The Wishing Well

something caught in between dimensions – on its way to becoming more.

Summary

The Wishing Well is the physical manifestation, a snap-shot, of a creature caught in between dimensions – frozen in time. It is a digital entity that has been extracted from its home in the fractured planes of the mathematical realm; a differentially grown curve in bloom, organically filling space in the material world.

The notion of geometry in between dimensions is explored in a previous post: Shapes, Fractals, Time & the Dimensions they Belong to

 

Description

The piece will be built from the bottom-up. Starting with the profile of a differentially grown curve (a squiggly line), an initial layer will be set in pieces of 2 x 4 inch wooden studs (38 x 89 millimeter profile) laid flat, and anchored to the ground. Each subsequent layer will be built upon and fixed to the last, where each new layer is a slightly smoother version than the last. 210 layers will be used to reach a height of 26 feet (8 meters). The horizontal spaces in between each of the pieces will automatically generate hand and foot holes, making the structure easily climbable. The footprint of the build will be bound to a space 32 x 32 feet.

The design may utilize two layers, inner and out, that meet at the top to increase the structural integrity for the whole build. It will be lit from within, either from the ground with spotlights or with LED strip lights following patterns along the walls.

Different Recursive Steps of a Dragon Curve

Ambition

At the Wishing Well, visitors embark on a small journey, exploring the uniquely complex geometry of the structure before them. As they approach the foot of the well, it will stand towering above them, undulating organically across the landscape. The nature of the structure’s curves beckons visitors to explore the piece’s every nook and cranny. Moreover, its stature grants a certain degree of shelter to any traveller seeking refuge from the Playa’s extreme weather conditions. The well’s shape and scale allows natural, and artificial, light to interact in curious ways with the structure throughout the day and night. The horizontal gaps between every ‘brick’ in the wall allows light to filter through each layer, which in turn casts intriguing shadows across the desert. This perforation also allows Burners to easily, and relatively safely, scale the face of the build. Visitors will have the opportunity to grant a wish by writing it down on a tag and fixing it to the well’s interior.

171108 - Burning Man Timber Brick Laying Proposal View 2.jpg

 

Philosophy

If you had one magical (paradox free) wish, to do anything you like, what would it be?

Anything can be wished for at the Wishing Well, but a wish will not come true if it is deemed too greedy. Visitors must write their wish down on a tag and fix it to the inside of the well. They must choose wisely, as they are only allowed one. Additionally, they may choose to leave a single, precious, offering. However, if the offering does not burn, it will not be accepted. Visitors will also find that they must tread lightly on other people’s wishes and offerings.

The color of the tag and offering are important as they are associated with different meanings:

  • ► PINK – love
  • ► RED – happiness, joy, success, good luck, passion, vitality, celebration
  • ► ORANGE – change, adaptability, spontaneity, concentration
  • ► YELLOW – nourishment, warmth, clarity, empathy, being free from worldly cares
  • ► GREEN – growth, balance, healing, self-assurance, benevolence, patience
  • ► BLUE – conservation, healing, relaxation, exploration, trust, calmness
  • ► PURPLE – spiritual awareness, physical and mental healing
  • ► BLACK – profoundness,  stability, knowledge, trust, adaptability, spontaneity,
  • ► WHITE – mourning, righteousness, purity, confidence, intuition, spirits, courage

The Wishing Well is a physical manifestation of the wishes it holds. They are something caught in between – on their way to becoming more. I wish for guests to reflect on where they’ve been, where they are, where they are going, and where they wish to go.

171108 - Burning Man Timber Brick Laying Proposal View 1.jpg

Life’s First Flicker

LifeFirstFlicker_External_Night.png

Project Summary

Translucent fractal ball animated by dancing color changing lights symbolizing the very first spark at the beginning of the universe as well as the spark of life that our species is on both an eternal mission to keep alight and is in the final stages of creating anew with artificial intelligence.

Physical Description

A 20 foot diameter translucent form, made of twelve identical five petal polypropylene origami flowers arranged as a dodecahedron each with two smaller flower at their centers and intricately lazercut with a 2d filigree depicting the overall form. All the flowers are tied to each other and to a timber dodecahedral internal skeleton with concealed zip ties. The creased polypropylene held in tension by the origami folds themselves provide the rest of the stability. LED DMX lights sit in the five points which touch the ground, facing upwards, illuminating the entire form.

