Emerging Complexity: order at the edge of chaos

The Polar Sea. Caspar David Friedrich. 1824

‘Ars Sine Scientia Nihil’

Jean VignotGothic Master Builder1392

‘the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of

mathematical beauty’

D’Arcy Wentworth ThompsonOn Growth and Form

1917

The Golden Section

(http://en.wikipedia.org/wiki/Golden_ratio)

‘The ‘‘symphonic’’, organized planning which, through all the great periods of

European Art, was its characteristic feature, was without any doubt conscious’

Matila Ghyka. The Geometry of Art and Life.

Emerging Complexity: order at the edge of chaos

The Polar Sea. Caspar David Friedrich. 1824

“The passion caused by the great and sublime in nature . . . is Astonishment…… and astonishment is that state of the soul, in which all its motions are suspended, with some degree of horror”

Edmund Burke. Philosophical Enquiry into the Origin of our Ideas of the Sublime and Beautiful. 1757

Descending from the region of the clouds,And starting from the hollows of the earthMore multitudinous every moment, rendTheir way before them - what a joy to roamAn equal among mightiest energies

William Wordsworth. 1770-1850

The Age of Reason

“A mere naturalistic copy of a plant on to

an industrial object will not in itself form

ornament….In order to become ornament,

natural forms must be arranged in some orderly pattern…”

1895

Eugene Grasset. 1897.

“Modern thought”Jencks. 1995

• “The snare laid down in the 17th century that proved to most scientists and thinking people that nature was a machine, that L’homme Machine ruled over the other animals, and that everything was as deterministic, mechanistic and rational as a machine”

Octagonia. The Garden of Cosmic Speculation. Charles and Maggie Jencks

“Nature, however, seems to be based neither on a game of snakes and ladders, where some win and some lose, nor

on a completely pre-ordained set of plans”

“an excessive respect for order is self defeating, since it restricts the possibility of growth”

Alan Powers. Nature in Design. 1999

Tao Ho. 1936-

• …Hinduism, Buddhism and Taoism, particularly those ideas related to cosmology and nature, bear a remarkable similarity to the spirit of new physics and scientific thoughts developed this century…..unity amongst Heaven, Earth and Man….

Cosmic Harmony. Crystal candle stand. For Swarovsky. 1996

A Paradigm Shift

“great towns, are usually badly constructed in comparison with those which are regularly laid out on a plain by a surveyor……The former have large buildings and small buildings indiscriminately placed together…rendering the streets crooked and irregular…it might be said that it was chance rather than the will of men guided by reason, that led to such an arrangement”

Discourse on Method. Descartes. 1637

Le Corbusier. Ville Radieuse. 1930 Batty and Longley. The Fractal City. 1997

“The Universe is much more like a butterfly than a Newtonian machine” Jencks. 1995

“The universe is as unpredictably creative as a mad nineteenth century inventor; it changes its mind and jumps”

ComplexityOrder and chaosSelf regulationNon linear dynamics

Bifurcating Weather Systems

The Lorenz Attractor

Does the Flap of a Butterfly’s Wings in Brazil Set off a Tornado in Texas?

Edward Lorenz. 1972

Order and chaos in dynamic systems

A strange attractor depicts the “chaotic but still ordered organisation of movement around a maxima and minima” It is the symbol of deterministic chaos; nature as wild, unpredictable and disordered but constrained

Strange Attractor

Gallery of Modern Art. Edinburgh. Jencks

The Henan Attractor

This new world view will be most visibly expressed in architecture. Architects express the ideals of an age….Architecture is “built” meaning….architecture reveals what we believe…. Jencks. 1995

It is not just a case of copying forms; but rather it is a matter of getting inside the processes of nature and transforming them through the medium of the human mind........ Powers. 1999

Model. Boilerhouse extension. 1996-9 V & A Museum. Daniel Libeskind.

Aesthetic parallelism between Westernand Eastern art is possible, if the artistis able to penetrate beyond apparent reality in the search for a universalexpression of nature…Tao Ho. 1998

Complexity is the theory of how emergent organisation may be achieved by interacting components pushed far from equilibrium (by increasing energy, matter or information) to the threshold between order and chaos.

The important border or threshold is where the system often jumps, bifurcates or creatively interacts in a new nonlinear, unpredictable way.

Jencks. 1997

Catastrophe theory, folds and bifurcations: the edge between order and chaos

Daisyworld and the Rabbit Cabinet.

Kitchen. Portrack House. Charles Jencks

Nature’s patterns – order and chaos in form and structure

The Guggenheim Museum. Bilbao. Frank Gehry. 1993-7

“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightening travel in a straight line” The Mandelbrot Set

The Fractal Geometry of Nature. Benoit Mandelbrot. 1977

Barnsley’s Fern. 1988

A special mathematical technique…takes a real fern, computes how its branches transform into one another at different scales…then applies the formula by computer using the identified mathematical structure

Bifurcating systems and self similarity

Any form in nature which is self similar is likely to be fractal

Fractal spiral waves in a virtual heart. Dr Arun Holden

Peano Curve. Mandelbrot

Fractal objects are irregular in shape but their irregularity is similar across many scales….enabling them to be described mathematically and to be generated computationally.

Fractal Cities

Michael Batty and Paul Longley

1994

Kagari Miyoshi

Le Soir. Lacquer Box

1991

Eisenman Architects. Staten Island Institute of Arts and Sciences.St George Ferry Terminal. Computer rendering.

Eisenman Architects. Aronoff Centre for Design and Art. University of Cincinnati. 1986-96

“matter in the throes of creation”

Sanford Kwinter

Pyrite

Libeskind. Boilerhouse Exension. V&A

Octagonia. Charles Jencks.

Gatehouse. The Garden of Cosmic Speculation

Portrack

1988-2003

“a clunky multi coloured stick and ball plaything”

This art…..proposes the layering of ideas and patterns into a complex whole. The layers should make one slow down and think, and wonder about received notions. It should celebrate the beauty and organisation of the universe but above all re-supply that sense of awe and wonder

Charles Jencks. 2003

Unlike computer brains, human brains change, develop, deterioriate and forget; this gives us the capacity to think subjectively, to change our opinions, and to forgive.

It is the difference between a mechanical brain and a human mind.

These are our flaws, and they make us human. They also determine whether our creations will be spiritual, inspirational, and poignant.

If we diminish our beautiful capacity to forget and to forgive, to err and to gauge our surroundings with subjectivity, we render ourselves less human and our designs, less personal

Tao Ho. 1998

Subjective rather than rational, Change rather than rule,

Flawed rather than perfect,

Human rather than machine,

Chaos and order,

Fractal rather than geometric,

Random rather than regular

Complexity before purity

Pattern Structure Form & Line