Developing Space-Filling Fractals

Delving deeper into the world of mathematics, fractals, geometry, and space-filling curves.

 

Foreword

Following my last post on the “…first, second, and third dimensions, and why fractals don’t belong to any of them…“, this post is about documenting my journey as I delve deeper into the subject of fractals, mathematics, and geometry.
The study of fractals is an intensely vast topic. So much so that I’m convinced you could easily spend several lifetimes studying them. That being said, I chose to focus specifically on single-curve geometry. But, keep in mind that I’m only really scratching the surface of what there is to explore.

4.0 Classic Space-Filling

Inspired by Georg Cantor’s research on infinity near the end of the 19th century, mathematicians were interested in finding a mapping of a one-dimensional line into two-dimensional space – a curve that will pass through through every single point in a given space.
Jeffrey Ventrella writes that “a space-filling curve can be described as a continuous mapping from a lower-dimensional space into a higher-dimensional space.” In other words, an initial one-dimensional curve is developed to increase its length and curvature – the amount of space in occupies in two dimensions. And in the mathematical world, where a curve technically has no thickness and space is infinitely vast, this can be done indefinitely.

4.1 Early Examples

In 1890, Giuseppe Peano discovered the first of what would be called space-filing curves:

Peano-space-filling-Curve_-four-approximations_-version-A_1 4i.gif
4 Iterations of the Peano Curve
An initial ‘curve’ is drawn, then each element of the curve is replace by the whole thing. Here it is done four times, and it’s easy to imagine how you can keep doing this over and over again. One would think that if you kept doing this indefinitely, this one-dimensional curve would eventually fill all of two-dimensional space and become a surface. However it can’t, since it technically has no thickness. So it will be as close as you can get to a surface, without actually being a surface (I think.. I’m not that sure..)
A year later, David Hilbert followed with his slightly simpler space-filing curve:
Hilbert_curve 8i.gif
8 Iterations of the Hilbert Curve
In 1904, Helge von Koch describes a single complex continuous curve, generated with rudimentary geometry.
Von_Koch_curve 7i.gif
7 Iterations of the Koch Curve
Around 1967, NASA physicists John Heighway, Bruce Banks, and William Harter discovered what is now commonly known as the Dragon Curve.
Dragon_Curve_Unfolding 13i.gif
13 Iterations of the Dragon Curve

4.2 Later Examples

You may have noticed that some of these curves are better at filling space than others, and this is related to their dimensional measure. They fall under the category of fractals because they’re neither one-dimensional, nor two-dimensional, but sit somewhere in between. For these examples, their dimension is often defined by exactly how much space they fill when iterated infinitely.
While these are some of the earliest space-filling curves to be discovered, they are just a handful of the likely endless different variations that are possible. Jeffrey Ventrella spent over twenty-five years exploring fractal curves, and has illustrated over 200 hundred of them in his book ‘Brain-Filling Curves, A Fractal Bestiary.’ They are organised according to a taxonomy of fractal curve families, and are shown with a unique genetic code.
Incidentally, in an attempt to recreate one of the fractals I found in Jeffery Ventrella’s book, I accidentally created a slightly different fractal. As far as I’m concerned, I’ve created a new fractal and am unofficially naming it ‘Nicolino’s Quatrefoil.’ The following was created in Rhino and Grasshopper, in conjunction Anemone.
Nicolino-Quatrefoil_Animation i5.gif
5 Iterations of Nicolino’s Quatrefoil
You can find beautifully animated space-filling curves here:
(along with some other great videos by ‘3Blue1Brown’ discussing the nature of space-filling curves, fractals, infinite math, and more)

On A Strange Note:

It’s possible to iterate a version of the Hilbert Curve that (once repeated infinity) can fill three-dimensional space.
As an object, it seems perplexingly difficult to categorize. It is a single, one-dimensional, curve that is ‘bent’ in space following simple, repeating rules. Following the same logic as the original Hilbert Curve, we know that this can be done indefinitely, but this time it is transforming into a volume instead of a surface. (Ignoring the fact that it is represented with a thickness) It is a one-dimensional curve transforming into a three-dimensional volume, but is never a two-dimensional surface? As you keep iterating it, its dimension gradually increases from 1 to eventually 3, but will never, ever, ever be 2??
giphy.gif
Nevertheless this does actually support a statement I made in my last post suggesting “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…

