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:
The Amazing Surf is a complex fractal geometry which ascends toward the light, symbolizing our obsession with reaching for the stars. We use our increasingly digital world to help us extend our reach, but at what point do the shadows we cast reach out above us?
The shape is inspired by the Amazing surf fractal which is generated by a mathematical formula and visualized in Mandelbulb3D. A visually imposing 25ft tall Ply wood hyperbolic structure, with intricate evolving folded panels. Each folded panel is digitally unrolled into a 2D net and CNC milled, the resultant ply components will be glued to a layer of fabric and folded back to their original 3D shape. This construction technique removes the need for a supporting frame, keeping the complex geometry unobstructed from view. A few panels have been removed at the base to make way for an entry point. Neon strips attached to each panel will produce dramatic light patterns on the surface at night. The installation will orient toward the sunset, where the sun appears at it’s closest.
The piece is intended to be used as an impromptu climbing frame, a ladder to ascend burners above the desert and into the stars. Sunlight will bounce off the multi-faceted shapes, creating intricate patterns of light and shadow. Burners are invited to dance in the light shafts and seek shelter in the shadows. As the shape begins to flatten toward the top, the folded panels can be used as armchairs, where vision will be limited to that of the sky and light above; burners can sit and watch as the sky transforms from day to night.
“Keep your face always toward the sunshine – and shadows will fall behind you”
As a race we strive to advance, developing new tools and machines to help us in this process. There will come a point in the not too distant future where the machines we have developed to help us will supersede us; we will become so reliant on technology, it will begin to control us. I see the Amazing Surf installation as a juxtaposition to this potential future; on the one hand we are using technology to create built environments that are intricate, beautiful and unique, on the other hand these environments are only attainable through the use of technology. If only we took a moment to look back into the shadows, we could avoid the fate that we are gradually bringing upon ourselves.
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.
– Limitless Sound –
“Vocal music is considered to be the highest, for it is natural; the effect produced by an instrument which is merely a machine cannot be compared with that of the human voice. However perfect strings maybe, they cannot make the same impression on the listener as the voice which comes directly from the soul-breath and has been brought to the surface through the medium of the mind and the vocal organs of the body”.
– Harzat Inayat Khan, The Mysticism of Music, Sound and Word –
The combination of architecture, derived from fractal geometry, and the power of sound led to the creation of Anahad. This installation is an interactive musical display, which will be acting as musical instrument giving voice to the burners and the surrounding environment.
This art installation, which challenges the perception of nature, is called Anahad. I am planning to build 3 free-standing “trees”, each measuring 1.5m in diameter at the base and 3m at the top. The trees are 5m tall and they are composed of 105 copper pipes or mild metal tubes each measuring 6m long and ranging between 30 and 45mm in diameter. A central column connected to a solid base is the main structural element supporting 2 concentric layers of pipes.
The most external pipes are bent and perforated and filled with LED strips that will shine through the openings. Every pipe will generate a different sound based on the perforation pattern and the bends. The inner pipes, which are only bent and connected to a propane tank, will spit fire from the top.
Anahad establishes a connection among the user, the art, and the environment.
Can you recall how the wind blowing sounds? Is it always the same? This design will act as a musical instrument, which will be playable both by burners and the Playa itself.
During nighttime, the user will be transported both visually and sensorially into a digital forest through a LED light show mimicking sun rays penetrating the forest treetops. Then flames will be shooting out from the top to mark every hour.
The aim of this installation is to create an uninterrupted musical performance, combining the sounds produced by burners hitting the pipes or by the wind blowing through the pipes. The central space between the three trees and the niches at their base will provide a space to meditate and be mindful of the soundless sound of the Playa. This installation in its simplicity will connect people and natural environment through the use of musical harmony.
Anahad is solely an instrument through which the breath of the Playa will blow, singing for the burners. Vice versa, burners will be able to express themselves striking the metal pipes playing melodies for the community and the surroundings.
This installation aims to connect the people to the Playa. The three “trees” are a digital fabricated representation of a natural forest. In a world where disconnecting from reality becomes a luxury, where innovation takes over simplicity, and nature gets left aside in our busy lives, music is what makes us human. Anahad challenges the way we experience reality, by combining the digital and virtual world with the natural environment. The aim is to provide the participants with an ideal environment for them to meditate in and be mindful of their whole experience.
dis/integration[loops], inspired by the composer William Basinski’s seminal works of the same name, explores the limitations of digital processes in our world – and the chaos that can unfold from overreliance on them.
