{"id":35751,"date":"2014-11-24T15:54:05","date_gmt":"2014-11-24T15:54:05","guid":{"rendered":"http:\/\/www.labri.fr\/perso\/barla\/blog\/?p=35751"},"modified":"2014-11-24T16:16:47","modified_gmt":"2014-11-24T16:16:47","slug":"35751","status":"publish","type":"post","link":"https:\/\/www.labri.fr\/perso\/barla\/blog\/?p=35751","title":{"rendered":"The Self-made Tapestry &#8211; Pattern Formation in Nature"},"content":{"rendered":"<p id=\"top\" \/>by Phillip Ball<\/p>\n<p>&nbsp;<\/p>\n<h3><b>Patterns<\/b><\/h3>\n<p>Complex form may not require an organic origin, but similarly geometric form does not exclude it. There are, in other words, forces guiding appearances that run deeper than those that govern life. p.4<\/p>\n<p>You can&#8217;t avoid concluding, once you begin to examine this tapestry, that much of it is woven from a blueprint of archetypes, that there are themes to be discerned within the colourful fabric. Nature&#8217;s artistry may be spontaneous, but it is not arbitrary. p.5<\/p>\n<p>But as an explanation for natural form, natural selection is not entirely satisfying. Not because it is wrong, but because it says nothing about mechanism. It is like asking how a car gets from London to Edinburgh. One answer might be &#8216;Because I got in, switched on the engine, and drove&#8217;. That is not so much an explanation as a narrative, and natural selection is a bit like that-a narrative of evolution. p.6<\/p>\n<p>This prompts the idea that a pattern might be regarded as a regularly repeating array of identical units. I want to broaden that concept slightly, and include in my definition arrays of units that are similar but not necessarily identical, and which repeat but not necessarily regularly or with a well-defined symmetry. p.9<\/p>\n<p>Form is a more individual affair. I would define it loosely as the characteristic shape of a class of objects. Like the elements of a pattern as described above, objects with the same form do not have to be identical, or even similar in size; they simply have to share certain features that we can recognize as typical. The true form of objects is that which remains after we have averaged away all the slight and levitable variations between individuals. p.9<\/p>\n<p>The logarithmic spiral has the unique property that the curve is everywhere &#8216;similar&#8217;, differing in size but not in shape. In other words, as the curve rotates through a fixed angle, it grows uniformly in scale. This, and the description above, help us to see what are the fundamental generating mechanisms of such a form. Some things remain constant, for example the angular speed of the curve&#8217;s tip, and the shape of the curve, while other things, for example the linear (tangential) speed of the tip, change in a well-defined way. p.12 <i>Similarly, a material pattern might firstly be defined as an array of elements that may differ in a number of parameters, but not in fundamental shape.<\/i><\/p>\n<p>Once we know the mathematical algorithm, we can start to ask what kind of physical processes might provide a form-generating rule to which the algorithm is a good approximation. p.13 <i>One should also be able to explain why some patterns that have been created virtually are NOT found or even possible in the real world.<\/i><\/p>\n<p>Physicists generally regard gases and (to a lesser degree) liquids as uniform, fully symmetrical systems. Yet on the atomic scale all one sees is random disorder, atoms and molecules whizzing about with no apparent symmetry at all. The uniformity and high symmetry become apparent only by average features of these systems, which we can do either by focusing our attention on one region and averaging the molecular motions over time or by comparing a large number of different regions at any instant. In both cases, a gas then appears to have a completely uniform density of molecules, on average, at all points in space (it is homogeneous); and they travel in all directions with equal probability (the gas is isotropic). p.15<\/p>\n<p>The Problem of creating patterns and forms that we tend to recognize as such is therefore not one of how to generate the symmetry that they often possess, but of how to reduce the perfect symmetry that total randomness engenders, to give rise to the lower symmetry of the pattern. How do the water molecules moving at random in the atmosphere end up into a six-petalled snowflake? Patterns like this are the result of symmetry breaking. p.15<\/p>\n<p>We might intuitively expect that this will always be so: that the final symmetry of a system will be dictated by that of the symmetry-breaking force that destroys an initially uniform state. But it is the central surprise of the science of pattern formation that this is not necessarily so. The symmetry of a pattern formed by a symmetry-breaking force does not always reflect the symmetry of that force. p.15<\/p>\n<h3><b>Bubbles<\/b><\/h3>\n<p>Whereas in a liquid droplet the surface tension is the same in all directions, the different