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- 1. Shapes andForms in Nature,from the perspective ofComplexity Science Dr. Florin Munteanu
- 2. Summary: • About Complexity Science • Shapes and Forms (natural and artifact) • The essential role of the recursive process • The golden number • The golden Volume • The n-D generalization of the Golden cut • Conclusions for a natural technology
- 3. Breakthroughs of XX-th centuryThe science of XX-th century bring up the importance of theMan in the metabolism of the socio-economical system (GAIAvision) - The science of Complex Systems that define anonlinear approach on Reality (fractals, chaos theory, dissipativesystems, constructal theory etc.) - Computational science (or scientific computing) thatcreate extraordinary tools for the modeling and simulations of thedynamic and evolutions of real objects - Quantum physics, Cognitive Science focus on theimportance of the Observer and his intentionality on the evolution ofthe Reality - The science of Mind – a new approach on the study ofthe Consciousness and Free Will
- 4. Complexity scienceTo start with a definition: Latin word complexus, signifies "entwined", "twisted together". This may be interpreted in the following way: in order to have a complex you need two or more components, which are joined in such a way that it is difficult to separate them. Similarly, the Oxford Dictionary defines something as "complex" if it is "made of (usually several) closely connected parts". Escher
- 5. Some islands of the complexity theory • An important knowledge database; • new scientific domains; • a candidate for a new paradigm = Complexity
- 6. Dissipative systems Ilya Prigogines non-equilibrium thermodynamics Order, Predictability Between Order and disorder a Disorder, Randomness, Analitical approach realm of Complexity Statistical approach Disipative systems, Patterns Bifurcations, •sensitivity to initial conditions INFORMATION •self-organize criticality •context dependency •synchronizations of chaotic oscillators …… •new models •new tools www.complexity.ro •new techniqueswww.complexity.ro
- 7. A profound bifurcaton 1) The studies of the flux of energy and matter Interactons, force, impusl, inteactions, gradient, thermodynamics, Dynamical systems, 2) The studies of the generaton, propagation and decoding messages form a streamimg of data (embedded in • Concept • Perception a energo-material flux). • Constrains • Representaton • Control • Knowledge • Regulation • Meaning • Data, codess, • Wisdom, ACTIV patterns,signal Comunication • Procedures Semantic pocessor PASIV • Instructions meaning reacton
- 8. Shapes and Forms in Nature www.complexity.ro
- 9. Pattern FORM + DYNAMICS www.complexity.rowww.complexity.ro
- 10. Behavior FORM + DYNAMICS + “history” www.complexity.rowww.complexity.ro
- 11. Notice the differences between Natural and Artifact…Foto David Hall
- 12. Self – similar, rough, never identical … Smooth, ever identical, notFoto Chuon Szen Ong related with environment..
- 13. Natural vs. Artifact Logos? external streaming of information- the human mind Project Semantic filed ? Innovation Internal streaming of information; Cognitive process Discovery, self referential in growth o David Hallwww.complexity.ro
- 14. Complicated… …or complex? or COMPLEXPhoto by Dinu Lazar
- 15. Complicated to Euclid…Mankind has simplified Nature in order to copy, control, and dominate it.“Structure” vs. reproducibility
- 16. …but not to Mandelbrot! Benoit B. Mandelbrothttp://www.math.yale.edu/users/mandelbrot/ The need for a new language
- 17. The recursion surprise
- 18. The recursion surprise
- 19. Formal recursion: IFS xi T xf T n T T ... T yi yf n N N cos sin a 0 b1 T R A B i b i 1 i 1 sin cos 0 a 2 i xi N=3F limT n ai =1/2 T nF F yi n bi =0, 1/4, 1/2 Fixed point of T
- 20. Recursively generated structuresIf such geometric objects are materialized,what kind of new physical properties mayhave? How it shows the field distributionaround them if through them pass an electriccurrent, or are exposed to mechanical 1/fnoise, or ...
- 21. Fractal antennas• Fractal antenna theory uses a fractal geometry that is a natural extension of Euclidian geometry.• The geometry of the fractal antenna is a candidate for a multiband solution and also as a small (physical size) antenna. We expect that a self-similar antenna (which contains many copies of itself at several scales) operate in a similar way at several wavelengths.