5.0 Avant-Garde Space-Filling

In the case of the original space-filling curve, the goal was to fill all of infinite space. However the fundamental behaviour of these curves change quite drastically when we start to play with the rules used to generate them. For starters, they do not have to be so mathematically tidy, or geometrically pure. The following curves can be subdivided infinitely, making them true space-filling curves. But, what makes them special is the ability to control the space-filling process, whereas the original space-filling curves offer little to no artistic license.

5.1 The Traveling Salesman Problem

Let’s say that we change the criteria, from passing through every single point in space, to passing only through the ones we choose. This now becomes a well documented computational problem that has immediate ‘real world’ applications.
Our figurative traveling salesman wishes to travel the country selling his goods in as many cities as he can. In order to maximize his net profit, he must make his journey as short as possible, while of course still visiting every city on his list. His best possible route becomes exponentially more challenging to work out, as even just a handful of cities can generate thousands of permutations.
There are a variety of different strategies to tackle this problem, a few of which are described here:
The result is ultimately a single curve, filling a space in a uniquely controlled fashion. This method can be used to create single-lined drawings based on points extracted from Voronoi diagrams, a topic explored by Arjan Westerdiep:
Traveling Salesman Portrait.png
This illustration, commissioned by Bill Cook at University of Waterloo, is a solution to the Traveling Salesman Problem.

5.2 Differential Growth

If we let physics (rather than math) dictate the growth of the curve, the result becomes more organic and less controlled.
In this example Rhino is used with Grasshopper and Kangaroo 2. A curve is drawn on a plain, broken into segments, then gradually increased in length. As long as the curve is not allowed to cross itself (which is achieved here with ‘Collision Spheres’), the result is a curve that is pretty good at uniformly filling space.
Differential-Growth-With-Kangaroo-2.gif
Differential Growth with Rhino & Grasshopper – Kangaroo 2 – Planar
The geometry doesn’t even have to be bound by a planar surface; It can be done on any two-dimensional surface (or in three-dimensions (even higher spacial dimensions I guess..)).
Bunny-Differential-Growth.gif
Differential Growth with Rhino & Grasshopper – Kangaroo 2 – NonPlanar
Rotating-Stanford-Bunny.GIF
Differential Growth with Rhino & Grasshopper – Kangaroo 2 – Single-Curved Stanford Rabbit
Additionally, Anemone can be used in conjunction with Kangaroo 2 to continuously subdivide the curve as it grows. The result is much smoother, as well as far more organic.
Kangaroo & Anemone - Octo-Growth.gif
Differential Growth with Rhino & Grasshopper – Kangaroo 2 & Anemone – Octopus
Of course the process can also be reversed, allowing the curve to flow seamlessly from one space to another.
Kangaroo & Anemone - Batman Duck.gif
Differential Growth with Rhino & Grasshopper – Kangaroo 2 & Anemone – BatmanDuck
Here are far more complex examples of growth simulations exploring various rules and parameters:

6.0 Developing Fractal Curves

In the interest of creating something a little more tangible, it is possible to increase the dimension of these curves. Recording the progressive iterations of a space filling curve allow us to generate what is essentially a space-filling surface. This new surface has the unique quality of being able to fill a three-dimensional space of any shape and size, while being a single surface. It of course also shares the same qualities as its source curves, where it keep increasing in surface area (and can do so indefinitely).
Unrolling Surfaces.jpg
Surface Unrolling Study
If you were to keep gradually (but indefinitely) increasing the area of a surface this way in a finite space, the result will be a two-dimensional surface seamlessly transforming into a three-dimensional volume.