A towering array is assembled from recursive fragments of an inherently destructive process. It explores the tension that exists between the digital and physical realms; challenging an immortal, digital world, the glorious ruin of the analogue realm confronts the perceived perfection of the artificial.
Existing in a state of intended incompleteness, dis/integration[loops] eschews vanity in favour of exhibiting procedural rawness; the power of ruinous accident reveals itself through the tarnishing of idyllic digitalism.
Pressure-laminated plywood modules, form-found through iterative casting experiments, connect to form a pervious, fragmented structure; it’s transcience and impermanence exaggerated as night follows day.
In the same way that Basinski’s fragile recordings were destroyed upon being processed by the human ear, dis/integration[loops] exists in a contented, lush and shimmering state prior to being activated by human presence.
Proximity-controlled LED lighting impregnates the structure. When combined with sounds inspired by those Basinski’s (de)generative process created, this affords a level of animated deconstruction upon activation; visually and sonically, the imperfect presence of humanity causes dis/integration[loops] to be engulfed in chaotic ripples of distortion.
It’s most perfect (yet still decidedly imperfect) state is one in which it lies dormant and peaceful, undiscovered by the presence of people. It experientially disintegrates upon activation.
The fragmented structure exaggerates ever-changing natural light conditions and provides shelter, as well as an intimate, tactile space withi it’s permeable walls.
‘And then as the last crackle faded and the music was no more, I took in my surroundings and looked around at the faces and I was right there with everybody and we were alive.’
dis/integration[loops] is a reminder than everything we encounter eventually falls apart and returns to dust. It challenges the perfect, edited, occularcentrism that blights our social lives, explores the sound of decay, and the beauty that can exist in destruction. It is a meditation on death and loss, and exploration on a theme that some things are better left untouched.
The experience of life – a gradual disintegration – is simultaneously enriched and eroded by the imperfect nature of our encounters; pristine digitalism deserves a tarnished, ruinous quality symbolic of our experiences.
‘and I was right there with everybody and we were alive.’
In mathematics a fractal is an abstract object used to describe and simulate naturally occurring objects. Artificially created fractals commonly exhibit similar patterns at increasingly small scales. It is also known as expanding symmetry or evolving symmetry. Mandelbulb 3D allows us to explore fractals in 3D, creating a seamless amalgamation of maths, art and science.
Understanding how this geometry can become infinite and how it can be built within the constraints of the physical reality was part of the philosophy of my piece.
Mandelbulb 3d fractals:
From these specific chosen 3d Fractals I noticed a clear correlation with the natural formation of crystalline structures, in particular Hopper crystals.
Hopper crystals form when there is more rapid growth at the outer edges of a face than at the centre. This results in what appears to be a hollowed out step lattice formation, as if someone had removed interior sections of the individual crystals. This missing part was never actually developed as the crystals grow so rapidly that there is never time for this to be developed. Hopper crystals are very similar to the cubic halite skeletal crystals formed from extreme supersaturation in salt lakes existing in nature. Hopper crystals can be found in rose quartz, gold, calcite, bismuth, salt and ice. I looked at the growth of these crystals to better understand the structural qualities.
Hopper Crystal Formation:
From looking at the crystalline structure it became apparent that the connection between the tapered levels was very important to the structure and adaptability of the proposal. The versatility of this connection allows for flexibility and movement within the module. The connector can be placed on any material simply by adapting the end nodes width to factor for the material depth. By creating this modular junction I can join all the stepped timber elements of the proposal in such a way that they are all supporting each other.
Hopper crystal growth is never as predicted due to outside influences such as movement and temperature change. These influences creates the beautiful images we see of their crystalline forms and without these the fractal crystal growth would be predictable and simplistic. It is with these outside interactions that the crystals have their own idiosyncrasies. By combining the hopper crystal growth with the organic forms created with the 3d fractal generator, I created a pavilion proposal. Using a stepped form and the junction designed above I could use the unpredictable growth lines to create an interesting pavilion which can be experienced in the same way that crystals would grow, naturally and not within their algorithmic form. Nature does not always conform to predictability. The pavilion expresses this individuality and in turn expresses the way in which we grow as individuals, adapting to our environments and moulded by our experiences.
