Shapes, Fractals, Time &, the Dimensions they Belong to

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.

Excerpt 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&y, y&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

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.

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.

Source: http://www.wahl.org/fe/HTML_version/link/FE4W/c4.htm#box

 

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.

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.

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, R₇ etc.)

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.

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

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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..” – bp.com

 

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

 

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.

 

 

 

 

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                                                                                                                                 

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

Compassion

Sympathy

Equanimity

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.

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.

Interior View

Interior View

Duality

This project is a physical exploration of anamorphosis in three dimensions centred around the theme of duality. It aims to combine two widely recognisable figures into a pavilion that will attract burners, provoke debate, and catalyse interaction.

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The theme of this project arose from the realisation that even the most widely recognisable symbols contain multiple layers of meaning and mystery.  Social, historical and sometimes even spiritual contexts give a symbol its perceived meaning. For example, while the Christian cross is a symbol of hope it is literally a scaled representation of an ancient torture device – an icon synonymous with good carries with it a darker elucidation. This interpretation led to the emergence of duality as a topic and a title. There are many symbols which have multiple meanings and nuances to those who interpret them.

I began by looking at the Ankh, the Egyptian symbol for life/fertility. The Loop of the Ankh represents the feminine discipline or the womb, while the elongated section represent the masculine discipline or the penis. These two sacred units then come together and form life. This is a perfect representation of man and woman in perfect union. I then was led to study the symbol for mercury, which is used in botany to indicate a flower with both male and female reproductive organs.

This duality of meaning in symbols led me to the desire to study how I could physically combine other symbols and forms to create one form. Anamorphosis, from the Greek anamorphōsis meaning ‘transformation,’ from ana- ‘back, again’ + morphosis ‘a shaping’, became an interesting opportunity to do just this.

 

I want to explore this theme using the iconic faces of Donald Trump and Kim Kardashian as instigators. From a random vantage point or even from up close, the subject matter of the piece is evidently unclear, the image changes until the viewer arrives at a specific pre-set location, only then does the likeness reveal itself. This echoes our warped perception of figures in limelight; anything the media choose to present to the world is an engineered production and if taken out of its context it becomes incomprehensible. My aim is to stir ambivalence among the burners, for them to engage in discussion with one another about these two incredibly famous personalities and what they seemingly represent.

As a physical entity, the sculpture is purposefully made durable enough to be able to endure the brunt of any elicited reactions. Its exposed surfaces are smooth, an open invitation to graffiti, carve or deface in any manner possible. It is large enough to climb and to gather within as a group – it only takes a spontaneous suggestion from a creative festival goer to give the sculpture another unforeseen use.

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The aim of my proposed sculpture is to provoke an exchange of opinions and interactions between burners. It depicts two iconic and highly controversial public figures who personify two tremendously important issues that we as a society face today; political and social change.

As festival goers approach the installation, and the two widely recognisable faces reveal themselves, comments about the likenesses will spiral inevitably highlighting or at least touching upon the shift that these two personalities represent.

The sculpture’s physical form comprises of several spatial elements that lend themselves to fostering the kind of debates that I wished to promote. The hollow centre creates an enclosure, to enable hosting or housing for a meeting, it gives its participants a sense of protection; this is an open forum, please take part. The raised base on the peripheries can act as stages or podia. The expansive smooth external surfaces can act as billboards or banners, the skin of the sculpture will bear the physical outcome of the issues discussed here.

Whether people get photographed with it, or whether they deface, damage or even burn it to the ground, I will have succeeded if among any of the interactions the agenda was heard and a heartfelt reaction was made.

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The sculpture will be made of 8mm CNC routed plywood sheets fixed to a heavy plywood formwork. Standing at 6m tall, one side will represent a 25:1 scale stencilled portrait of president-elect Donald Trump, the other side; the likeness of reality television personality and socialite Kim Kardashian. Much like the oblique anamorphosis incorporated in Holbien’s The Ambassadors, the sculpture’s subject matters will reveal themselves only from some 60m away, but from close up, the installation will seem like a mass of abstract wooden extrusions, something suggestive of an adult-sized climbing frame. Fluorescent LEDs recessed into junctions of the outer plywood skin layer will illuminate the piece at night.