- 22. From Golden Section toGolden Volume- the need for a new approach in the design of Artifact- From efficiency to … harmony- Beyond functionality, esthetics, ergonomics …
- 23. bringing the philosophy into engineering in a natural and useful way =contemplate and understand Natural things
- 24. Qualitative and Quantitative Morphogenesis - qualitative growth - structuring process Development - quantitative growth, which preserve the form, but increase the weight (homothetic growth)A1 < A2 < A3…B1 < B2 < B3 …t1 < t2 < t3 … A1/B2 = A2/B2=..ct
- 25. 1,1,2,3,5,8,13,21,34,55,89,..
- 26. Ag – the center of convergence of the recursive process. “Fragmentation" of a golden rectangle B4 If A0 B0 B1 B2 is a golden rectangle, then: A0, Ag, A2 are collinear A1, Ag, A3 are collinear The two lines are cut at right angles Etc. ...
- 27. esthetics and the theory of art - Matila Ghyka
- 28. Golden section - a prototype of thinking! Can be extrapolated in 3D? …but in nD? 1,1,2,3,5,… xn,, x n+1,… xn+2=xn-1+x n x n+1/xn -> 1.618034… A0 A s2 a/b=x A0 / As1 = A1/A s2 A1b A s1 x2-x-1=0; x= (1+√5)/2 = Φ a
- 29. 1,1,1,2,2,3,4,5,7,… an,, a n+1,… a n+1/an -> ? x3-x-1=0;What we discover was anoriginal geometrical 3Dinterpretation of …
- 30. … The plastic numberIn mathematics, the plastic number ρ (also known as the plastic constant) is a mathematicalconstant which is the unique real solution of the cubic equation [2] It has the value its decimal expansion begins with 1.324717957244746025960908854....The plastic number is also sometimes called the silver number
- 31. The name plastic number (het plastische getal in Dutch) was given to this number in 1928 by DomHans van der Laan. Unlike the names of the golden ratio and silver ratio, the word plastic was notintended to refer to a specific substance, but rather in its adjectival sense, meaning something that canbe given a three-dimensional shape
- 32. An other approach to the sameproblem
- 33. The GoldenVolume
- 34. The name plastic number (het plastische getal in Dutch) was given to this number in 1928 by DomHans van der Laan. Unlike the names of the golden ratio and silver ratio, the word plastic was notintended to refer to a specific substance, but rather in its adjectival sense, meaning something that canbe given a three-dimensional shape
- 35. 02D alfa = 45 3D alfa = 600
- 36. 1988-89 3D Leafs from the same tree archetype ? 45 o 60 oThe social revolution of 1989… a result of aprofound change in… Logos? Somethingmore profound is happening?
- 37. Let V1 (n), an initial n-dimensional parallelepiped; the sides L1> L2> L3 >...> Ln, which can be viewed as a set of type: we cut from V1 (n), a parallelipipedic volume:whose projection in 0x1xn plan is a square. The remaining volume,denotedby C 1 (n) is defined as:
- 38. In these conditions,Quantitative relationship between the parts resulting from this iterative algorithm(analogous from our adopted model in the transition from the 2D in 3D) is: and lead to determine the n-dimensional "golden number” in a similar manner to that defined in the transition from 2D to 3D n = space dimension
- 39. n=2 x2=x+1 x(x-1)-1=0 ɸ= 1.618034… Golden 2D number; Golden sectionn=3 x3=x+1 x(x-1)2-1=0 ξ = 1.324717…. Golden 3D number; Golden Volumen=4 x4=x+1 x(x-1)3-1=0 Ψ4=1.220744…n=5 x5=x+1 x(x-1)4-1=0 Ψ5=1.1673043..n xn=x+1 x(x-1)n-1-1 =0 XP is a positive real root of the n-1 equation x(x-1) -1 =0 Returning to the general case of n-dimensional, can be calculated: a) The arithmetic mean of the sides of the body: b) The geometric mean of the sides:
- 40. c) The harmonic mean of the sides of a golden volume, generated in n-dimensional space:it can verify the expresion: The Volume of the n-dimensional golden body is equal to the Mg of itssides, raised to the power n: http://www.csc.matco.ro/conferinta.html
- 41. 2004 Summer school in Gura HumoruluiWe build a golden Volume, talking about natural engineering
- 42. Philosophers, Engineers, Artists…students and professors together …
- 43. Florin Munteanu florin@complexity.ro http://implexus.org/profile/FlorinMunteanuThanks for your attention