faces of a crystal have different surface tensions (because the arrangement of atoms is different on each). The face that grows the fastest will often be that with the greatest surface tension. Surface tension controls the shapes that droplets tdopt when they sit on surfaces. If a droplet spreads, it ncreases its surface area and thus its surface excess nergy; but on the other hand, it covers the surface below, which also has a surface excess energy. If the total surface excess energy is lower for a fully liquid-covered surface, the droplet will spread into a liquid film; if not, it remains a glistening bead. p.18<\/p>\n<p>Two common aspects of pattern-forming instabilities are that they involve symmetry-breaking (in the present case, the liquid film is initially uniform (symmetric) along the thread&#8217;s axis, but the instability breaks this symmetry) and that they have a characteristic wavelength, so that the features of the pattern have a specific size. p.19<\/p>\n<p>The thickening of the walls and curving of the bubble sides apparently changes the balance in surface energies so that this structure becomes more stable instead. So in thicker-walled honeycombs, maybe the bees do have the best solution. p.27<\/p>\n<p>The way that shape affects the curvature energy is rather subtle, and it may turn out that the lowest-energy shape is not that with constant mean curvature-a sphere-but some other, more complex hape. This balance can be shifted by changing the nature of the vesicle&#8217;s environment-for example, by warming it up-and so the vesicle may undergo changes in shape as the temperature is changed. p.28<\/p>\n<p>For a separation between lamellar bilayers greater han a certain threshold, it can become energetically favourable for two adjacent layers to fuse together at one point around a hole or pore. Under these conditions, pores can proliferate between sheets, and the stacked layers break up into a web of tunnels that divides the system into two distinct subspaces. The channels of a bicontinuous phase of surfactant bilayers may be arranged in a haphazard way, in which case the system has the random, perforated structure characteristic of a sponge (and is indeed called the sponge phase-or more figuratively, the plumber&#8217;s nightmare). But more interesting from the perspective of pattern formation is the alternative in which the pores are positioned in a regular, orderly manner. Why should the pores be ordered? Because they have a tendency to repel one another: if two pores get too close together, they create very pronounced curvature of the bilayers in their vicinity, and this costs energy. So when there are many pores, they tend to sit at an optimal distance from each other on a regular lattice. p.35<\/p>\n<p>Whether or not complex, regular membrane pattern play a role in the biology of the cell, one thing is for sure: many organisms use membranes as scaffolds for erecting stronger, more rigid superstructures with fantastic architectures. p.38<\/p>\n<p>&nbsp;<\/p>\n<h3><b>Waves<\/b><\/h3>\n<p>The theme of rich behaviour in systems out of equilibrium is one that will recur many times throughout this book-it is one of the unifying themes of pattern formation, and has been developed into a formal and exact science. For now, I wish to make a crucial point about such systems: they do not corne for free, but need a supply of energy. Without this, they will decay-be it slowly or quickly-to a bland equilibrium. p.52<\/p>\n<p>Living organisms can be considered as approximations to continuous stirred-tank reactors insofar as they (we) continally (though perhaps not continuously) ingest food (fresh material for metabolism) and excrete waste product. In this way we sustain our out-of-equilibrium (and sometimes oscillatory) biochemistry. p.52<\/p>\n<p>Periodic pulsations can arise only in a medium that is excitable, but a propagating wavefront is a rather more a common beast, something that could arise for instance from a single, one-off disturbance. The inadequacies of diffusional transport create the refractory period in the medium just behind an advancing wavefront, where the reaction has exhausted itself but has not yet been replenished with fresh reagents. The poorly mixed BZ reaction is thus an example of reaction-diffusion system, which is now clearly recognized as one of the most fertile generic pattern-forming systems that we know of. p.58<\/p>\n<p>There is now good reason to suppose that many banded rock formations do indeed arise from cyclic precipitation as mineral-rich water infiltrates a porous rock and reacts to form an insoluble product. Amongst the mineral patterns that have been attributed to Liesegang-type processes are the bands seen in some iron oxide minerals, the wood-grain texture of cherts, the striations of a mineral called zebrastone, and perhaps most familiarly of all, the bands of agates. p.63<\/p>\n<p>&nbsp;<\/p>\n<h3><b>Bodies<\/b><\/h3>\n<p>Natural selection does not tell us what is on the palette; it