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 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.


Except from ‘minutephysics’

We usually arbitrarily pick a dimension and calling it the ‘first’ one.


1.1 – Zero Dimensions


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


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


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 define on the surface of a sphere with latitude and longitude.


1.4 – Three Dimensions


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 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.

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.

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


2.2 – Between the Second & Third Dimensions


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.


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 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.

Except 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.


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.



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.


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.




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.

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.
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:


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 physicist are using to help us understand the universe work.


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.

“This is the classic reference on how the golden ratio applies to spirals and helices in nature.” – Martin Gardner

The Curves Of Life

What makes this book particularly enjoyable to flip through is an abundance of beautiful hand drawings and diagrams. Sir Theodore Andrea Cook explores, in great detail, the nature of spirals in the structure of plants, animals, physiology, the periodic table, galaxies etc. – from tusks, to rare seashells, to exquisite architecture.

He writes, “a staircase whose form and construction so vividly recalled a natural growth would, it appeared to me, be more probably the work of a man to whom biology and architecture were equally familiar than that of a builder of less wide attainments. It would, in fact, be likely that the design had come from some great artist and architect who had studied Nature for the sake of his art, and had deeply investigated the secrets of the one in order to employ them as the principles of the other.

Cook especially believes in a hands-on approach, as oppose to mathematic nation or scientific nomenclature – seeing and drawing curves is far more revealing than formulas.

252264because I believe very strongly that if a man can make a thing and see what he has made, he will understand it much better than if he read a score of books about it or studied a hundred diagrams and formulae. And I have pursued this method here, in defiance of all modern mathematical technicalities, because my main object is not mathematics, but the growth of natural objects and the beauty (either in Nature or in art) which is inherent in vitality.

Despite this, it is clear that Theodore Cook has a deep love of mathematics. He describes it at the beautifully precise instrument that allows humans to satisfy their need to catalog, label and define the innumerable facts of life. This ultimately leads him into profoundly fascinating investigations into the geometry of the natural world.


Relevant Material


“An organism is so complex a thing, and growth so complex a phenomenon, that for growth to be so uniform and constant in all the parts as to keep the whole shape unchanged would indeed be an unlikely and an unusual circumstance. Rates vary, proportions change, and the whole configuration alters accordingly.” – D’Arcy Wentworth Thompson

D’Arcy Wentworth Thompson wrote, on an extensive level, why living things and physical phenomena take the form that they do. By analysing mathematical and physical aspects of biological processes, he expresses correlations between biological forms and mechanical phenomena.

He puts emphasis on the roles of physical laws and mechanics as the fundamental determinants of form and structure of living organisms. D’Arcy describes how certain patterns of growth conform to the golden ratio, the Fibonacci sequence, as well as mathematics principles described by Vitruvius, Da Vinci, Dürer, Plato, Pythagoras, Archimedes, and more.

While his work does not reject natural selection, it holds ‘survival of the fittest’ as secondary to the origin of biological form. The shape of any structure is, to a large degree, imposed by what materials are used, and how. A simple analogy would be looking at it in terms of architects and engineers. They cannot create any shape building they want, they are confined by physical limits of the properties of the materials they use. The same is true to any living organism; the limits of what is possible are set by the laws of physics, and there can be no exception.


Further Reading:


Biomimicry in Architecture by Michael Pawlyn

“You could look at nature as being like a catalogue of products, and all of those have benefited from a 3.8 billion year research and development period. And given that level of investment, it makes sense to use it.” – Michael Pawlyn

Michael Pawlyn, one of the leading advocates of biomimicry, describes nature as being a kind of source-book that will help facilitate our transition from the industrial age to the ecological age of mankind. He distinguishes three major aspects of the built environment that benefit from studying biological organisms:

The first being the quantity on resources that use, the second being the type of energy we consume and the third being how effectively we are using the energy that we are consuming.

Exemplary use of materials could often be seen in plants, as they use a minimal amount of material to create relatively large structures with high surface to material ratios. As observed by Julian Vincent, a professor in Biomimetics, “materials are expensive and shape is cheap” as opposed to technology where the inverse is often true.

Plants, and other organisms, are well know to use double curves, ribs, folding, vaulting, inflation, as well as a plethora of other techniques to create forms that demonstrate incredible efficiency.


Symbol- Language and Sound into System

Language has a strong symbolic meaning to the mankind. It is not just a sound but with meanings which then allows to self-express, communicate and inspire. The mechanism of the sound system of languages is translated into visually represented geometries using Chladni’s Law.

3-Dimensional computer generated Chladni Patterns 

When the frequencies increase, the pattern gets more complicated.


BabelTower of Babel – The origin of different languages

“Come, let’s make bricks and bake them thoroughly. […] Come let us build ourselves a city, with a tower that reaches to the heavens, so that we may make a name for ourselves and not be scattered over the face of the whole earth.” (Genesis 11:3~4)

(The Tower of Babel by Pieter Bruegel)

It is the story from the Bible but also architectural structure found in Mesopotamia Civilisation – called Ziggurat. It was made of asphalt and baked bricks with total dimensions of 90m x 90m, 90m high. This is equivalent 30th floor building.

