4.0 Classic Space-Filling
4.1 Early Examples
In 1890, Giuseppe Peano discovered the first of what would be called space-filing curves:
Delving deeper into the world of mathematics, fractals, geometry, and space-filling curves.
In 1890, Giuseppe Peano discovered the first of what would be called space-filing curves:
something caught in between dimensions – on its way to becoming more.
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
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.
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.
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:
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
Love at Burning Man
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
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.
Every time someone is married within the Tower a coloured heart is added to the Structure.
Developing the design to be more fluid and natural, as love isn’t hard and spiky.
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:
By laser cutting a line pattern into the heart I achieved a material that bends easily
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
Looking at what effects the curvature of the heart.
Variable – Length of cut for bending
Results – The Longer the cut the smoother the curve
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
Thousand Line Construction :
A spatial exploration into the interplay of materials, construction techniques, and delicate and precise design.
Inspired by Hanakago; the craft of Japanese Bamboo basketry, to celebrate the western discovery of tea and its associated culture during the renaissance.
A deployable structure includes an enclosed mechanical linkage capable of transformation between expanded and collapsed configurations while maintaining its shape.
These types of structures have the advantage of creating versatile, modulated spaces, with easy and fast assembly which generate benefits such as adaptability, flexibility and space transformation.
Charles Hoberman pioneered a type of deployable structure based on curved scissor pairs as seen in his Hoberman sphere. The unfolding structure resembles an expanding geodesic sphere which can reach a size up to five times larger than the initial one. It consists of six loop assemblies (or great circles), each made of 60 elements which fold and unfold in a scissor-like motion.
Hoberman Sphere by Charles Hoberman
A loop assembly is formed of at least three scissors-pairs, at least two of the pairs comprising two identical rigid angulated strut elements, each having a central and two terminal pivot points with centres which do not lie in a straight line, each strut being pivotally joined to the other of its pair by their central pivot points. The terminal pivot points of each of the scissors-pairs are pivotally joined to the terminal pivot points of the adjacent pair such that both scissors-pairs lie essentially in the same plane.
Regular curved scissor-pairs in motion
When this loop is folded and unfolded certain critical angles are constant and unchanging. These unchanging angles allow for the overall geometry of structure to remain constant as it expands or collapses.
Regular and irregular curved scissor-pairs in motion
The above diagrams show a closed loop-assembly of irregular scissors pairs where each scissors-pair is pivotally joined by its two pairs of terminal pivot points to the terminal pivot points of its two adjacent scissors-pairs. This loop-assembly is an approximation of a polygon in the sense that the distances between adjacent central pivot points are equal to the corresponding lengths of the sides of the polygon. Further, the angles between the lines joining adjacent central pivot points with other similarly formed lines in the assembly are equal to the corresponding angles in the polygon.
The beams forming scissor-pairs can be of almost any shape, providing that the three connection points form a triangle. The angle of the apex would dictate the number of scissor-pairs that can be linked together to form a closed loop.
Scissor-pairs of varying morphologies
My physical experiments started with materials that would allow a degree of bending and torsion in order to test the limits of the system. Using polypropylene for the angular beams and metal screws for the joints, I created these playful models that bend as they expand and contract.
Later I started using MDF for the beams as well as joints and noticed that a degree of bending was present in the expanded state of the larger circle.
After using curved scissor pairs of the same angle to form closed linkages, I decided to combine two types of scissors and vary the proportion between the elements to achieve a loop which would offer the highest ratio between the expanded and contracted state.
900 curved scissors loops
900 curved scissors with linear scissors loops
The above diagrams show a combination of 900 curved scissors with linear (1800) scissors to form rectangles that expand and contract. The length of the 900 beam was gradually increased and by measuring the diagonals of the most expanded and most contracted forms, I obtained the following ratios for the three rectangles:
R1 = 0.87
R2 = 0.67
R3 = 0.64
By keeping the curved scissor with the best ratio, I created three more rectangles, this time by varying the length of the linear beam. The following ratios were obtained:
R1 = 0.64
R2 = 0.59
R3 = 0.67
900 curved scissors with linear scissors loops
I then took the linkage with the best ratio of 0.59 and rotated it 900 to form a cube which expands and contracts.
Combined linkage cubes
The change of state from open to closed is visually attractive and could have the potential of creating spaces that are transitional.If more linear scissors are placed between the 900 scissors, a better contraction ratio is obtained.
Combined linkage cubes with two linear scissors
Narrative | ‘Hayam’: a filigree temple of light and shelter, a spiritual retreat resting lightly on the Playa, a tiny tessellated palace named for love and open to the sky, a miniature caravansary to welcome the weary traveller.
The Hayam embodies the spirit of Islamic geometry: intricately interwoven patterns and repeating themes that speak of infinity. Geometry is the language of the universe; in the very small the infinite can be found.
Physical Description | Erupting flowers of perforated plywood seamlessly joined together to form a beautiful curvilinear structure. Reminiscent of muqarnas and moucharaby but stripped back to the pure essential fretwork and form, leaving behind only what is necessary. Enamels, glazes and precious metals are replaced by the gold of scattered light filtering through the delicate tracery of the screen, elevating the spirit. The treasures are not material things; they are spiritual. A place of illumination, intended for contemplation.
Emerging from a study into the geometry of Islamic art the pavilion references motifs and arabesques traditionally found in mosques and other sacred places though in itself the Hayam has ties to no religion; it transcends time and space, language and culture.
Interactivity | The structure provides a refuge from the heat of the sun and an intimate spiritual place for people to gather and rest. During the night the four pillars illuminate like a giant lantern with gas fires and the flames can be seen dancing behind the filigree patterns. The gas fires heat the area during the cold night so the space continues to function as a comfortable retreat.