is a tool for retrospective rationalization, and rarely if ever for prediction. Does nature really have an infinite choice of skin patterns, or must it select from just a few? And how do each of those arise? There is a fertile tension inherent in the question of whether the form of living organisms should be regarded either as a haphazard assembly of components that together make up an evolutionarily viable being, or instead as a highly complex, spontaneously patterned form. p.78<\/p>\n<p>The beauty of all this is that the diverse range of pelt patterns and markings can be explained with the same basic mechanism. The location and size of each of a zebra&#8217;s stripes does not have to be specified by a personalized, paint-by-numbers genetic plan; all that the genes have to record is the blueprint for making the activator and inhibitor substances at the right stage in development. p.84<\/p>\n<p>Each of the chemical morphogens has a limited potential by itself to structure the egg, but several of them, launched from different sources, are enough to get the growth process underway by providing a criss-crossing of diffusional gradients that establish top from bottom, right from left. In other words, they suffice to break the symmetry of the egg and to sketch out the fundamentals of the body plan. p.100 <i>This is like weighted coordinated weighted by harmonic diffusion !<\/i><\/p>\n<p>If the formation of patterns by symmetry-breaking proves to pose limitations on evolutionary choices, that will add just one more nuance to Darwin&#8217;s towering achievement. p.104<\/p>\n<p>&nbsp;<\/p>\n<h3><b>Branches <\/b><\/h3>\n<p>I doubt if too many tree experts could give a precise 1 explanation for how they distinguish one system of branches from another-they might be able to identify a few pronounced features such as the sharpness of the tingle between diverging branches, but it wouldn&#8217;t by any means amount to the kind of mathematical criterion that could be programmed into a computer to give it the same facility for telling apart an elm from a sycamore. We just seem able to &#8216;sense&#8217; the pattern.\u00a0 p.111 <i>Maybe humans learn a combination of flow combined with outline cues ?<\/i><\/p>\n<p>The branched clusters are another example of non-equilibrium structures. The mechanism of non-equilibrium electrochemical growth shares the same broad features as the DLA model-random diffusion of ions and irreversible attachment to the electrode deposit. p.114<\/p>\n<p>Preferential growth at a tip ensures that any tiny bumps formed by chance at the cluster surface will have a tendency to grow faster than flat parts ot the surface, because there is a better chance that a randomly diffusing particle will hit it. And crucially, this growth advantage is self-enhancing-the more the bump develops, the greater the chance of new particles striking and sticking to it. The probability of this is always greatest at the very tip of the bump, since this is always greatest at the very tip of the bump, since this is the most exposed part. So the slightes small bump grows into a sharp finger. Because inegularities are springing up by chance all over the surface all the time, the deposit becomes increasingly branched, with each new tip constantly sprouting extra appendages. p.114 <i>It is thus the harmonic distance that matters as each random particle is newly fired into the system!<\/i><\/p>\n<p>Yet it turns out that even forms as apparently irregular as these branched aggregates have a measurable property that is almost as precise, reproducible and characteristic as the number of legs on an insect. It is called the fractal dimension, and is a measure of how densely packed the branches are. You can perhaps see that the smaller the fractal dimension, the wispier the cluster.\u00a0 p.115<\/p>\n<p>The fractals that we see in the natural world do not generally have the &#8216;symmetry&#8217; evident in the Mandelbrot set (which is the product of a rather esoteric and exact mathematical procedure); they lire irregular, like a branching DLA deposit, because they are formed in a noisy, random environment. What both the Mandelbrot set and DLA clusters have in common-along with all other breeds of fractal structure&#8211;is the property of scale invariance. p.117 <i>But in nature, this is limited to a given interval, at the boundaries of which other physical processes take the lead as seen in Fig 5.6b.<\/i><\/p>\n<p>Just saying that a structure is fractal doesn&#8217;t bring you any closer to understanding how it forms. There is not a unique fractal-forming process, nor a uniquely fractal kind of pattern. The fractal dimension can be a useful measure for classifying self-similar structures, but does not necessarily represent a magic key to deeper understanding. p.117 <i>INDEED!