LifesFirstFlicker_External_Day

Philosophy

At the end of Isaac Asmiov’s book ‘The last question’ a disembodied AI is the last mark of the human race left in an empty entropic universe. It remains calculating the answer to the last question it was asked, and, unable to find a recipient for it’s solution it says ‘Let there be light’ and creation begins again.

This piece is shaped as a tangible interpretation of this spark. The spark at the first second of the universe and the spark of life which our civilization is racing to create in a sentient self learning AI. This moment, when our creations become self aware, is the theme of burning man 2018 and also likely to be the most important moment in our species’ history. Self teaching AI will rapidly become so powerful it will effectively be a deity. This pavilion’s purpose is to draw the visitors attention to this rapidly approaching moment and consider how we should design this mind before it is too late.

Burners can pass by or play with the spark and think it is just a cool shape, but those who climb up inside what is figuratively a snapshot right at the beginning of new life and the universe, can take a moment to pause and ponder from within, whether their life’s endeavor is relevant in the face of coming AI, what our species’ current knowledge may lack and how it could be codified and explained to a machine and how lucky we are as a generation to have both been born late enough to see AI’s birth, and early enough to have known life before it.


<p><a href=”https://vimeo.com/244593633″>Life’s First Flicker: Burning Man 2018 Art proposal</a> from <a href=”https://vimeo.com/user71835996″>Benjamin Street</a> on <a href=”https://vimeo.com”>Vimeo</a&gt;.</p>

Fractals vs Digital Fabrication

Since the last post on the 23rd October our students have been exploring how to materialise their research into fractals (which they generated with Mandelbulb3D). The conflict between endless geometry and finite material world creates a creative tension that pushes innovation in digital design and fabrication. From parametric equations to parametric design, students have explored fractals as self-generating computer images and attempted to control them, first through changing their variables and then by extracting the most appealing fragments and recreating them using Grasshopper3D . From pure voxel-based images to NURBS or meshes and to 3D printing, laser-cutting, thermo-forming, casting..etc… students are confronted to the limitation of the computer’s memory and processing power as well as materials and numerical control (NC) programming language such as Gcode.

Navigating through fractals, exploring their recursive unpredictability to create more finite prototypes is like walking through the forest and noticing a beautiful flower to design your next building – it helps to let go of a fully top-down approach to architecture, it encourages a collaborations with your computer and a deep understanding of machines and materials. It anticipates a world in which the computers will have an intelligence of their own, where the architect will guide it onto a learning path instead of giving him instructions.  Using infinite fractals to inspire designs helps instill infinity within the finite world – bringing a spiritual dimension to our everyday life. 

Below is a selection of our students Brief01 journey so far:

Manveer Sembi's  Aexion Fractal imported from Mandelbulb3D to Rhino and 3D Printed
Manveer Sembi’s Aexion Fractal imported from Mandelbulb3D to Rhino and 3D Printed
Alexandra Goulds' MIXPINSKI4EX fractal
Alexandra Goulds’ MIXPINSKI4EX fractal
Michael Armfield's parametric exploration of the Amazing Surf Fractal
Michael Armfield’s parametric exploration of the Amazing Surf Fractal
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Michael Armfield’s parametric exploration of the Amazing Surf Fractal
Michael Armfield's parametric exploration of the Amazing Surf Fractal
Michael Armfield’s parametric exploration of the Amazing Surf Fractal
Henry McNeil's Fibreglass modelling of the Apollonian Gasket.
Henry McNeil’s Fibreglass modelling of the Apollonian Gasket.
Henry McNeil's 3D printed support for his fractal
Henry McNeil’s 3D printed support for his fractal
Henry McNeil's 3D printed fractal imported from Mandelbulb3d to Rhino
Henry McNeil’s 3D printed fractal imported from Mandelbulb3d to Rhino
Henry McNeil's Fibreglass prototype from Ping-Pong and tennis balls
Henry McNeil’s Fibreglass Fractal prototype from Ping-Pong and tennis balls
Ed Mack's laser-cut Fractal Dodecahedron.
Ed Mack’s laser-cut Fractal Dodecahedron.