The united humanity spoke a single language and agreed to build a city and a tower that is ‘tall enough to reach heaven’. God found such behaviour as rude and disrespectful. He confounded man’s speech so that they could no longer understand each other. 


Concept Development through systematic studies of Ziggurat



The frequency and nodes of the word is analysed and recreated as two geometrical forms. They are proportioned according to the Ziggurat Algorithm ratio and timber pieces are stacked up vertically reaching the highest deck at 8m above. The structure encourages to climb complex geometry.

While reaching the top, less intense the space becomes. The LEDs are placed underneath the timber pieces which are concentrated on the top of the tower and scattered following the central void of the structure. Lights illuminate with the voice reactive sensor placed at the top of the tower.cymatictotal2

Human always wanted to reach higher points either physical or spiritual. The height of architecture symbolised one’s power and control. This can be observed from the tower of Babel and continues in architectural history. Such expression of the desire of heights lead to competition of building higher structure.

High rise buildings were often found in religious architecture where they had few typical characteristics. First, it was the only tower to observe your land and the only tower which can be seen from everywhere in town. It has a visual meaning that the land within the perspective is the land within control. Second, religious architecture often had music instruments embedded within. This represented the control of the land where music reaches. And finally, high-rise tower was a representation of the centre of universe and sacred space in religious term. The tower, architecture of height is a spatial symbol of man’s deep desires.

The ritual is all about finding the true desire of your own. This begins with constructing the tower where the ritual follows the biblical story of Babel. Climbing up 8m high construct is a challenge then the climbers are rewarded with the beautiful panoramic view of Black Rock city. The climbers will also interact with the installation by continuously stacking up the Babels with anything they can find. Eventually it will deform from the original shape. Then the Babels will be the collective symbol of the Burners’ pure desire.

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.


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 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 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.


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..” –



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.



Physical model light testing



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.



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 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.



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.


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.








Dream Catchers by Nick Huard

Legend of the Dream Catcher

‘The legend of a dream catcher began long time ago, when the child of a Woodland chief fell ill. Unsettled by fever, the child was plagued with bad dreams and unable to sleep. In an attempt to heal him, the tribe’s Medicine Woman created a device that would ‘catch’ these bad dreams. Forming a circle with a slender willow branch, she filled the centre with sinew, using a pattern borrowed from our brother the Spider, who weaves a web. This dream catcher was then hung over the bed of the child. Soon the fever broke, and the child slept peacefully.

It is said that at night, when dreams visit, they are caught in the dream catcher’s web, and only the good dreams are able to find their way to the dreamer, filtering down through the feather. When the warmth of the morning sun arrives, it burns away the bad dreams that have been caught. The good dreams, now knowing the path,visit again on other nights.’ (Oberholtzer, 2012, p9).



Dreamcatchers originated with the Ojibwe, a tribe of Native Americans scattered throughout the areas of the lake country in northern Michigan, Wisconsin, and Minnesota, and along the southern border of Canada, along the shores of Lakes Huron, Superior and Michigan, whose survival relied on fishing, hunting and trapping.  

Traditionally, the dream catchers were made by tying sinew strands onto a few inches in diameter round or tear-shaped frames of willow and were often wrapped in leather.

The spiritual life of the Ojibwa centred around the Midewiwin, the Grand Medicine Society and focused on the individual spiritual growth, gaining the insight through their dreams or visions.



Grey Owl repairing an Ojibwa-style shoe

Mystical Experience

My project is a re-interpretation of the beliefs that dreams have magical qualities with the ability to change or direct one’s path in life. The bawaajige nagwaagan intends to create a mystical experience, where people are caught inside, similar to the way that bad dreams are caught in the dreamcatcher’s web, and good dreams escape through the centre. The participants are encouraged to climb through the centre and escape their bad dreams and feelings, releasing their spirit through the enclosure. Now they can sleep in the peaceful environment, stimulated by the fantasy of glowing feathers and luminescent rope structures. The pavilion aims for people to sleep, relax and free themselves from stress while being protected by the magical webs of the dream catcher.



The Bawaajige Nagwaagan at night


Close-up render at night

Romantic essence of the Native American Culture

The proposal is a celebration of the romantic essence of the Native American Culture. The large scale, three dimensional net is inspired by the native methods and techniques of making dream catchers. It is a manifestation of the traditions and significance of the Native Americans, paying respect and pledging support to the indigenous people of America.

The structure situated in the Burning Man festival commemorates the ceremonies of Native Americans, dedicated to acquiring an insight through dreams and visions. Fasting, or giving up of certain necessities for a certain length of time was a common practice used to enhance one’s ability to access different dreams or visions. Another method was to pour water over hot rocks to produce steam, which enhanced the occurrence of dreams, used as source of introspection. These rituals relate to the festival’s assertion of disconnecting from the necessities of our contemporary world, supplemented by the extreme weather conditions, which are hoped to encourage reflection.