This project is a physical exploration of crystal formation centred around the theme of fractals. It aims to combine one joint in order to create a crystalline structure. Inspired by the geometry from the crystalline growth the lattice structure provides sanctuary and calm in a sea of dust and at night mesmerising myriads of stepped lights will illuminate the playa.The proposed installation will be formed of a mixture of 2 x 4 timber with CNC curved plywood pieces incorporated into the structure. Each 2 x 4 will have a joint or a pocket in order for it to slot into and support the weight of the neighbouring beam or column. The project will appear out of the sand as an elegant stepped fractal structure which gives the proposal an ecclesiastical ambiance.
The intertwined stepped lattice timber elements form congregation and celebratory spaces, whilst capturing special views of the playa. The stepped elements promote Burners to climb and crawl between the spaces created by the overlapped timbers. At night when you ascend through the individual spaces the lights will constantly change and oscillate. With the lights constantly changing and staggering further through the elements the stepped structure will be enhanced. The project aims to play with the burners’ perception of depth where the lattice stepped geometry is staggered and rotated. At night this perception is further confused by the LED coloured strips oscillating along the staggered stepped beams and columns. The burners can seek sanctuary in a space in which dimensionality and form is confused and adapted.
Think back to when you were younger – how many times were you exposed to technology in a day? Whether it was a phone, a computer or watching TV. The world has had a dramatic advancement in technology and the questions that should be asked are, “are we as humans becoming more robotic? Running day-to-day tasks repeatedly?” My aim with the project below and the help of Burning man is to try to make us human again by reflecting on the 5 senses. Part of my childhood in Kenya was filled with no technology at times especially because it was a third world country. Weather I spent an hour climbing trees or just playing several different sports – no technology was involved. From a more personal experience babies/ kids at the age of 1 are already watching TV and playing games on phones. Where were we 30 or 100 years ago and where are we now? Who are you? What is your identity? When was the last time you experienced something that moved you spiritually/ emotionally? The journey through a temple or certain spaces can personally move me at times. If it’s just experiencing the space or listening to religious hymns – having a connection with something greater than yourself can not be described but just needs to be experienced.
Art installation name: To Make One Human Again
Fractal geometry has always existed but was very recently discovered. The chosen design is based a fractal (as shown above) and the research of temples. At this stage in time everyone around has become very dependent on computers and technology as days go on – systematically – wake up, go to work, have lunch, work again, come home, sleep, repeat. It appears we have become robots running day to day tasks.
The structure is to have several entrances with a variety of different spaces – each space can be used in different ways. The proposed idea is to focus on most of the senses and finally introduce the user/ occupant to an area which can be used as he or she prefers. People who visit the installation will have a range of different background and want to reflect in different ways. The idea of interfaith participation with the installation will be a focus and even if one is an atheist, they should still be able to reflect with the installation. Experiencing the senses in the art piece/ sculpture shall take away the user from their day to day working/ life and try to make them experience a change in conditions which would make them feel “Human” .
Interactivity and mission
The proposal uses the 5 senses, so in order to enter into the main space, the user will need to experience one of the 5 senses. The space in the middle/ communal space can be used for multiple purposes (as burners see fit).
This is a preliminary installation for myself. The project is still at its concept stage and through experimentation and learning a working design can easily be constructed. The assembly process may need more than a one person (burner/ volunteers can help).
Although the burners may use this installation in different ways, possibly climbing it – the final product should be partially combustible, and any material left can be re-used by recycling.
The sensory installation will allow people to reflect with their inner self. Some memories are brought back with certain smells etc. For the installation to work, all the spaces must be kept clean at all times and each person’s privacy respected.
Philosophy of the piece
Focusing on fractal geometries at university – I was drawn to looking at Sikh and Hindu temples. Some of these temples use fractals in their construction. I have studied and worked in the UK but was born and brought up in Kenya. I have come across a range of different people with backgrounds which vary dramatically. The first world counties highly depend on technology and even now certain third world countries value technology over day to day necessities such as food. The idea of using the senses allows technology to be minimised in the installation and for one to be made human again. This is one of my major motivations, however, the objective of the installation at burning man is to experiment with the scalability of materials, construction techniques and to provide a sensory experience.
The proposal of using the 5 senses.
Sight – Certain LED lights can be added to the structure – so that it is visible at night.
Smell – Scent infused timber can be used so during the burn, these can be released or as people occupy the space the timber can have a smell to it.
Touch – Some of the timber can be engraved/ have different textures
Taste – The users can sit in the space to have their snacks/ meals
Hear – Chimes or other instruments which harness the wind can be hung in this area.