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Painting – Paul Klee, detail from “U struji sest pragova“, 1929.

“Nous avons une notion palpable de la métamorphose de la chenille. Nous, certainement, mais non la chenille.” ~ Edgar Allan Poe / “Le principe de l´evolution est beaucoup plus rapide en informatique que chez le bipède.” ~ Jean Dion / “Let chaos storm!… Let cloud shapes swarm!… I wait for form.” ~ Robert Frost

[…] In his notebooks the painter Paul Klee repeatedly insisted, and demonstrated by example, that the processes of genesis and growth that give rise to forms in the world we inhabit are more important than the forms themselves. ‘Form is the end, death’, he wrote. ‘Form-giving is movement, action. Form-giving is life’ (Klee 1973: 269). This, in turn, lay at the heart of his celebrated ‘Creative Credo’ of 1920: ‘Art does not reproduce the visible but makes visible’ (Klee 1961: 76). It does not, in other words, seek to replicate finished forms that are already settled, whether as images in the mind or as objects in the world. It seeks, rather, to join with those very forces that bring form into being. Thus the line grows from a point that has been set in motion, as the plant grows from its seed. Taking their cue from Klee, philosophers Gilles Deleuze and Félix Guattari argue that the essential relation, in a world of life, is not between matter and form, or between substance and attributes, but between materials and forces (Deleuze and Guattari 2004: 377). It is about the way in which materials of all sorts, with various and variable properties, and enlivened by the forces of the Cosmos, mix and meld with one another in the generation of things. And what they seek to overcome in their rhetoric is the lingering influence of a way of thinking about things, and about how they are made and used, that has been around in the western world for the past two millennia and more. It goes back to Aristotle. To create any thing, Aristotle reasoned, you have to bring together form (morphe) and matter (hyle). In the subsequent history of western thought, this hylomorphic model of creation became ever more deeply embedded. But it also became increasingly unbalanced. Form came to be seen as imposed, by an agent with a particular end or goal in mind, while matter – thus rendered passive and inert – was that which was imposed upon. […], in Tim Ingold, “Bringing Things to Life: Creative Entanglements in a World of Materials“, University of Aberdeen, July 2010 – Original version (April 2008 ) presented at ‘Vital Signs: Researching Real Life’, 9 September 2008, University of Manchester. (pdf link)


Figure – Subcritical Turing bifurcation: formation of a hexagonal pattern from noisy initial conditions in the two-component reaction-diffusion system of Fitzhugh-Nagumo type. From left to rigth:a) Noisy initial conditions at t = 0. b) State of the system at t = 10. c) Almost converged state at t = 100. (source link)

Figure – Other patterns found in the above two-component reaction-diffusion system of Fitzhugh-Nagumo type. From left to rigth: a) Rotating spiral.b) Target pattern. c) Stationary localized pulse (dissipative soliton). (source link)

When an activator-inhibitor system undergoes a change of parameters, one may pass from conditions under which a homogeneous ground state is stable to conditions under which it is linearly unstable. The corresponding bifurcation may be either a Hopf bifurcation to a globally oscillating homogeneous state with a dominant wave number k=0 or a Turing bifurcation to a globally patterned state with a dominant finite wave number. The latter in two spatial dimensions typically leads to stripe or hexagonal patterns. [p.s. – a related lovely beach bay!.. state-phase diagram; Reaction-Diffusion by the Gray-Scott model: Pearson’s Parameterization (link) ]

Video – “BIG BANG BIG BOOM”: an unscientific point of view on the beginning and evolution of life … and how it could probably end. Direction and animation by BLU / production and distribution by / sountrack by Andrea Martignoni.

[…] It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically, unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading. […], A. M. Turing, “The Chemical Basis of Morphogenesis“, in Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, Vol. 237, No. 641. (Aug. 14, 1952), pp. 37-72. (link)

[...] People should learn how to play Lego with their minds. Concepts are building bricks [...] V. Ramos, 2002.

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