 

Ben Street's auxetic double curved paper models
Ben Street’s auxetic double curved paper models
Ben Street's single curved paper models
Ben Street’s single curved paper models
Lewis Toghill's composite shells with Jesmonite, plaster, wax and fibre glass
Lewis Toghill’s composite shells with Jesmonite, plaster, wax and fibre glass

20171109_114548Alexandra Goulds' flexible timber node

Alexandra Goulds' flexible timber node
Alexandra Goulds’ flexible timber node
Manveer Sembi's paper cutting for double curved paper sphere
Manveer Sembi’s paper cutting for double curved paper sphere
James Marr's single curved wood node with rotational geometry for subdivided mesh geometry
James Marr’s single curved wood node with rotational geometry for subdivided mesh geometry
Nick Leung's 3D prints of the different recursive steps of a space-filling curve
Nick Leung’s 3D prints of the different recursive steps of a space-filling curve

 

Rebecca Cooper's Fractal truss study on parametric structural analysis tool Karamba3D
Rebecca Cooper’s Fractal truss study on parametric structural analysis tool Karamba3D
Manon Vajou's burnt polypropelene studies
Manon Vajou’s burnt polypropelene studies

20171026_154920

Thursday 19th October Pin-Up

Diploma Studio 10 is back with 21 talented architecture students from 4th and 5th year working on the Brief01:Fractals. Here is an overview of their experiments so far after 4 weeks of workshops.

Sara Malik’s Dodecahedron IFS Fractal (with Julia set) modelling with a handheld 3D printing pen.
Sara Malik’s matrix of fractals using Mandelbulb3D
Ola Wojciak’s beautiful collection of Mandelbulb3D experiments using the Msltoe_Sym Formula with the Koch Surface.
Ola Wojciak’s beautiful collection of Mandelbulb3D experiments using the Msltoe_Sym Formula with the Koch Surface.
Ola Wojciak’s beautiful collection of Mandelbulb3D experiments using the Msltoe_Sym Formula with the Koch Surface.
Ola Wojciak’s first physical model expressing her fractals using ropes cast in plaster
Beautiful twisting L-System from James Marr on Grasshopper3D using Anemone.
Matthew Chamberlain’s Strange Attractors Study using a combination of Blender and Grasshopper3D
Matthew Chamberlain’s Strange Attractors Study using a combination of Blender and Grasshopper3D
Matthew Chamberlain’s Strange Attractors Study using a combination of Blender and Grasshopper3D
Matthew Chamberlain’s Strange Attractors Study using a combination of Blender and Grasshopper3D
Manveer Sembi’s Aexion Fractal Matrix with Julia Set.
Michael Armfield’s Amazing Surf Fractal on Mandelbulb3d
Lewis Toghill’s Fractal Matrix using the cyripple , KalilinComb, sphereIFS, Isocahedron and genIFS fractals.

 

Shapes, Fractals, Time & the Dimensions they Belong to

First, second and third dimensions, and why fractals don’t belong to any of them, as well as what happens when you get into higher dimensions.

Foreword

In this post, I’m going to try my best to explain the first, second, and third dimensions, and why fractals don’t belong to any of them, as well as what happens when you get into higher dimensions. But before getting into the nitty-gritty of the subject, I think it’s worth prefacing this post with a short note on the nature of mathematics itself:

Alain Badiou said that mathematics is a rigorous aesthetic; it tells us nothing of real being, but forges a fiction of intelligible consistency. That being said, I think it’s interesting to think about whether or not mathematics were invented or discovered – whether or not numbers exist outside of the human mind.

While I don’t have an answer to this question (and there are at least three different schools of thought on the subject), I do think it’s important to keep in mind that we only use math as a tool to measure and represent ‘real world’ things. In other words, our knowledge of mathematics has its limitations as far as understanding the space-time continuum goes.

 

1.0 Traditional Dimensions

In physics and mathematics, dimensions are used to define the Cartesian plains. The measure of a mathematical space is based on the number of variables require to define it. The dimension of an object is defined by how many coordinates are required to specify a point on it.

It’s important to note that there is no ‘first’ or ‘second’ dimension. It’s a bit like pouring three cups of water into a vase and asking someone which cup is the first one. The question doesn’t even make sense.

Capture4
Excerpt from ‘minutephysics’
We usually arbitrarily pick a dimension and calling it the ‘first’ one.

 

1.1 – Zero Dimensions

 O2FFp

Something of zero dimensions give us a point. While a point can inhabit (and be defined in) higher dimensions, the point itself has a dimension of zero; you cannot move anywhere on a point.