<\/i><\/p>\n<p>To a first approximation, you could say that the characteristic wavelength of viscous fingering is set by the point at which the advantage in growth rate of ever narrower branches is counterbalanced by their cost in surface energy. p.120<\/p>\n<p>The lesson here is that noise or randomness can influence a growth pattern in pronounced ways. p.120 <i>What does produce noise or randomness in nature? Is it a hard-to-predict, yet deterministic process at a smaller scale?<\/i><\/p>\n<p>A tree is a form with a purpose. There are many problems that a tree must solve if it is to survive. How can it pump water from the roots to the leaves? How can it support its own tremendous weight? How to maximize its light -gathering efficiency? How to grow tall enough to compete for light with its neighbours, without becoming too massive for the roots to bear? In the face of these dilemmas there is little chance that a simple physical model will tell all about the shape of a tree. Even if the various factors influencing tree growth are too numerous and too complicated to account for, we can attempt to develop mathematical models that, while ignoring the biology and mechanics, nevertheless aim to reproduce the essential shapes of trees. p.128 <i>The same approach may be taken to describe images of trees, by relying on flow properties.<\/i><\/p>\n<p>The biology of angiogenesis is complicated, and doesn&#8217;t always generate a diverging, randomly branched structure &#8211; often the vessels are interconnected in more complex ways. p.130<\/p>\n<p>Whether the models that have been developed so far for bacterial growth share anything more than accidental features with the patterns seen experimentally is still an open question. -Iowever crude the present models, hey promise that a marriage of physics with biology will surely have much to tell us about the ramifications of growth and form. p.139<\/p>\n<p>&nbsp;<\/p>\n<h3><b>Breakdowns<\/b><i><\/i><\/h3>\n<p>The essential feature of most of these models, however, is that the fracture process involves a strong dash of randomness. It is not hard to justify this: most real materials have microscopic structures that embrace a considerable degree of randomness. Rocks are typically haphazard compactions of grains of many different sizes and shapes, welded together at their boundaries. Metals too, while possessing crystalline orderliness at the atomic scale, are at larger scales agglomerates of many domains, each with their crystal planes pointing I in different directions. Cement and porous rocks like a sandstone are shot through with random networks of pores. Hard, brittle plastics contain a tangle of polymer chains that are partly aligned but partly entangled and disordered. p.147<\/p>\n<p>What should we conclude from all of this about the web-like branches of cracks? The detailed investigations of the stresses around a rapidly propagating crack tip performed in recent years have enabled us to understand why it is that these fast cracks tend to split intI branches: there is a dynamical instability which make: simple forward movement of the tip untenable. Beyond this threshold there is an underlying unpredictability in the motion of the crack tip, so that the crack carves out l jagged path that splits the material into rugged (and\u00a0\u00a0 generally fractal) fracture surfaces. Randomness and disorder in a material&#8217;s structure provide a background &#8216;noise&#8217; that can accentuate the pattern. p151<\/p>\n<p>The surface textures that fractures generate are rich and varied. Wood cracks into a spiky array of splinters, reflecting its fibrous texture. Sheets of soft plastics like polyethylene rupture under tension into webs of aligned fibres (Fig. 6.25), a consequence of the fact that the material is made up of entangled chain-like polymel molecules. No single theory can account for all of these textures, since they are generally a consequence of the differing microstructures and atomic-scale structures of the materials. p.158<\/p>\n<p>Self-similar fractals are the easiest sort to understand. But fractal surfaces are, I&#8217;m afraid, not like that. . Although they have a fractal dimension of between 2 and 3, indicating that they have a tendency to fill up three-dimensional space in a way that a flat or smooth surface does not, this space-filling tendency is not isotropic. It is instead said to be self-affine, which crudely means that the ratio by which the component features are scaled at successive levels of nagnification is different in different directions. Notice, however, that the perimeter of a vertical cut through a self-affine surface is self-similar-it is a line with a fractal dimension of between 1 and 2 (generally closer to 1, since the line does not tend to bend back on itself so as to more completely fill two-dimensional space). p.160<\/p>\n<p>In general, the smaller, shorterlived features of a landscape-rills, gullies, hill slopes are self-organized by interactions between them and the other intrinsic elements of the system, whereas larger, long-lived features like mountain ranges come about through external, eksystemic influences. p.161<\/p>\n<p>But recently some researchers have suggested that the kind of self-affine relief seen in nature is a robust form that emerges automatically as an erosive river network develops across an initially flat or randomly corrugated (non-fractal) landscape, regardless of the finer points of a particular flow model. p.162 <i>Even though two terrains at different scales are both fractal, they are not necessarily self-similar as they are shapes by slightly different processes.