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:
This project involves the conception and design of a new way of mapping constellations, based on subdivision processes like Stellation. It explores how subdivision can define and embellish architectural design with an elaborate system of fractals based on mathematics and complex algorithms.
An abstracted form of galaxy is used as an input form to the subdivision process called Stellation. In geometry, meaning the process of extending a polytope in n dimensions to form a new figure. Starting with an original figure, the process extends specific elements such as its edges or face planes, usually in a symmetrical way, until they meet each other again to form the closed boundary of a new figure.
The material used for this installation will be timber sheets of 1/3 of an inch thickness that will be laser-cut.The panels will be connected to each other with standard connection elements which have already been tested structurally based on an origami structure.
The lighting of the installation will consist on LED strips that will light with burners interactions.
Although stars in constellations appear near each other in the sky, they usually lie at a variety of distances away from the observer. Since stars also travel along their own orbits through the Milky Way, the constellation outlines change slowly over time and through perspective.
There are 88 constellations set at the moment, but I would like to prove that there are infinite amount of stars that have infinite amount of connections with each other.The installation will show you all the possible connections between this stars, but will never rule which connection is the one you need to make.
I would like burners to choose their own stars and draw their own constellations. Any constellation that they can possibly imagine from their one and only perspective, using coloured lights that react to their touch.
The end result will have thousands of different geometries/constellations that will have a meaning for each one of the burners and together will create a new meaningful lighted galaxy full of stars.
On a clear night, away from artificial light, it’s possible to see over 5000 stars with the naked eye. These appear to orbit the Earth in a fixed pattern, as if they are attached to a giant sphere that makes one revolution a day.This stars though are organised in Constellations.
The word “constellation” seems to come from the Late Latin term cōnstellātiō, which can be translated as “set of stars”. The relationship between this sets of stars has been drawn by the perspective of the human eye.
“Omnis Stellae” is a manifestation of the existence of different perspectives. For me, there is great value in recognising different perspectives in life, because nothing is really Black and White, everything relates to the point of view and whose point of view and background that is.
As a fractal geometry this installation embodies an endless number of stars that each person can connect and imagine endless geometries, that will only make sense from their own perspective. The stellated geometry will show you all the possible connections but will never impose any.
“Omnis Stellae” is about creating your own constellations and sharing them with the rest of the burners, is about sharing your own perspective of the galaxy and create some meaningful geometries that might not mean anything to other people but would mean the world to you.
The grand finale is if it could become the physical illustration of all the perspectives of the participants at Burning Man 2018 shown as one.
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.
Translucent fractal ball animated by dancing color changing lights symbolizing the very first spark at the beginning of the universe as well as the spark of life that our species is on both an eternal mission to keep alight and is in the final stages of creating anew with artificial intelligence.
A 20 foot diameter translucent form, made of twelve identical five petal polypropylene origami flowers arranged as a dodecahedron each with two smaller flower at their centers and intricately lazercut with a 2d filigree depicting the overall form. All the flowers are tied to each other and to a timber dodecahedral internal skeleton with concealed zip ties. The creased polypropylene held in tension by the origami folds themselves provide the rest of the stability. LED DMX lights sit in the five points which touch the ground, facing upwards, illuminating the entire form.
At the end of Isaac Asmiov’s book ‘The last question’ a disembodied AI is the last mark of the human race left in an empty entropic universe. It remains calculating the answer to the last question it was asked, and, unable to find a recipient for it’s solution it says ‘Let there be light’ and creation begins again.
This piece is shaped as a tangible interpretation of this spark. The spark at the first second of the universe and the spark of life which our civilization is racing to create in a sentient self learning AI. This moment, when our creations become self aware, is the theme of burning man 2018 and also likely to be the most important moment in our species’ history. Self teaching AI will rapidly become so powerful it will effectively be a deity. This pavilion’s purpose is to draw the visitors attention to this rapidly approaching moment and consider how we should design this mind before it is too late.
