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.
As our studio dipped into the complexity of fractals, it became easy to get lost. Suddenly, these geometries were everywhere. Trees, clouds, coastlines, our own bodies – all examples of fractals. Systems, that are made up of smaller self-simular parts until they reach infinity. Systems, that travel between dimension (more about it here https://wewanttolearn.wordpress.com/2017/10/18/shapes-fractals-time-the-dimensions-they-belong-to/). Wanting to understand these geometries better, I found a Fractal plugin for Grasshopper by albertovalis on Food4Rhino. Playing around with various parameters and GH components gave me interesting shapes, but which seemed far away from an architectural object. I then decided to give it a try and allow the program to randomly select elements by assigning different true/false patterns. Finally, an error happened and it was beautiful.
Error 101 is a visual representation of relationships between machines and humans. It illustrates what we can learn from each other (what does this mean?). The geometry was generated through a combination of fractal mathematics properties, parametric design tools and finally a computer error, which were all guided by human decisions.
The artwork will be made out of ‘chaotically’ arranged ribbons that, together, form a tetrahedron. From far, the geometry will look well defined – a triangle or pyramid. As you get closer you notice the complexity. When you experience is physically, you find logic in the chaos. Inside the tetrahedron is a void.
Error 101 will be constructed using bent cross-laminated timber modules that are interlocked together with flitch plates. Their arrangement will allow the object to be self-supporting. The whole piece is 18’x18’x18’ (5.5 metres). Timber strips create the outer shell and are 25 inches wide (635 mm). Their surface will be treated to achieve a smooth finish to protect both the piece and visitors. Light strips will be fixed to edges of timber curves and turned on at night. Assembly will be completed on site.
Interactivity and Mission
Error 101 is left open to interpretation – everyone can have their personal take on the piece. Visual and emotional perception of Error 101 may change depending on how close you get to it. It may encourage visitors to think of it, as something that travels between dimensions, which is a liberating allegory of how one thing can become another and how the whole is just a collection of its parts. Just like water can be liquid, ice or vapor, Error 101 can be a triangle, pyramid or chaotic curves.
The structure is climbable and each of many unique curves can be treated as a nest. Occupying empty spaces on different levels may make burners feel like a part of the ‘chaos’, that has a space for everyone. Different curvature can suggest different positioning of a body that may influence visual as well as physical experience. Entering the structure’s core shifts the visitor’s focus away from the idea of a pyramid and allows them to focus on what’s within. Such study erases preconceptions and allows new ideas to be born. This notion is also enhanced with the use of lights at night.
Error 101 is a product of human ability to perceive beauty, and computer’s power to process complex mathematics. Its development started with an attempt to try to understand fractal geometries that only became possible to study in the recent years due to the development of computer processing power. A continuous human-computer-human processes that involved both logic and error allowed for the piece to be born.
Error 101 is a common error in Internet browsing. A simple solution to it is clearing browsing history and cache. It may also appear in other spheres of digital world when software or a device is out of date. Burning Man participants are invited to clear their mind, update the ‘software’ and reset their system to become a new advanced version of themselves. The final steps of error 101 creation involved chance and error. The chaos led to something beautiful. We, as humans, can learn from this – learn to let go, to acknowledge and even appreciate mistakes, complexity of the world and our own selves. The geometry of an artwork is essentially a continuous strip that can be unrolled into one flat curve on the ground. This idea of continuity and interdependence is an allegory of a world’s structure.
The closer you get to Error 101, the more you can learn from it. A 2D triangle turns into 3D pyramid and then into a collection of overlaying shapes that are not truly from our dimension. With the speed of the modern world we tend to simplify things, which leads to inability to see details. Visitors are invited to come take time to study and appreciate the complexity of the Error, and to realize the beauty of a whole. From this, they may find that, in fact, all processes in our lives have a similar structure. Chaos generates order and order generates chaos.
Geometry can be found on the smallest of scales, as is proven by the beautiful work of the butterfly in creating her eggs. The butterflies’ metamorphosis is a recognised story, but few know about the start of the journey. The egg from which the caterpillar emerges is in itself a magnificently beautiful object.