<\/i><\/p>\n<p>&nbsp;<\/p>\n<h3><b>Fluids<\/b><\/h3>\n<p>In the flows that I have considered so far, the driving force of patterning has been constant through time. For convection it was the buoyancy force created by a temperature gradient; for shear flows, it was a shear created either by the frictional drag experienced by a constant-velocity flow as it passed over a solid body or by the movement one confining surface relative to another. p. 188<\/p>\n<p>What has emerged from this sort of approach is that even apparently random, structureless systems like turbulent fluids may have characteristic forms if looked at statistically. p.192<\/p>\n<p>Somehow the energy that is fed into the flow at large scales, creating big eddies that we can see with the laked eye, has to find its way down to these small scales before being dissipated. What happens is that there is an energy cascade: big eddies transfer their energy to smaIler eddies, which do likewise at ever smaIler scales. p.193<\/p>\n<p>&nbsp;<\/p>\n<h3><b>Principles<\/b><\/h3>\n<p>Perhaps it is a matter of taste, but I feel that there is much more wonder in a world that weaves its own tapestry using countless elegant and subtle variations, combinations and modifications of a handful of common processes than one in which the details become irrelevant, in which a few recondite equations are supposed to provide us with all we need. p.252 <i>Why is that that the scales at which we see so mayny different patterns and so much complexity is close to ours? Might well be because we too are a product of such complexity, which only has a small spatio-temporal window to express itself&#8230;<\/i><\/p>\n<p>Competition lies at the heart of beauty and complexity in pattern formation. If the competition is too one-sided, all form disappears, and one gets either unstructured, shifting randomness or featureless homogeneity &#8211; bland, in either event. Patterns live on the edge, in a fertile borderland between these extremes, where small changes can have large effects. This is, I suppose, what we are to infer from the clich\u00e9d phrase &#8216;the edge of chaos&#8217;, beloved of complexity enthusiasts. Pattern appears when competing forces banish uniformity but cannot quite induce chaos. It sounds like a dangerous place to be, but it is where we have always lived. p.253<\/p>\n<p>In contrast to most equilibrium structures, the spatial scale of the pattern features in a dissipative structure bears no relation to the size of its constituents (the size of convection cells is much, much larger than the size of the circulating molecules), and this scale is robust in the face of perturbations. A transient perturbation may disrupt the structure temporarily, but the disturbance will pass and eventually the structure will regain the same period as before. Thus the characteristics of a dissipative structure are not at the mercy of perturbations, but are set by the intrinsic interactions in the system. These structures are said to possess an attractor in the set of variables that describe the system (the so-called phase space), because the system will always be drawn back to this particular set of variables (provided that it is not knocked so far that it falls into the basin of another attractor). p.256<\/p>\n<p>Even chaotic non-equilibrium states are dissipative structures of a kind, since they too have corresponding attractors in phase space. The difference from ordered states is that the attractors are fractal &#8211; the trajectories spin a web with an infinite hierarchy of structure, so that the behaviour of the system never repeats itself exactly. All the same, these chaotic or &#8216;strange&#8217; attractors have a characteristic form (Fig. 10.3), a &#8216;hidden&#8217; pattern that constrains the extent to which the behaviour of the system can meander through and explore the phase space of its variables. p.256<\/p>\n<p>So equilibrium phase transitions, like the abrupt transitions that characterize much of pattern formation, are spontaneous, global instabilities that set in when a threshold is crossed and they may involve symmetry breaking. p.257<\/p>\n<p>Second-order and continuous phase transitions always involve symmetry breaking. Furthermore, there can be no coexistence of the states between which the system switches, even exactly at the transition point: it is all or nothing. And there is no hysteresis. p.259<\/p>\n<p>In other words, to address the problem of pattern selection, we are forced to consider the specific details of each system, including the nature