Emerging Complexity: order at the edge of chaos
The Polar Sea. Caspar David Friedrich. 1824
‘Ars Sine Scientia Nihil’
Jean Vignot
Gothic Master Builder
1392
‘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 Thompson
On Growth and Form
1917
The Golden Section
(http://en.wikipedia.or
g/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 earth
More multitudinous every moment, rend
Their way before them - what a joy to roam
An 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
Le Corbusier. Ville Radieuse. 1930
Batty and Longley. The Fractal City. 1997
“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
“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”
Complexity
Order and chaos
Self regulation
Non linear dynamics
Order and chaos in dynamic systems
The Lorenz Attractor
Does the Flap of a Butterfly’s Wings
in Brazil Set off a Tornado in Texas?
Edward Lorenz. 1972
Bifurcating Weather 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
The Henan Attractor
Gallery of Modern Art. Edinburgh. Jencks
Strange 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
Aesthetic parallelism between Western
and Eastern art is possible, if the artist
is able to penetrate beyond apparent
reality in the search for a universal
expression of nature…
Tao Ho. 1998
Model. Boilerhouse extension. 1996-9
V & A Museum. Daniel Libeskind.
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
Any form in nature
which is self similar is
likely to be fractal
Bifurcating systems and self similarity
Peano Curve. Mandelbrot
Fractal spiral waves in a virtual
heart. Dr Arun Holden
Fractal Cities
Michael Batty and Paul Longley
1994
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.
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 resupply 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
Pattern Structure Form & Line
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