Geometry can be found on the smallest of scales, as is proven by the beautiful work of the butterfly in creating her eggs. The butterflies’ metamorphosis is a recognised story, but few know about the start of the journey. The egg from which the caterpillar emerges is in itself a magnificently beautiful object. The tiny eggs, barely visible to the naked eye, serve as home for the developing larva as well as their first meal.
Each kind of butterfly has its unique egg design, creating a myriad of beautiful variations.
These are some of the typical shapes that each family produce.
But it is the Lycaenidae family that have the most geometrical and intricate eggs.
Biomimetics, or biomimicry is an exciting concept that suggests that every field and industry has something to learn from the natural world. The story of evolution is full of problems that have been innovatively solved.
There are thousands of species of butterfly, each with their unique egg design. A truncated icosahedron for a frame, the opposite of a football. Instead of panels pushed out, they are pulled in.
Fractals are commonly occurring in nature, and can be described as a never-ending pattern on different scales. People are subconsciously familiar with fractals, so are inherently more relaxed when surrounded by them.
3D Printing is a relatively new technology that is set to change our world. Innovations in the uses of 3D printers, combined with falling costs, means that they could be a ubiquitous tool in every home and industry. 3D printers and scanners are already used a great deal in everything from the biomedical field to art studios, and experiments are currently being done to construct entire homes. This technology is in its infancy, and it is exactly for this reason that every effort should be taken to research its potential. It is common to use 3D printers in architecture to show small working models, I would like to now use it to make a large and complex structure at full scale.
This research will underpin the design of a sculptural installation in which people can interact with live butterflies. With the ever-declining numbers of butterflies worldwide and in the UK, conservation and education are paramount.
The link between butterflies and humans in our ecosystem is one that is vital and should be conserved and celebrated.
I can imagine an ethereal space filled with dappled light where people can come for contemplation and perhaps their own personal metamorphosis.
We are pleased to announce that DS10 student Andrei Jipa has been nominated for the RIBA Silver Medal 2014, for the best part II student project in the UK.
Andrei’s futuristic proposal “Solanopolis” blended a radical futuristic vision with an advanced understanding of mathematics and 3D printing technologies to create a 3D printed city whose design sprang directly from the underlying code in fractals, creating stunning architecture which echoes the implicit mathematical beauty found in Baroque architecture.
In order to physically recreate these proposals Andrei pushed the boundaries of 3D printing, rewriting the code sent to the 3D printer, devising and publicly sharing a new way of 3d printing with the world.
This was all set against a fantastically creative post apocalyptic narrative of an entire culture and economy based around growing potatoes and turning potato starch into plastic for an army of large scale 3d printers to keep on building up from the rising waters of a future flooded world.
It was in our opinion a very creative blending of brave ideas backed up by rigorous technical research and real world physical results, and we think he has a great chance of winning this years prestigious prize.
Andrei’s proposal will be featured soon on the RIBA website http://www.presidentsmedals.com/
But wait, there’s more! On top of that yet another DS10 project, Hayam Temple designed by Josh Haywood, has been built over the Summer by a team including past and present DS10 students and is currently bringing joy to the revellers at this year’s Burning Man festival in Nevada and has been receiving praise all over the place.
The beautiful project inspired by the delicate muqarnas found in Islamic architecture has received great international praise and has been featured across the web…
My study about a custom G-Code for FDM 3d printing geometries based on a central axis (not necessarily a straight line! – any curve would do). Rather than printing layer by layer horizontal sections that are uneven and inefficient in terms of travel time, the slices are consistent and always perpendicular to the central axes. Moreover the transition between layers – rather than being done from a single point through a vertical motion which is the traditional approach – is a continuous gradual motion upwards, the travel path resembling a spiral, thus improving efficiency.
1. Types of 3D printers (SLA, FDM, SLS and Z-printers)
The first 3d Printer, built in 1983 by Chuck Hull was using SLA technology to print with a photoplymer.