1.2 – One Dimension

R1

A line or a curve gives us a one-dimensional object, and is typically bound by two zero-dimensional things.
Only one coordinate is required to define a point on the curve.
Similarly to the point, a curve can inhabit higher dimension (i.e. you can plot a curve in three dimensions), but as an object, it only possesses one dimension.
Another way to think about it is: if you were to walk along this curve, you could only go forwards or backward – you’d only have access to one dimension, even though you’d be technically moving through three dimensions.

 

1.3 – Two Dimensions

 R2

Surfaces or plains gives us two-dimensional shapes, and are typically bound by one-dimensional shapes (lines/curves).

A plain can be defined by x&yy&z or x&z; more complex surfaces are commonly defined by u&v values. These variable are arbitrary, what is important is that there are two of them.

A surface can live in three+ dimensions, but still only possesses two dimension. Two coordinate are required to define a point on a surface. For example a sphere is a three-dimensional object, but the surface of a sphere is two-dimensional – a point can be defined on the surface of a sphere with latitude and longitude.

 

1.4 – Three Dimensions

rotated-cube

A volume gives us a three-dimensional shape, and can be bound by two-dimensional shapes (surfaces).

Shapes in three dimensions are most commonly represented in relation to an x, y and z axis. If a person were to swim in a body of water, their position could be defined by no less than three coordinates – their latitude, longitude and depth. Traveling through this body of water grants access to three dimensions.

 

2.0 Fractal Dimensions

Fractals can be generally classified as shapes with a non-integer dimension (a dimension that is not a whole number). They may or may not be self-similar, but are typically measured by their properties at different scales.

Felix Hausdorff and Abram Besicovitch demonstrated that, though a line has a dimension of one and a square a dimension of two, many curves fit in-between dimensions due to the varying amounts of information they contain. These dimensions between whole numbers are known as Hausdorff-Besicovitch dimensions.

 

2.1 – Between the First & Second Dimensions

A line or a curve gives us a one-dimensional object that allows us to move forwards and backwards, where only one coordinate is required to define a point on them.

Surfaces give us two-dimensional shapes, where two coordinate are required to define a point on them.

ch08_04-660x313
Here is a shape that cannot be classified as a one-dimensional shape, or a two-dimensional shape. It can be plotted in two dimensions, or even three dimensions, but the object itself does not have access the two whole dimensions.

If you were to walk along the shape starting from the base, you could go forwards and backwards, but suddenly you have an option that’s more than forwards and backwards, but less than left and right.

You cannot define a point on this shape with a single coordinate, and a two coordinate system would define a point off of the shape more often than not.

hausdorff_dimension_by_dnangel7
Each fractal has a unique dimensional measure based on how much space they fill.

 

2.2 – Between the Second & Third Dimensions

koch-render.png
Developing Koch Snowflake
The same logic applies when exploring fractals plotted in three dimensions:

Surfaces give us two-dimensional shapes, where two coordinate are required to define a point on them.

A volume gives us a three-dimensional shape where a point could be defined by no less than three coordinates.

While these models live in three dimensions, they do not quite have access to all of them. You cannot define a point on them with two coordinates: they are more than a surface and less than a volume.

d60e89184e7eb476ccfce4112c948f47
Fourth Iteration Menger Sponge
The Menger Sponge for example has (mathematically) a volume of zero, but an infinite surface area.

 

2.3 – Calculating Fractal Dimensions

The following are three methods of calculating Hausdorff-Besicovitch dimension:
• The exactly self-similar method for calculating dimensions of mathematically generated repeating patterns.
• The Richardson method for calculating a dimensional slope.
• The box-counting method for determining the ratios of a fractal’s area or volume.

 

On another note:

In theory, higher (non-integer) dimensional fractals are possible.
As far as I’m concerned however, they’re not particularly good for anything in a three-dimensional world. You are more than welcome to prove me wrong though.

 

3.0 Higher Dimensions

Sadly, living in a three-dimensional world makes it especially difficult to think about, and nearly impossible to visualise, higher dimensions. This is in the same way that a two-dimensional being would find it impossibly hard to think about our three-dimensional world, a subject explored in the novel ‘Flatland’ by Edwin A. Abbott.

That being said, it’s plausible that we experience much higher dimensions that are just too hard to perceive. For example, an ant walking along the surface of a sphere will only ever perceive two dimensions, but is moving through three dimensions, and is subject to the fourth (temporal) dimension.