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DE INTERES CULTURAL !

VA FELICIT PENTRU TOATE PREZENTARILE !

Alexandra Vasilescu

- Engineering is the pragmatic dimension of human activity, which develop the intellect in disadvantage of the emotional and intuitive behavior; Implications in the imbalance human society development, especially now, in the process of globalization;

- It is needed a 'humanization' of the social ladder; a change of mentality in such a way that the man can be able to focus his mental energy to innovate and create for the Humans quality of life, not only for the raising of the market, for efficiency, for money ;

- Is necessary to develop new emotional/rational skills to interact with Nature, having as a practical effect... increasing the range of sensitivity (just to perceive the ...others and Nature like your own body), ... increasing the responsibility of each individual (it this way we bring the philosophy in the engineering education); a direct approach, by introducing abruptly some philosophy courses in engineering education will not work - it is my opinion;

- To involve indirect and open a natural path to philosophy we can integrate in the engineering studies some basic notion of Complexity Science, we can develop projects related to interaction and co-evolution between 'Living' and 'non-Living' entities in ecosystems (Gaia Vision), generate discussions about social networks and econophysics, etc.. It allows the formation of some holistic skills, the involvement of students in real experiments and finaly can generate a change in the engineers attitude towards the production and techology; (philosophy as a life style)

- Biomimetics, biosemiotics, infodynamic, orto-physics... are disciplines

that can be used like 'awakening' disciplines. In this respect, Complexity Science may be able help the change the actual mentality in engineering education!

The paper tries to focus on some theoretical aspects on morphogenesis phenomena (DLA, Cellular Automata, chaos theory) in order to find out some characteristics of natural patterns (in opposition with the shapes and forms of artefacts). Due to the sensitivity of to the initial conditions, in some cases, this semiotic approach is able to discriminate/decode some very subtle properties of the environment. In this way, the paper suggests a nonconventional approach to characterise/discriminate some geomorphologic arias [4], trying a link with culture and socio-economical behaviour of the habitants. This quite “strange” correlation between the shapes and forms of natural objects and the geophysical environment is now under scientific attention due to the Gaia vision (Planet Earth as a living holistic system) [5]. Again, science of Complexity plays an important role because it allows understanding the structuring role of recursive processes that can model feedback loops and implicitly, auto-regulation processes. The negentropy production, generated by living beings through metabolic processes that ensues the homeostasis of living systems, is put into balance with the implacable trend towards entropy growth, the fundamental property of non-living matter. This “competition” between order vs. disorder, information production vs. entropy growth, etc., induces a special dynamic in Living systems that develops on a non-living 'substrate', and this non-trivial dynamic must be studied using a special methodology. Our work tries to improve the GAIA theory by revealing natural codes, defining special methodologies in archetype finding.

----------------------

[1] Péter Érdi, Complexity Explained, Springer Complexity, (2008)

[2] Marion G. Ceruti, Stuart H. Rubin, Infodynamics: Analogical analysis of states of matter and information, Information Sciences 177 (2007) 969–987

[3] Favareau, D. (Ed.) Essential Readings in Biosemiotics: Anthology and Commentary. Berlin: Springer. (2010)

[4] Stephan Harrison, Philip Dunham; Decoherence, Quantum Theory and Their Implications for the Philosophy of Geomorphology; Transactions of the Institute of British Geographers, New Series, Vol. 23, No. 4, (1998), pp. 501-514

[5] Karnani, M., Annila, A. 'Gaia Again'. Biosystems 95 (1) (2009) pp82–87.