Layer by layer, a liquid polymer is exposed to light from a low-power laser and hardens locally. It produces very accurate prints, theoretically capable of tolerances within 100 nm (0.0001 mm), smaller than visible light wavelength, because of the capacity of lasers to focus beams of only a few photons in diameter.
Traditionally a very expensive technology using expensive polymers, recently it became affordable through the Formlab Form 1:
Fused deposition modeling (FDM)
A very popular technology developed in the 80s by Scott Crump and widely available today after the expiration of patents when the large Rep-Rap open-source community started to develop affordable machines using this technology.
The material is supplied as a roll of filament (generally ABS or PLA), a hot nozzle melts it, extrudes it and deposes it in layers to build up a 3d model.
Selective laser sintering (SLS) and other variations (DMLS, SHS, SLM, EBM)
Developed in the mid 80s by Carl Deckard in Austin, Texas. Similar to SLA, SLS machines use a more powerful laser to fuse together powdered particles of a variety of materials (plastic, metal, glass, porcelain etc). The advantage of this technology over SLA and FDM is that prints do not require support structures, because of the ability of the powder to support cantilevering layers above.
Plaster-bed printing (PP)
Z-printers were developed in 1995 at MIT use layers of plasters and an ink-jet print-head that uses a binding resin to harden the plaster powder. Because of the possibility of using different colours of resin, the Z-corps are capable of building full-colour models. They are also capable of printing cantilevering structures without support. Plaster 3d prints have a very good resolution but are soft and fragile and need to be glued.
2. Replicating Rapid-prototyper (Rep-Rap)
A Rep-rap is a machine that can be built using only standard off-the-shelf parts (nuts, bolts, stepper motors etc) and parts that it can 3d-print itself (generally joints and connection pieces).
Adrian Bowyer developed the first prototype in 2004 at the University of Bath. Since then, the project grew exponentially, currently having hundreds of family members, versions, updates and spin-offs. The original Darwin used FDM technology and a cartesian movement system, the nozzle moving in the two horizontal axes XY while the print bed moves vertically in Z direction.
To day most rep-raps are FDM machines based on cartesian coordinate systems, the two most advanced branches in the family being the Prusa Mendel (XZ Head; Y Bed), the PrintrBot/Up! (X Head YZ Bed); the MakerBot (Z Head; YZ Bed) and the Ultimaker (XY Head; Z Bed).
Other technologies have been adapted to be used in Rep-Raps, such as the CandyFab, a selective sintering machine that uses a heat source and sugar as raw material:
A reprap SLA machine is also available as a kit for about 600$ from Veloso, only one available as far as I am aware.
Newest trends are in developing rep-rap printers that are non-cartesian and based on different coordinate systems. Check out these cool machines:
A SCARA coordinate system machine:
A POLAR coordinate system machine:
A DELTA coordinate system machine:
Amazing projects are always kickstarted, check this one out for a printer under $100:
3.Be the first to 3d print a house!
Currently in the world there are three working large scale 3d printers aimed at manufacturing buildings:
1. The Italian based D-Shape by Enrico Dini:
And a prototype for Foster’s Moon Base also done with the D-Shape:
3. And the Contour Crafting by Behrokh Khoshnevis from the University of Southern California:
What if Bioplastic could be used as a green construction material ?
Plastic can acquire any shape you give it.
But what about the natural behaviour of the viscous material?
Experiments consisting in elongating the viscous material can reveal an interesting form configuration that has inherent structural properties.
The rules defining the the material configuration are then coded into a script that enables to digitally replicate the shape. The structural performace of the shape opens the opportunity for many applications.
A bridge is imagined following the same formal configuration.
A fascinating TEDX lecture with Dr. Siavash Mahdavi, director of Within Technologies Ltd, a London-based consultancy company specialising in higher-end engineering applications and design using 3D printing.The very diverse work includes medical software for bone implants, customized high-heel shoes and spaceship material.
Above: 3D printed titanium engine part with varying density for force distribution.
Above: 3D printed cranial implants with varying density.