at some other scale levels of structuring of experimental substances, one may reproduce or conduct new experiments, which are close by their idea to the experiments described in the next section.

3. Low-Temperature Pyrolysis of Hydrocarbons Using Dynamically Changing Fractal Interfaces

Historically such pyrolysis, as designated in the title of this section, was conducted first by the owners of patent [24]. There was another theoretical explanation of the process. This explanation has put its main emphasis on the combinations of constituents of composite substances being in contact with the hydrocarbons, which were subjected to simultaneous action of dynamic potentials driving the heat and mass transfers. This theoretical explanation is presented on a personal site of one of coauthors of this paper (O.I. Vyhoniailo), who is also coowner of the patent [24]. Another explanation, which is presented in this paper, is illustrated by the following report about the concept of proof experiment. Next subsection after the report represents a short description of experimental predecessors for this experiment joined with a discussion.

3.1. A Concept Proof Experiment

The experimental setup for a concept proof experiment on low-temperature pyrolysis of gaseous hydrocarbons is presented in Figure 1.

1: volume containing propane/butane mixture 2: valve to regulate flow of gas 3, 4, 5: thermocouples 6: heating wire 7: U shape test glass with Sn : Bi alloy 8: volume with water 9: output tube.

The heating wire has been attached to the source of direct current. The number of heating wire windings around the test glass was tuned to support its constant temperature around the 200 ± 20°C with the approximate flow of gas via the melted alloy 1 mL/sec. No thermocouple was submerged into the alloy. The setup was designed for a concept proof experiment. Therefore no gas composition measurements on output were made and estimations of the gas flow were performed using visual observations of the size and frequency of gas bubbles flowing from bottom of a volume with water to the open atmosphere via the output tube.

Such a simple experimental setup allows tuning of the gas flow via the alloy with direct observation of the carbon appearing on top of the metal from the right side of U tube. Typical result of a short (10–15 minutes) experiment is shown by the photo in Figure 2. Here the alloy is cooled down. The temperatures measured by the three thermocouples were 186°C of gas coming to the alloy from the left input to the U tube, 204°C temperature of a heating wire, and 82°C of gas coming to the outlet at the right side of U tube. Short video of this experiment is presented in the Supplementary Material available online at

The thermocouples were inserted to the U tube via the gummy locks having drilled holes. As the thermocouples had two wires in a plastic insulation, they were inserted not totally tightly into the locks. Achievements of the stable temperature and gas flow regimes allowed the removal of the thermocouples and application of tightly set solid gummy locks. This allowed the detection of slow diffusion of gases remaining in the slang between the right side of U tube and the volume with liquid. The diffusion was into the solidified alloy, which obtained high porosity with presumably fractal internal surfaces of the pores with carbon on their walls. One can see it in Figure 3 in the photo taken after 8 hours after the end of the carbon producing experiment. Water from the volume with it was sucked into the alloy.

We exclude significant effect on the sucking from a thermal decrease of a gas volume in the tubes due to the cooling, because we could not observe significant change of a water level in the volume on output during the time of complete cooling to the room temperature of all the parts of experimental setup.

Exact reason of this phenomenon is unknown, as detailed characterization of the alloy and its pores was not conducted. It was possible to observe using an optical microscope the highly developed fractal geometry of the pores with carbon on the metal after breaking of the glass with it. No analysis of internal porosity of the alloy was conducted. We make preliminary conclusion that main reason of sucking of water into the alloy might be in presence of a big internal volume in the fractal pores inside the alloy, which had mainly hydrogen and carbon during its solidification.

3.2. Experimental History and Discussion

Historically the same process (by the hypothesis) under the same temperatures took place in the experiments conducted prior filling of application for the patent [24]. The gas (methane) was moved by a mixer in the glass bulb along the surface of a mixture of fractured solids and porous salts, which were lying on the bottom of the bulb being heated by an electrical heater beneath the bulb. It is assumed from the common knowledge about fractals [1] that the substances lying on the bottom of the bulb possess the fractal geometry of their surface and pores. Temperature inside the bulb was monitored by a thermocouple inserted together with the mixer via lock at the top of the bulb. Carbon particles were formed directly in gas. Then they flew out of the bulb to the same volume with water as in the above-described experiment. With progress of methane pyrolysis the volume becomes dark being filled by the trapped particles. A short video of this experiment is presented in the supplementary material of this paper.

One may note that such an experiment has a difference with an alloy-based experiment in respect to the fractal interfaces. Here the interface is between the gas and solids, whose surfaces are assumed (not proved) to have a fractal geometry. The solids are also relatively stable. In contrast to this, the convective surface layers of gas being heated and moved in the bulb by a mixer with unavoidable turbulence definitely possess fractal properties of temperature and pressure fluctuations accordingly to many researches referenced in [25].

This note adds some ambiguity to the consideration regarding unstable fractal interfaces between the gas and liquid, as both phases may contribute to the dynamics on their interface. Yet it may provide another aspect to research of turbulence towards finding out of such possibilities, as described in the beginning of Section 2.