of the randomizing &#8216;noise&#8217; it experiences. p.261<\/p>\n<p>The minimal way to break the symmetry of a uniform two-dimensional system-that is, the way to break as little symmetry as possible-is to impose a periodic variation in just one dimension. After breaking symmetry periodically in one dimension, the next &#8216;minimal&#8217; pattern in a two-dimensional system involves breaking it in the other. This imposition of a second periodic variation breaks the system into discrete cells. If the state is to remain ordered and as symmetric as possible, there are only two options: to impose the periodic variation perpendicular to the rolls, creating square cells, or to impose two such variations at 60\u00b0 angles, creating triangles or hexagons. p.262<\/p>\n<p>The shape of the boundary can occasionally change a pattern to something qualitatively different. Moreover, the need for a whole number of pattern features to fit within the container may determine the wavelength, just as the wavelength and thus the frequency of an organ note is determined by the length of the pipe. In some systems, the pattern may also change locally to adapt to the presence of a boundary. p.263<\/p>\n<p>Finally, we should include noise as a pattern-selecting influence. The message here is that noise does not necessarily affect all patterns equally &#8211; it may favour some over others. Rolf Landauer has argued that noise is central to the transitions between different states of a nonequilibrium multistable system, and so is a critical (but commonly neglected) feature of pattern formation and selection. p.264<\/p>\n<p>This behaviour can be depicted as a cascade of pitchfork bifurcation. One might liken this (albeit very loosely) to ile excitation of additional harmonics as a trumpeter lows harder. Eventually the oscillations become chaotic (non-periodic), as if the system becomes overwhelmed with choices. Then the cascade loses its branched structure and breaks up into a dense forest of spots &#8211; and we lose sight of any order at all. p.264<\/p>\n<p>Far from the critical point, only the behaviour of a magnetic atom&#8217;s nearest neighbours matters &#8211; if these all point in one direction, the atom in question will be inclined to follow suit. But as the critical point is approached, each atom&#8217;s sphere of influence (called its correlation length) extends wider and wider. And exactly at the critical point, the correlation length becomes as big as the entire system. p.266<\/p>\n<p>That universal power-law scaling arises in self organized critical systems is at least in one sense no surprise &#8211; yet again, it is found in equilibrium continuous phase transitions too. As a system approaches its critical point, the variables that describe its behaviour-the correlation length, the density differences betwee liquid and gas, or more technical quantities such as the magnetic susceptibility or the compressibility &#8211; start to pbey power laws. That is to say, their value is proportional to the distance from the critical point. p.266<\/p>\n<p>I believe it is one of the principal messages of this book that we can map many of nature&#8217;s tapestries onto some universal blueprints, in which specifics cease to matter. At the same time, I want to stress that it is a mapping that is being performed here, and that &#8216;the map is not the territory&#8217;. Maps have a fascination of their own, but that&#8217;s nothing compared to the real thing. p.267<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>by Phillip Ball &nbsp; Patterns Complex form may not require an organic origin, but similarly geometric form does not exclude it. There are, in other words, forces guiding appearances that run deeper than those that govern life. p.4 You can&#8217;t avoid concluding, once you begin to examine this tapestry, that much of it is woven &#8230; <a title=\"The Self-made Tapestry &#8211; Pattern Formation in Nature\" class=\"read-more\" href=\"https:\/\/www.labri.fr\/perso\/barla\/blog\/?p=35751\" aria-label=\"Read more about The Self-made Tapestry &#8211; Pattern Formation in Nature\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[621],"tags":[],"class_list":["post-35751","post","type-post","status-publish","format-standard","hentry","category-books"],"_links":{"self":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts\/35751","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=35751"}],"version-history":[{"count":13,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts\/35751\/revisions"}],"predecessor-version":[{"id":35911,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=\/wp\/v2\/posts\/35751\/revisions\/35911"}],"wp:attachment":[{"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=35751"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=35751"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.labri.fr\/perso\/barla\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=35751"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}