Burners can pass by or play with the spark and think it is just a cool shape, but those who climb up inside what is figuratively a snapshot right at the beginning of new life and the universe, can take a moment to pause and ponder from within, whether their life’s endeavor is relevant in the face of coming AI, what our species’ current knowledge may lack and how it could be codified and explained to a machine and how lucky we are as a generation to have both been born late enough to see AI’s birth, and early enough to have known life before it.
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.
Some images of our final cross-crit of the year! Our students presented their Brief03:FutureCities. Have a look at how the next generation of architects envision the future of our cities.
Thank you to Andrei Jipa, Kester Rattenbury and Lindsay Bremner. Final sprint to the portfolio submission and end of year!
Our WeWantToLearn.net students have submitted their final portfolios! After an inspiring day going through the projects, we gave them a final mark with the help of the other tutors from the University of Westminster. Below is a selection of the inspiring work that was submitted.
The projects range from a temple at the Burning Man Festival made of an unprecedented reciprocal structure (Joe Leach) to a 3D printed city based on a fractal algorithm and built using potato starch-based plastic grown by the inhabitants of Solanopolis (Andrei Jipa) all the way to a Pop-Up plywood mosque for Trafalgar Square (Josh Haywood) and a lace tent for the London Burlesque Festival (Georgia Collard-Watson) as well as a Kabbalah Centre in the City made from large spiralohedron (Jessica Beagleman), our students have explored a new kind of joyful and spiritual Architecture using the latest digital design and fabrication technique.
Our studio is back after a month of holidays. Here are couple pictures from our tutorials today. Impressive progress from our students including a 3D printed potato-based fractal civilization (Andrei Jipa), a series of recursive bamboo structures for the Durga Puja festival (Dhiren Patel), an origami roof for the fashion week (Charlotte Yates), a spiky eco-retreat to meet the Sami people (Natasha Coutts), a temple for the Burning Man festival made of reciprocal plywood components (Joe Leach), a hypar tower for the Damyang Bamboo festival (William Garforth-Bless), a Pop-Up book drop pavilion (Ieva Ciocyte), a surreal Dali Museum in the Park (Lorna Jackson), a promenade concert in Hyde Park (Sarah Shuttleworth) and many more… We are so excited by the diversity of projects this year and the clear continuity between our brief2A and brief2B. Looking forward to the final crit on Thursday 15th May!
We’re back from the desert! Very proud to have completed two beautiful projects at the Burning Man festival 2013 with our DS10 students and guests from the Architectural Association, Columbia University and UCL.
Credits to the team:
Team: Toby Burgess and Arthur Mamou-Mani a.k.a. Ratchet and Baby Cup (Project Directors), Thanasis Korras (Designer of Fractal Cult), Georgia Rose Collard-Watson (Designer of Shipwreck), Jessica Beagleman (Food & Meals), Natasha Coutts (Camp and Rentals), Sarah Shuttlesworth, Andy Rixson, Luka Kreze, Tim Strnad, Philippos Philippidis, Nataly Matathias, Marina Karamali, Harikleia Karamali, Antony Joury, Emma Whitehead, , Jo Cook, Caitlin Hudson, Dan Dodds and Chris Ingram.
Engineers: Ramboll Computational Design (RCD) – Stephen Melville, Harri Lewis, James Solly
Special Thanks: BettieJune, Ben Stoelting, Kevin Meers, Caroline Holmes, Chloe Brubaker, Papa Bear,
Photos by Jo Cook, Arthur Mamou-Mani, Toby Burgess, Luka Kreze, Thanasis Korras, Antony Joury.