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The pavilion achieves the incredible feat of allowing the viewer to have a personal and intimate connection with it whilst also allowing for reflection. The two images are intended to bring moments of delight to viewers to allow for interaction even from a distance.

Combined with its symbolic and evocative power, it should indeed conjure a deeper sense of place and self, and bring a subtlety and complexity to what might have been just another pavilion.

 

Love Nest

The Heart is an internationally known Symbol for Love.

The Love Nest is a Pavilion designed for Burning Man as a destination to express your Love to another. Wedding ceremonies will take place within the Heart structure, this is the biggest gesture of Love, joining together as one, declaring your Love for everyone to see

The wooden hearts floating toward the sky create a Tower of Love

 

Inside the Love Nest

1:20 Model and Heart Bending

Love Nest – Night Time

 

Developing the Love Nest

The origin of the Heart Symbol

Symbols as a System

At Burning Man within the Temple (also known as the Temple of Love) people leave messages to remember there loved ones that they have lost, the temple is then burnt so the messages can get to those who are being remembered. The Idea of the below design was inspired by a book, being a place of words, people add to the pages of the book of love.

Interlocking Hearts – Heart Tower

The Tower

Every time someone is married within the Tower a coloured heart is added to the Structure. 

Progression of the Form

Developing the design to be more fluid and natural, as love isn’t hard and spiky.

Bending Hearts

Looking at different ways of bending wooden Hearts to be able to work with the newly designed form and being able to attach to the ‘Ribs’ of the design. I looked at two ways of achieving this:

Laser Cutting

By laser cutting a line pattern into the heart I achieved a material that bends easily

Cutting and folding

Cutting a slit from the bottom of the heart to the centre and taking the two half and bending one on top of the other

Results – The Laser Heart bent easily but did not stay in place and became more fragile whereas the folded heart keeps its shape and is a more solid form

The Love Nest – Initial Renders

The Love Nest – Initial Model

 

Folding Hearts – Further Research

Looking at what effects the curvature of the heart.

Variable – Length of cut for bending

Results – The Longer the cut the smoother the curve

 

Final Design – Love Nest

The Final Design looks at creating a form by connecting the folding hearts, removing the structural ‘Ribs’ from the previous design and creating a system to achieve a Form

Love Nest – Final Model

Love Nest – Internal Views

Love Nest – Lighting

Love Nest – Night Time

TriNect

The aim is to generate an architectural response through a playful loop between the digital and the physical. Digital tools such as Rhino and Grasshopper are used  in order to carry out analysis and generate buildable three-dimensional forms. Interplay between physical fabrication and digital experiments enable to become an inventor of a system. Here is mine.

TriNect is a flexible system of triangular elements with slots at their vertices. Elements interlock with one another creating different space filling polyhedra. The system can be applied in various scales and adapted for different needs.

TriNect

PURSUIT Kickstarter Launched!

KICKSTARTER VIDEO & CAMPAIGN LINK: http://kck.st/1qGLHSw

PURSUIT is an interactive art installation that celebrates humanity’s ongoing quest for Peace, Freedom and Joy – in Life, Love and Art. The design aims to create an interactive and unique sculptural playground for visitors of the 2016 Burning Man Festival, which takes place from August 28th to September 5th in Black Rock Desert, Nevada.

THE PROJECT

PURSUIT emerges from the playa in tiers of intertwined timber elements that ascend seamlessly in unison to form a series of congregation and celebratory spaces. The final design is the result of a year-long study into the sensuous geometry generated from a mathematical theory known as Pursuit Curvature. This theory was explored as I wanted to utilise something that could fully embody the notion of people coming together from different places and striving towards a common goal. With Pursuit Curvature, each point starts at a unique position of a polygon, and moves incrementally towards the nearest adjacent point until they all converge in the centre. The path travelled is directly influenced by the points around it, so the final curves represent the effects all of the points have on one another as a group.

Central Space

Burners can rest inside the ornate central space of Pursuit, which frames the ongoings of the playa and provides burners with a place of respite from the open sun. The six inhabitable pillars connect the playa directly to the platforms that lie atop Pursuit. Here, a glorious vantage point in which to congregate and take in the festival is gifted to Burners. During the day the interiors of the pillars are concealed from the elements, and their curved form helps to guides burners ascent to the open air. Here they can bathe in the wondrous light of either sunrise or sunset, a truly magical playa experience indeed.