For example, if one will find out such a special regime of turbulence in the ionic flame-based magnetohydrodynamic generators, which obtains its support from accelerated reactions in lower scale of the fractal geodesics being disturbed, one may directly produce electrical energy from the energy of disturbed and decayed structures in lower scales. With regard to such a possibility one may develop an alternative explanation of acceleration of chemical reactions in reactive turbulent flows in comparison with the explanation based on the idea about an increase of mixing in turbulence.

Furthermore, if one will apply the approach to control the dynamic chaos of turbulence by the external perturbations analogous to the controlling actions of Nottale’s hydraulic experiment [6], one may achieve intensification of the whole process and of the energy transfer process between the scales. By our opinion, such intensification takes place in the experiments with combustion of wood powder, which are described in [26]. The external perturbation, which stabilizes the flame, is applied to a burner in the form of low frequency sound (around 17 Hz). It makes combustion much more intensive, and it increases the levels of NOx generation in the process. The large-scale dynamic parameters of the flame are changed drastically. Therefore it might be reasonable to conclude that analogous application of low-frequency sound in the same burner of a magnetohydrodynamic generator might bring unexpected increase of its efficiency.

Another prospective engineering system to explore the discussed side effects may be built using intentional creation of dynamic fractal structures in sound waves. This proposal logically follows from the notes about general ways of geometrisation of physics, discussed also by Nottale in his works. In context of these discussions, the geodesics may become the only entity, which is considered. In such a case the main meaning of the concept moves from the approach based on consideration of geodesics for particles in empty space to the approach based on consideration of purely relative differences between the geodesics, which are entangled in motion at several scale levels to form the space itself and to support their steady structures in the forms of particles and matter.

With respect to this particularity in the theoretical considerations, the self-organized fractal structures in turbulent flows and in convective surface layers become totally analogous to the fractal structures to be intentionally created in sound waves. Here the main role has to play the spatially oriented fractal structure of differences in pressure along some number of sound wave periods, many of which may have intentionally introduced disturbances of harmonic wave forms to create a dynamic fractal.

We do not know real engineering systems, which exactly utilize such an approach.

There is, however, one example of electromechanical system [27], which by opinion of its inventor and producers acts destructively on the hydrogen bonds in water. This destructive action is in possibility to produce atomic hydrogen, whose flows out of water purges various impurities from it. One may see various salts expunged from ordinary drink water on the photo in supplementary material of this paper. The photo of the device is presented along with another photo of volume with purified water having voltmeter in it. It shows 1.4 Volt of potential difference between the electrode in center of volume and metallic volume itself. Inventor of the device argued that this electric potential and cleaning of water appear due to the generation and motion of atomic hydrogen. As inventor was a medical doctor, the device has received its application as a physiotherapeutic device, which is certified for medical use in Kazakhstan. Nowadays this device is also applied for a fabrication of biologically active and purified bottled water.

The photo of volumes with water was taken from a report in popular Russian magazine about the technical exhibition, where the device was presented [28]. Photo of the device in a cabinet for physiotherapy was taken from one of the sites of its sellers [29].

By our opinion, the special action of the device on water is created by a passage of initially harmonic infrasound (around 14 Hz) via specially designed composite substance. This composite substance modulates the infrasound in a special way due to its nonlinear mechanical properties. We may hypothesize about destructive effect on water from an excitation of internal fractal structures in the composite substance by the sound, and from modulation of this sound. Despite such an ambiguity, the effect on water being subjected to the sound, which is produced by the device [27], may be considered as analogous to the effect on hydrocarbons from the fractal structures in the convective layers between the gaseous hydrocarbons and Sn : Bi alloy in our own experiments, or the sound waves resemble the form of macro quantum wave packets.

4. Conclusions

We have presented a general description of relatively rare engineering systems utilizing side effects arising from the dynamics involving self-organizing fractal interfaces. Both theoretical and practical backgrounds to explore and develop such systems were presented. We encourage readers to develop their own prospective engineering applications based on the presented theoretical approach and experimental examples, which were interpreted using this approach.


The authors would like to express their gratitude and thanks for a public discussion and experimental cooperation to another coowner of the patent [24], Shostak Taras Anatolievich, and to the Sintos Systems OU for financial support of this work.

Supplementary Materials

The supplementary materials include two videos of AVI and MP4 formats. The first video was recorded in Ukraine, the second - in Sweden. The first video shows low-temperature pyrolysis of methane in the glass bulb with mixer, thermocouple, and heated porous solids. The gas is delivered from the natural gas supplying network in Ukraine.

The second video shows also low-temperature pyrolysis of propane/butane mixture being pumped through Sn : Bi alloy melted in the U-shaped test glass tube. Temperature of the solids and alloy, which are in contact with the gases, is in the range of 200 +/- 20 °C.

It also includes two photos: 1. Infra-sound device ИФС-1 in the cabinet for physiotherapy. 2. Volumes with water processed by the device.


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Copyright © 2013 Aliaksandr Yurievich Alevanau et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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