Here are couple more pictures of the finished projects:
Some images of the construction of Shipwreck, from the collection of the pieces all the way to the assembly
Images of the construction process of Fractal Cult until the burn:
Finally, how we made our camp look more like a home and less like a refugee camp:
A beautiful view of the festival itself at sunrise:
Here is a text that we wrote about the experience:
Diploma Studio 10:
Diploma Studio 10 at the University of Westminster is led by Toby Burgess and Arthur Mamou-Mani. They both believe that involvement is key to the process of learning and therefore always try to get their students to “get out and build” their designs in the real world. The studio starts the year with the study of systems, natural, mathematical and architectural systems of all sort, paired with intense software training in order to build up skills and a set of rules to design a small scale project which they will be able to build during a real event in the summer. Throughout the year, they build large scale prototypes and draw very accurate technical drawings, they also need to provide a budget and explain how it makes sense within the wider context of the festival, some of them will event start crowd-funding campaign to self-finance the projects. Our ultimate goal is to give them an awareness of entrepreneurship in Architecture and how to initiate projects as this is for us the best way to fight unemployment in our profession.
Burning Man and the 10 Principles:
The Burning Man festival takes place every summer in Black Rock desert, Nevada. It is a “participant-led” festival in which the activities are initiated by the people attending it. There are around 60,000 “burners” every year building a giant temporary city in which they create a social experiment which follows the 10 principles of Burning Man. They conclude the festival by burning a large sculpture of a Man.
What interested Toby and Arthur are the 10 principle which guide the “burners”: Radical Self-Reliance, Radical Inclusion, Gifting, Leaving No trace, to name a few. Designing with these rules in mind help students understand basic issues of sustainability. Designing for Burning Man also helps the students to design with “playfulness” in mind, as all the structures have to be climbable and interactive. We are not the only one inspired by these rules, Sergei Brin, co-founder of Google, asks all his staff to follow the principles when they come up with new ideas.
On our first year at Westminster we found out that our student could submit their Burning Man proposals and receive a grant from the organizers. After receiving 20 submissions from the same school, the organizers were very intrigued and decided to contact us. The director of the Art Grant told us that she loved the project but that all of them were just not possible in the context. She decided to visit us in London to explain what we could do to submit better projects the following year which we did. On the second run, the festival chose two projects, Shipwreck by Georgia Rose Collard-Watson and Fractal Cult by Thanasis Korras.
These two projects are representative of the way we run our studio: Thanasis looked at Fractal on Brief01 and Georgia looked at ways to bend and assemble strips of wood together. They both explored these systems before submitting a project with a very strong narrative which fitted perfectly the burning man philosophy. Thanasis linked his Fractal to the symbol of “Merkaba” whereas Georgia told the story of a shipwreck which offered shelter from the dust storms.
Once the project got chosen, we partnered with an engineer, Ramboll and started researching for suppliers and fabrication facilities in the USA. We took the 3D files from concept all the way parametric models for fabrication. We started a Gantt chart with every step to take from rental of 24ft truck, collection of item all the way to demolition.
One of the main aspect that required a lot of planning was the camp. We had to plan every meal and food that would not perish under the extreme condition. We also found a way to rent a whole camp equipment from past burners.
The team grew little by little, many of our student could not afford the trip or could not take such a long time off so we asked around if anyone else would like to join us and thanks to our blog posts and active social networking online, students from the Architectural Association, Columbia or UCL started showing interest and joined the team.
Our first surprise on site was the power of the dust storm. One of our Yurt flew away and some of us got stuck in different places of the site seeking shelter. We were terrorised. Sleeping in tents was also extremely hard as you would be awaken by temperatures approaching 40degrees celcius, at the end of the construction, a lot of us would sleep in the foam hexayurts in which we were storing equipment at first.
We learned so much.
Thank you so much everyone – We received funding on Kickstarter ! You can still help us by donating on our Paypal button:
The past couple weeks since our last updates were very busy. We have sent all the fabrication files to our contact next to San Francisco. To make sure the files were alright we had several meetings with our engineers and made a lot of physical tests.
The team has shrunk so if you are keen to join us from the 18th August until the 6th September,you can email us at info@WeWantToLearn.net
Here are couple updates on the projects:
Click Here to see the full Assembly Sequence Diagrams