At night time each pillar’s interior is powerfully lit to envelop the burners in light, so they can experience a sense of weightlessness and freedom. The soft glow emanating from each of the pillars’ cores invites burners to commune atop Pursuit to celebrate the radiant beauty of the night sky.

OUR PURSUIT

Interior of each Pillar

“As I look back on my life, I realise that every time I thought I was being rejected from something good, I was actually being re-directed to something better.” – Steve Maroboli. 

Pursuit is a gift to the Burning Man community. Every year, we apply for funding from the Black Rock City LLC (Burning Man) to help fund our projects. Unfortunately this year, nobody received funding towards their project. Despite initial disappointment, I realised that this helped elevate the project’s intent and concept to a new level than originally planned. By crowdfunding the entirety of the project, we can manifest the collective Pursuit of people from all over the world to see this project built. This is not only tremendously exciting, but also a very humbling prospect, in that we have a passion to give this gift to the playa, but we need your help to give that gift. It is through this collective pursuit that we can embody the spirit of the festival and the project in a built architectural form.

REWARDS

To show our gratitude for any of your generous pledges, I have created some truly beautiful and unique rewards for all levels of contribution – Each inspired by the projects form and concept, that are all exclusive to this campaign. Please do go and have a look for yourself at them and support the campaign. If you can’t spare a donation at this time, then please share the campaign to as many people as you can – so that together, we can make the project a reality.

Thank you

Joshua

KICKSTARTER LINK: http://kck.st/1qGLHSw

Future Living Report: Predicting The Future of Homes, Cities and Technology

It’s official we are now futurologists! We knew it would happen soon enough!

A PDF of the report can be found here: Future-Living-Report

In the report we set out our visions on the future of living, the rise of technology, changing patterns of human behaviour and rapid urbanisation, huge advances in 3D printing and augmented/virtual reality in the home as well as material advances and seeking out alternative habitats such as underwater homes and even terraforming other planets.

The report was commissioned by Samsung and prepared in collaboration with Space Scientist Dr Aderin-Pocock, and professional urbanists Linda Aitken and Els Leclercq and has been featured in many international press publications:

Advances in material technology allowing huge skyscrapers dwarfing today’s versions, incorporating vertical gardens above the clouds.

Underwater city homes growing their own food and producing breathable oxygen and hydrogen for electricity through the splitting of water molecules.

3D printed space colonies harnessing solar power and the oxygen produced by plant life to create sealed internal environments.

Drone delivered prefabricated homes that can move wherever and whenever you want to creating digital nomads.

All images produced by Taylor Herring and licensed under creative commons

BBC World Service Business Daily Interview: A Virtual Reality Future

Toby and Arthur speaking on the BBC World Service’s Business Daily program on the incorporation of digital technology into our lives and our homes, 3D printing furniture, the future of virtual leisure,

Link to the original audio file here A Virtual Reality Future? (We start talking about half way through)

 

Link to the iplayer programme: http://www.bbc.co.uk/programmes/p03jtdt9

 

Auxetic Assemble

As the Maker World develops, we want to have a greater impact on our environment, the spaces we live in. Auxetic Assemble gives you a chance to build your own furniture and have a input in your product. Auxetic Assemble gives you the chance to buy either the cut parts for the product or the instructions and CNC cutting files to then source your own material, cut your own product and assemble your work. The future of this adaptable design system allows the product to be fitted and designed to your require space.

 

The Pavilion

I have set up a Kickstarter Campaign in order to Fund a Pavilion in Hackney. The Pavilion is the next step in the journey to developing this system to its future potential. The construction process used for the plywood shelves will be developed at the larger scale to develop a pavilion to display the process of constructing the shelves and to exhibit the product. The Pavilion walls will become the seating, shelving and tables for the space. This is a chance to explore the system at a larger scale in order for further development for future of housing, an adaptable system that can be applied to a unique space and engages everyone as its workforce to build it.

Kickstarter Page

 

The Products

 

The design system has been developed into shelving product to sell as rewards, both in cardboard and plywood.

 

Follow the links to the Kickstarter Page to help this project be realized, Click on any image for the Kickstarter page link. Thank you.