 

3.1 – The Fourth Dimension (Temporal)

If we consider time an additional variable, then despite the fact that we live in a three dimensional world, we are always subject to (even if we cannot visualize) a fourth dimension.

Neil deGrasse Tyson puts it quite plainly by saying:
“[…] you have never met someone at a place, unless it was at a time; you have never met someone at a time, unless it was at a place […]”

Suppose we call our first three dimensions x, y & z, and our fourth t: latitude, longitude, altitude and time, respectively. In this instance, time is linear, and time & space are one. As if the universe is a kind of film, where going forwards and backwards in time will always yield the exact same outcome; no matter how many times you return to a point in point time, you will always find yourself (and everything else) in the exact same place.
However time is only linear for us as three-dimensional beings. For a four-dimensional being, time is something that can be moved through as freely as swimming or walking.
Capture
Excerpt from ‘Seeker’

 

3.2 – The Fourth Dimension (Spacial)

If we explore spacial dimensions, a four-dimensional object may be achieved by ‘folding’ three-dimensional objects together. They cannot exist in our three-dimensional world, but there are tricks to visualise them.

roj5

We know that we can construct a cube by folding a series of two-dimensional surfaces together, but this is only possible with the third dimension, which we have access to.

Cube-Rotation

 

If we visualise, in two dimensions, a cube rotating (as seen above), it looks like each surface is distorting, growing and shrinking, and is passing through the other. However we are familiar enough with the cube as a shape to know that this is simply a trick of perspective – that objects only look smaller when they are farther away.

In the same way that a cube is made of six squares, a four-dimensional cube (hypercube or tesseract), is made of eight cubes.

  • A line is bound by two zero-dimensional things
  • A square is bound by four one-dimensional shapes
  • A cube is bound by six two-dimensional surfaces
  • A hypercube, bound by eight three-dimensional volumes

It looks like each cube is distorting, growing and shrinking, and passing through the other. This is because we can only represent eight cubes folding together in the fourth dimension with three-dimensional perspective animation.

HCube-Folding
3D representation of eight cubes folding in 4D space to form a Hypercube

Perspective makes it look like the cubes are growing and shrinking, when they are simply getting closer and further in four-dimensional space. If somehow we could access this higher dimension, we would see these cubes fold together unharmed the same way forming a cube leaves each square unharmed.

Below is a three-dimensional perspective view of hypercube rotating in four dimensions, where (in four-dimensional space) all eight cubes are always the same, but are being subjected to perspective.

 

AK986lrhNHiZq

 

3.3 – The Fifth and Sixth Dimensions

On the temporal side of things, adding the ability to move ‘left & right’ and ‘up & down’ in time gives us the fifth and sixth dimensions.

(For example: x, y, z, t1, t2, t3)

This is a space where one can move through time based on probability and permutations of what could have been, is, was, or will be on alternate timelines. For any one point in this space, there are six coordinates that describe its position.

terminator-arnold-as-terminator__131206182643
In spacial dimensions, it is theoretically possible to fold four-dimensional objects with a fifth dimension. However, it becomes increasingly difficult for us to visualise what is happening to the shapes that we’re folding.
s1-coxeter
In theory, objects can keep being folded together into higher and higher spacial dimensions indefinitely. (R1, R2, R3,R4,R5, R6, Retc.)

There’s a terrific explanation of what happens to platonic solids and regular polytopes in higher dimensions on Numberphile: https://youtu.be/2s4TqVAbfz4

 

3.4 – Even Higher Dimensions

If we can take a point and move it through space and time, including all the futures and pasts possible, for that point, we can then move along a number line where the laws of gravity are different, the speed of light has changed.

Dimensions seven though ten are different universes with different possibilities, and impossibilities, and even different laws of physics. These grasp all the possibilities and permutations of how each universe operates, and the whole of reality with all the permutations they’re in, throughout all of time and space. The highest dimension is the encompassment of all of those universes, possibilities, choices, times, places all into a single ‘thing.’

These ten time-space dimensions belong to something called Super-string Theory, which is what physicists are using to help us understand how the universe works.

Calabi_yau_formatted.svg
Cross section of the quintic Calabi–Yau manifold
There may very well be a link between temporal dimensions and spacial dimensions. For all I know, they are actually the same thing, but thinking about it for too long makes my head hurt. If the topic interests you, there is a philosophical approach to the nature of time called ‘eternalism’, where one may find answers to these questions. Other dimensional models include M-Theory, which suggests there are eleven dimensions.