The pavilion responds and works together with the Black Rock desert’s environment, and adds to the wider cultural context of leaving behind the essentials and expectations of the contemporary world while creating a moment for contemplation and tranquility in the magical weaves of the dream catcher.



The Bawaajige Nagwaagan during the day

Proposal Development_System





1.Aleksandra Wojciak_90gsm_A1_Merylbone_west

Form Experimentation_Platonic Forms



Development Model



Diagrams explaining model assembly




1:10 Model



Diagrams explaining model assembly


Physical Description

The structure will be composed out of three, seven meters in diameter, dream catchers, tilted to form a tetrahedron. Each dream catcher’s net will be made out of 275 meters, 18mm, synthetic hemp rope which will be entwined in 1320 meters of 3mm fluorescent cord. Attached to the frame uv lights will make the fluorescent rope glow at night. Three rings hold the net structure together, with the bottom ring anchored to the ground, made out of T-shape plywood frames. The web of the frame will be 4 layers of 15mm ‘banana’ shaped pieces which will create a circle, together with 4 layers of 230mm x 2400mm x 9mm flange pieces bent in shape of the banana edge. Smaller rings, supporting the centre of the dreamcatcher net will be of similar structure, with 2 layers of banana pieces and 2 layers of 150mm x 2400m x 9mm flange pieces, bent in shape. The frame will be wrapped in 13500 meters of 8mm synthetic hemp with attached fluorescent fabric feathers.



Axonometric View-Construction Development


assembly 1

Frame’s web assembly

assmbly 2

Frame’s flange assembly


assembly 3

Initial assembly diagrams


UV lighting-Construction Development

Testing Ideas in 1:1 Scale



1:1 Scale Test Model exploring the possibilities of glowing net structure and its connections.

Assembly of the net is inspired by a macrame knotting technique rather than weaving which means that the net could be made out of smaller 15 meters long pieces, rather than one 275 m coil of rope, making it easier to assemble and repair. Rope is anchored to the frame with thimbles and shackles, attached to the bolted staple on the plate. The rope is connected with simple S-shape stainless steel hooks. After testing the net I found that although these are easy to assemble, they can create some movement in a connection, therefore I am planning on exploring the idea of ferrules, which could be crimped in place.



Photographs of 1:1 Scale Model




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                                                                                                                                 


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.


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





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


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.


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


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


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.


Mandala Layers


Model Concept


Three Dimensional Mandala

The Final Proposal – The Cubic Mandala



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.


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.


Exploded Axonometric Diagram


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.


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.



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.


Interior View


Interior View

Truth is a personal conquest which one attains through a mystery.

The Burning Man festival has evolved from a simple gathering of people on a beach in San Francisco into a spectacular spectacle. Burners travel from all over the world to meet in the Black Rock desert of Nevada where they form a city of temporary structures and burn a huge towering figure of a man. The theme of the 2017 burning man event will be Radical Ritual, an attempt to reinvent ritual in our post-post-modern world disregarding assertions of belief and concentrating instead on the immediate experience of play. Fractured cosmos seeks to provide this year’s burners with an edible artwork experience in the playa, a crystalline structure made from hard boiled sugar candy.


Fractured Cosmos draws the inspiration for its form from the Shri Yantra Mandala, a mystical diagram used in the Shri Vidya school of Hindu Tantra. The diagram, nine Isosceles triangles interlaced to form 43 smaller triangles, is said to be symbolic of the entire cosmos. The geometry of this symbol, usually depicted as a flat, two-dimensional construct, has been inclined, distorted and fractalized out of its two-dimensional plane to create a series of inclined planes for Burners to inhabit and play within.



Those cultures which meditate using the Shri Yantra symbol believe life exists between two planes, that of Samsara, this earth plane, and Nirvana, a perfect heavenly plane. One transcends from Samsara to Nirvana when they have gained enough genuine insight into impermanence and non-self reality. This notion has been reinterpreted as a series of transparent colourful planes on the playa, casting colourful light onto the ground beneath our feet. Each of the planes will be made from coloured rock candy, offering burners the opportunity to perceive an altered sweeter perspective of the world, as well as a delicious treat if they’re brave enough to lick it.

Hard Boiled Candy Planes.png

The use of hard boiled candy as the structural material for the pavilion means the structure will be made by mixing sugar, liquid glucose and Creme de Tartar with water. This concoction will be boiled to a temperature of 145 degrees celsius before pouring into formwork to cure. Waterproof LED lights will be added once the liquid has cooled to a sufficient temperature, and these will be used to light the structure at night.


The plinth of Fractured Cosmos must be strong enough to support the weight of the candy structure above plus the added weight of any burners, tie the structure down, capture any waste which falls off the structure as it is consumed and house the power source for the night time lighting. This has been designed using the same method of recursion as the candy structure to create a plinth using the mandala’s cosmic gate element as its inspiration. the final form generates a climbable podium for burners to ascend before inspecting and consuming.