Corian 3d Maths Series

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Corian 3d Maths Series

Firm

Co-de-iT

YEAR

2009

Nature has a mathematical and algorithmic
substrate. Or, better, math and algorithms provide a key to describe and reproduce
natural processes of morphogenesis. Mathematic is a linking principle that
weaves together artists, physicians and mathematicians of course.
More to that extent, beauty also has a
mathematic bottom: throughout history many great artists realized that math was
the key to unlock higher levels of complexity in their expression and
technique, from ancient Greeks to our present day, rigorous exploration coupled
with a personal universe of sensibilities. It seems that we are witnessing an
interest for math in bridging disciplines belonging in origin to science and/or
art: such intensity has a precedent only in the Baroque, when tremendous
progresses of science and philosophy triggered a fruitful exploration of
complexity and continuity both in space and expression: the use of complex
curves, ellipses, platonic solids and derived rules. Looking at the ceiling of
Borromini’s S. Carlo alle Quattro Fontane in Rome what we see is parametric
tessellation in action, self-similar components forming a continuous surface.
The same process was explored several centuries later also by M.C. Escher,
challenging Borromini’s spatial complexity on a pure perceptive level, still
with the same underlying strong basis in mathematic principles that drive
geometry.
Designing panels is something that deals with
the issue of tessellation, the discretization of the continue through
components. These panels are an exploration of mathematical algorithms applied,
through parametric design in Rhinoscript and Grasshopper, to a new
3-dimensional production technique for DuPont Corian®. Even though each panel gravitates
around one dominating principle, they surely embed more than one: each of them
is a narration of a particular generative process, but reversing the direction
that goes from a process to its generated form, it is true that forms can be
descriptive of many processes. For example the Penrose tiling, the Fibonacci
sequence and the golden ratio are intricately related and they should be
considered as different aspects of the same phenomenon.
One of the more interesting aspects in our
design exploration is the application of algorithms through parametric
strategies to generate modulations, oscillations between stable states, (rather
than an unvaried repetition) and balance them with issues of seamless tiling
within a square-angled framed component, material logic and production
techniques.

Panels description

. Moiré
Moiré discovered that superimposed patterns
could generate other, unpredicted, interference patterns. The same phenomenon
happens when a couple of objects fall synchronously into the water. The way
waves create such patterns is fascinating in its poetic complexity. When waves
morph the water surface it smoothly passes from a quiet plane to a rippled skin,
rich of reflections and dynamic variations. Math here generates a wave
interference, catching that moment of smooth transition. The soft gradient
between flatness and ripples also denotes a curvilinear and plastic interplay
that enhances the surface’s qualities.

. parameters
The panel is subdivided into longitudinal
stripes, the distance of every stripe middle curve from an hypothetic attractor
point governs the height and the deviation of the sinusoidal curves which are
the surface generators. The optical result of this undulations determines vibrant
Moiré effect on the panel surface.

. Phyllotaxis

Phyllotaxis literally means the organization of
leaves around a stem, but it’s generally referred to any law of organization of
organs in an organism. The sunflower’s head is a typical example and piece of
design in itself: the seeds are densely packed and form spirals, both clockwise
(34) and counterclockwise (55). The hidden secret beneath this complex harmony
is a sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34 … this is the beginning of the
Fibonacci sequence. Any successive element is radially placed every 137.5° in growing
distance from the center. The overall result shows two opposite orders of
spirals, which respective number are a close couple in the Fibonacci sequence.

. parameters
The shape of the panel is inspired to the Fibonacci
spiral and spiral phyllotaxis algorithm based on two sets of spirals revolving
in opposite directions. The cell shapes emerging from this intersection are the
base for a series of inner curves scaled and moved proportionally to the
inverse of their distance from the center of the spiral. The result surface
looks like a flowerish bas-relief.
The holes in the surface are organized as a
whorl, which is calculated following the phyllotaxis algorithm (137.5 angle
spiral) filled with two sets of spirals generated by every nth point, where n
is a number in the Fibonacci sequence for one set (turning clockwise), and the
following number for the other set (counterclockwise). The generated cells are
completed by a closed curve passing from each vertex and scaled (according to
the inverse of the distance from the whorl center) to form the hole.

. Fourier
Vibrations are sudden moments when we sense a
rapid sequence of impulses changing an apparent calm or stability. Clusters of
mixed and apparently quasi-random short waves merge together and form a
composite signal which repeats and causes the vibration. Waves and undulatory
events are mathematically described by a function that belongs to trigonometry:
sine wave. It is a function that cyclically outputs numbers from -1 to 1 and
back. As simple as it may seem, this tiny function describes a lot of phenomena
linked to the flow of energy, from sea waves to light and sound, from the chirp
of chicadas to the shivers caused by emotions.

. parameters
The panel surface is striped lengthwise with
random height ribbons, then the ribbons themselves are subdivided in random
spans which alternately are bulged to form waves.

. Gauss
Gauss curve is quite an advanced mathematical
concept, but it has remarkable implications with the real world. Its most known
use is in the statistic graphic description of the distribution of a large
number of events. The Gaussian distribution is also commonly called the "normal
distribution" and is often described as a "bell-shaped curve".
This kind of curve is used in several ways, from the description of physical
events to the prediction of a process performance. Moreover, in software
programming Gaussian distribution is typically used to control soft transitions
and modulations.

. parameters
The shape of the panel is the results of a process of subdivision of it
into a variable number of cells. Every single surface is thought like a
diaphragm composed by two modular shapes. The aperture determinated by this
shapes is governed by the values of a fully controlled gaussian curve. One of
this shapes move into space with a distance parameter to create a sort of
pocket.

. Fibonacci
1, 1, 2, 3, 5, 8, 13, 21, 34 … this is the
beginning of the Fibonacci sequence, an infinite string of numbers (in which
each number is the sum of the 2 precedents) named after, but not invented by,
the 13th century Italian mathematician Fibonacci. It may look like a piece of
mathematical arcane, but the Fibonacci sequence shows up, time and time again,
among the structures of the natural world and even in the products of human
culture. From the Parthenon proportions to pine cones, from the petals and
seeds on a sunflower to the paintings of Leonardo da Vinci, the Fibonacci
sequence seems to be cast into the world around us.

. parameters
The shape of the panel is closely linked to the Fibonacci spiral path,
the squares built on it and the resulting golden rectangle. Every single
squares is transformed into a parametric cell with a variable maximum height,
taper angle and aperture size. The resulting squares materialize the
proportional Fibonacci sequence onto the final shape of the panel.

. Voronoi
The Voronoi diagram of a collection of
geometric objects is a partition of space into cells, each of which consists of
the place of points which are closer to one particular object than to any others.
These diagrams, their boundaries (medial axes) and their duals (Delaunay
triangulations) are descriptive models of close-packing processes and have been
reinvented (under different names), generalized, studied, and applied many
times over in many different fields. Voronoi diagrams tend to be involved in
situations where a space should be partitioned into "spheres of
influence", including models of crystal and cell growth as well as protein
molecule volume analysis. In the last years the Voronoi pattern has also been widely
used into computer graphics and design.
. parameters
The shape of the panel is the results of a
Voronoi diagram based on an array of points subdivision of a spiral. Every
single voronoi cell boundary generate another offset and interpolated curve
shifted at a parametric height. So the original Voronoi cell contour and those
curve are the base for an operationl patching that provides a characteristic
cell tessellation.Design: Co-de-iT (Alessio Erioli, Andrea Graziano), Corrado TibaldiCorian® is a registered trademark of E.I. Du Pont de Nemours

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Alessio Erioli

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