While we don’t have experimental or observational evidence to confirm whether or not any of these additional dimensions really exist, theoretical physicists continue to use these studies to help us learn more about how the universe works. Like how gravity affects time, or the higher dimensions affect quantum theory.

Celestial Field


Whatever your creed your reliance on the sun is unquestionable.

We have worshipped it as a God.

Spent lifetimes studying it through science.

Yet human hands will never touch its surface.

Celestial Field brings our sun to the Playa for us to dance in its glory.

Triggering our own solar flare.

light-rod-render_close-up-night
Internal perspective of the Celestial Field Pavilion

 

From the dawn of time the sun has been a constant in human life. It has been central to the beliefs of nearly every civilisation throughout history. What was once an astrological wonder sustaining life; dictating when to plant and harvest our crops; evolved into a god and deity, woven into the stories and teachings of nearly every culture, from the Egyptians to the Ancient Greeks and even Christianity.

sun-symbols-across-the-globe
Sun symbolism from across the globe and through the ages

 

The oldest man-made structures in the world have resounding astrological connections to both the sun and constellations, covered in carvings they unquestionably align to major astrological events.

Newgrange in Boyne Valley, Ireland, thought to be built in 3500BC, has a tomb in which sits a stone basin lit by a single beam of light at sunrise on the winter solstice.

 

newgrange-sunrise
Newgrange Tomb- Borne Valley, Ireland; built around a single beam of light that exists only for a moment each year

 

The Egyptians, Greeks, and Christians have all referenced the sun within their religion and beliefs.

The Egyptians in 3000BC had Ra, the Greeks in 400BC believed Helios to be God of the sun, and Christians have often depicted Jesus in front of what is thought by many to be the solar cross.

sun-worship-in-religion
Ra, Helios and Jesus all depicted with solar symbols

 

In the past the sun has been depicted as a 2Dimensional disk of light travelling across the sky before dying only to be reborn at sunrise.

The Ancient Greeks believed Helios to be the personification of the sun. A man with a many rayed crown of light, pulling the sun across the open sky with a horse drawn chariot. The Helios named after the Greek god has been used and adapted through the ages, with one of the most recognisable iterations being the logo of global corporation BP which symbolises “a number of things – not least the greatest source of energy … the sun itself..” – bp.com

 

helios-geometric-symbol_01
Building the Helios

 

This once celestial being has now become a tangible thing. Through advances in our technological and scientific capability we have gained an understanding of the suns chemical make-up, uncovering many of its secrets from sun spots to solar flares. Although we have developed an increased understanding of the forces driving the sun, it is still no more accessible to us mere humans than on the first day on earth remaining an impenetrable sphere in the sky only to viewed from a far.

 

light-sphere
Physical model light testing

 

digital-light-sphere

Digital animation of lighting tests

 

The suns surface has taught us much. Galileo’s sun spot diagrams unknowingly demonstrated the unique fluidity of the suns chromosphere. Further study of these sun spots and magnificent solar flares proved that the surface of the sun is covered in billions of interlaced magnetic fields all interacting together to form the whole. When these fields cross swirling plasma burst in an instance out into the corona bringing with it immense light displays that can be seen on earth as the aurora.

 

magnetic-fields
Recording magnetic fields with computer models and physical experiments

 

In an age where endless streams of newfound knowledge are accessible with the touch of a finger – it is easy to lose our sense of innocent amazement and unquestioning awe. We have a constant need for explanation of why and how phenomena exist, no longer blindly excepting their beauty and revelling in it.

The indescribable beauty of these gigantic magnetic fields can often be lost and forgotten in the mundane when scaled down to earthly objects. Viewing them at a micro scale allows us to connect with their other-worldly nature.

macro-magnets
Macro photographs of physical tests of magnetic structure using iron filings

 

Science has taught us how a magnet attracts and repels enabling use in industry, medicine and everyday life. And as our knowledge expands, we move from child to adulthood and our desire to play diminishes – burdened by explanations and reasoning; we are no longer in awe of our ability to make metal move without laying hands on it. It has become the norm and the expected, it is no longer ‘magic’.

Life should be fun and full of mesmerising moments. Our increased knowledge should enable and enhance our experience of ‘magic’ not hinder it.

 

suspended-pins
Experimenting with magnetism to define levels of sensitivity for large scale interaction

 

Celestial Fields captures the unexplainable wonderment the sun once held and makes it accessible through modern mediums, combining two worlds; science and enchantment, imbedding them on the Playa at Black Rock City, Nevada, for people to explore and lose themselves in.

Thousands of swaying rods made of tubes of one-way mirror form an undulating field, rising high above your head, and falling like the plasma pulled in all directions by the phenomenal magnetic forces found on our sun.

By day a field of mirrors reflect and intensify the suns natural beauty and power. Creating a maze of ever changing light to explore, push through and play within. At sunset everything transforms. The field morphs, bursting into a sea of glowing beams reacting to movement and mimicking the fluid, almost pulsing nature of the suns corona.

Like the chromosphere, magnetic fields have informed density and pattern, creating patches of pure brightness and areas as dark as sunspots. With each rod built on a spring loaded base it can be pushed a manipulated, enabling you to forge your own path through the densest areas of Celestial Field, parting rods like magnets repelling polarised iron.

 

Individual rods are clad in a one-way mirror film - creating a reflection of the desert in the day and an illuminated environment at night
Individual rods are clad in a one-way mirror film – creating a reflection of the desert in the day and an illuminated environment at night

 

Movement through the sprung rods creates interest not only for the participants but also onlookers. During daylight hours people weaving in and out can be seen across the playa through the constant glinting of the sun on the reflective rods. An ever changing shimmer, like sunlight dancing across water in the distance, drawing people in from all directions out of wonder and intrigue.

Once the sun has set the lights come on, and the show only gets better. The rods now glow and pulse, changing colour, transforming the world around them – each equipped with a sensor so as to react to movement as people push past; creating tracks of swirling light shifting like the turbulent surface of the sun. Areas of intense and overwhelming light can occur when people team together to trigger a cluster of rods forming a concentration of light evocative of a solar flare.

The sun is not solely about light, with it comes inevitable darkness. Shadows too have been used throughout time as a symbol in opposition to that of the sun; and in this instance the areas of shadow formed in the magnetic layout create areas of calm within the thrill of the lights where one can sit and ponder everything from the dessert to the sky and the sun that brings life to earth.

sun-spot-to-system
The pavilion layout is informed by the patterns of sunspots and flares forming on the suns surface

 

What was once worshipped as a distant god and celestial being can now exist on the surface of the earth as a Celestial Field in Nevada. The sun has risen and set, bringing with it heat and light; powering life on earth since the dawn of time, a focus of incomprehensible wonder and fascination for each and every culture across the globe.

Celestial Field intends to reignite our faith in the intangible, while showing us there are powers and beauty still to be found in the modern world.

 

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Cubic Mandala

The Symbol

The Mandala – Sacred Geometry in Buddhist Art

“We can also discuss the mandala in terms of the soul. The soul is the totality of the mandala. Essence arises in the soul, but for a long time… the soul is not completely essentialized; only part of it is. The rest of the field of the mandala – the rest of the consciousness of the soul – is composed of all your mental, emotional and physical experiences. The thread is defined by the center of the soul, and we can know that center most specifically and in a delineated way by recognizing the essential presence and what quality is manifesting.”   – A.H.Almaas                                                                                                                                 

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The word Mandala derives from:

manda =essence, la =container

Thus, the word Mandala translates as “the container of the essence”

However, as an image the mandala is a symbol representing both the mind and the body of the Buddha.

In esoteric Buddhism, the Mandala’s main principle is the presence of the Buddha in it. This can be represented either as a tree, a wheel or as a jewel, or in other symbolic manifestations.

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The Centre

The Mandala is consecrated to a deity. In its creation, a line materializes out of the dot, while other lines are drawn up to the point where they intersect, creating in that way triangular geometrical patterns. The central area of the Mandala is the residence of the deity. Each Mandala has its own resident deity, with whom the mandala is identified. The circle drawn around the deity’s residence stands for the dynamic consciousness of the initiated. It is the gathering point, in which all the outside forces are drawn.

The centre is visualised as the essence and the circumference as grasping.

In its complete form Mandala means:

Grasping the essence.

The residence of the deity is located in the square structure concentrically within the surrounding circles. The outlying square symbolizes the physical world bound in four directions, which are represented by the four gates, which in turn symbolize the bringing together of the four boundless thoughts.

Loving Kindness

Compassion

Sympathy

Equanimity

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The Square

The square structure is divided into four isosceles triangles by lines that run from the center of the Mandala to the four corners. Each detail in all four quadrants or triangles faces the center, where the deity of the mandala resides. The square form defines the architecture of the Mandala described as a four-sided palace or temple.

Palace – Residence of the presiding deity

Temple – Contains the essence of the Buddha

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The Colours

The four quadrants of the Palace or Temple are divided into isosceles triangles of colour.

white, yellow, red, green, dark blue

 Each of the aforementioned colors is associated with one of the five transcendental Buddhas, further associated with the five delusions of human nature. These delusions obscure our true nature, however spiritual practice can transform them into the wisdom of these five respective Buddhas.

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The Concentric Circles

The series of concentric circles surrounding the central palace or temple follow an intense symbolic structure.

Ring of Fire

Ring of Thunderbolt or Diamond Scepters (Vajra)

Eight Cremation Grounds or Graveyards

Ring of Lotus Leaves

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The Complete Mandala

A person meditating on a mandala visualizes himself going into the mandala and making his way through the levels of images until he arrives at the center. Buddhists believe that the Mandala meditation helps concentrate spiritual power and bring freedom from suffering.

 

Drawing the Mandala

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Component Diagram

After thorough research on the Indian Mandala, I started designing mine taking into consideration the various symbolizations and components that constitute the traditional Mandala.

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Mandala Layers
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Model Concept
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Three Dimensional Mandala

The Final Proposal – The Cubic Mandala

 

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Day Render

According to Buddhist religion, the mandala appears as a series of concentric circles that are a representation of the process of transformation that human beings are asked to undergo before entering the sacred area, located at the centre of the mandala. In other words, when meditating in front of a mandala, human beings move through the different layers, liberating themselves from the delusions that obscure our true nature, and consequently reach the centre of the mandala and attain enlightenment.

Based on that theory, the Cubic Mandala is a three dimensional, cubic representation of the traditional Indian Mandala and is designed in a way so that all the fundamental elements of the traditional mandala are being incorporated into the design. For instance, the central area, the palace or temple, the four quadrants along with the four gates, the ring of fire, the lotus and diamond ring, as well as the eight graveyards. The aforementioned are of great significance and vital to the process of transformation and the attainment of enlightenment and spiritualism.

This process is further emphasized by the introduction of 4 layers that form each side of the cubic mandala and represent the different stages that human beings have to overcome in order to reach the centre of the mandala. The cubic mandala is an actual representation of the difficulties one is asked to overcome in order to put an end to human suffering and acts as a means to discover divinity by the realization that it resides within one’s one self.

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Night Render

The Cubic Mandala is a 4,5 m high timber and acrylic construction consisting of layers that form four concentric cubes, creating a journey to the centre of the mandala. The twenty layers that form the four concentric cubes are made out of timber. However, a 10mm acrylic sheet is attached to the five layers that form the first cube as well as the third concentric cube. LED strips will be attached at the edges of the acrylic sheets, lighting up the whole structure during night-time.

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Exploded Axonometric Diagram
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Exploded Diagram – Front View

Each cube consists of five sides, instead of six, as the bottom side has been removed and replaced by a base that holds the whole structure. The sixteen vertical layers of the structure are being inserted to the pockets that have been created at the base of the structure. The remaining four horizontal layers are attached to the horizontal elements.

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The Base

The Experience

While observing a mandala, a kind of spiritual essence surrounds the one observing it, which as a result allows him a higher level of awareness and consciousness. Consequently, the creative mind of the individual is allowed to escape reality and run free. The mission of the “Cubic Mandala” is to encourage people to focus on it, absorb the beautiful designs and allow their minds to wander. People are tempted to let the “Cubic Mandala” absorb all their attention, by moving into the mandala and gazing into its patterns.

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Section

A feeling of lightness is what people are going to experience, while falling into the mandala. Intuitive thoughts might arise. People are encouraged to relax, embrace one another and let the feelings come to them. According to the tradition, the making process of the mandalas involved four monks – one at each quadrant – working simultaneously until the mandala was complete. Having said that, the original process of making highly encouraged interactivity. Therefore, the purpose of the “Cubic Mandala” is to bring people together and, through the ritual of mandala meditation, to raise their spiritualism, to promote self-expression and finally, to liberate them from the everyday life.

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Interior View
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Interior View