6.1 Dragon’s Feet

Here is an example of turning the dragon curve into a space-filling surface. Each iteration is recorded and offset in depth, all of which inform the generation of a surface that loosely flows through each of them. This was again achieved with Rhino and Grasshopper.
I don’t believe this geometry has a name beyond ‘the developing dragon curve’, so I’ve called it ‘Dragon’s Feet.’
Adding a little thickness to the model allow us to 3D print it.
3d Printed Dragon Curve.jpg
Developing Dragon Curve: Dragon’s Feet – 3D Print

6.2 Hilbert’s Curtain

Here is the Hilbert Curve going through the same process, which I am aptly naming ‘Hilbert’s Curtain.’
3D Printed Developing Hilbert Curve
Developing Hilbert Curve: Hilbert’s Curtain – 3D Print
3D Printing Space-Filling Curves with Henry Segerman at Numberphile:
‘Developing Fractal Curves’ by Geoffrey Irving & Henry Segerman:

6.3 Developing Whale Curve

Unsurprisingly this can also be done with differentially grown curve. The respective difference being that this method fills a specific space in a less controlled manner.
In this case with Kangaroo 2 is used to grow a curve into the shape of a whale. Like before, each iteration is used to inform a single-surface geometry.
Developing-Whale-Curve-b.gif
Iterative Steps of the Differentially Grown Whale Curve

3D print of the different recursive steps of a space-filling curve
Developing Whale Curve – 3D Print

Omnis Stellae

Omnis Stellae – Redrawing your own constellation

“Only in the darkness can you see the stars”
Martin Luther King

 

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.

Example of Stellation diagram on a platonic polygon

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.

Omnis Stellae – Daytime interior render view

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.

Omnis Stellae – Daytime exterior render view

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.

Omnis Stellae – Daytime interior render view from the ground

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.

 

Omnis Stellae – Nightime exterior render view

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 – Daytime interior render view from above

“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 – Daytime and Nightime

“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.

Omnis Stellae – Daytime interior render view

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.

With Love,

Maya

 

 

 

The Wishing Well

something caught in between dimensions – on its way to becoming more.

Summary

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

 

Description

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.

Different Recursive Steps of a Dragon Curve

Ambition

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.

171108 - Burning Man Timber Brick Laying Proposal View 2.jpg

 

Philosophy

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:

  • ► PINK – love
  • ► RED – happiness, joy, success, good luck, passion, vitality, celebration
  • ► ORANGE – change, adaptability, spontaneity, concentration
  • ► YELLOW – nourishment, warmth, clarity, empathy, being free from worldly cares
  • ► GREEN – growth, balance, healing, self-assurance, benevolence, patience
  • ► BLUE – conservation, healing, relaxation, exploration, trust, calmness
  • ► PURPLE – spiritual awareness, physical and mental healing
  • ► BLACK – profoundness,  stability, knowledge, trust, adaptability, spontaneity,
  • ► WHITE – mourning, righteousness, purity, confidence, intuition, spirits, courage

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.

171108 - Burning Man Timber Brick Laying Proposal View 1.jpg

Life’s First Flicker

LifeFirstFlicker_External_Night.png

Project Summary

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.

Physical Description

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.

LifesFirstFlicker_External_Day

Philosophy

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.


<p><a href=”https://vimeo.com/244593633″>Life’s First Flicker: Burning Man 2018 Art proposal</a> from <a href=”https://vimeo.com/user71835996″>Benjamin Street</a> on <a href=”https://vimeo.com”>Vimeo</a&gt;.</p>

The Butterfly Egg

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.

White Royal [Pratapa deva relata] HuDie's Microphotography
White Royal [Pratapa deva relata] HuDie’s Microphotography
shapes copy
Clockwise: Hesperidae, Nymphalidae, Satyridae, Pieridae

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.

lyc
Lycaenidae

Other eggs
Lycaenidae eggs from left to right: Acacia Blue [Surendra vivarna amisena], Aberrant Oakblue [Arhopala abseus], Miletus [Miletus biggsii], Malayan [Megisba malaya sikkima]. HuDie’s Microphotography
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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.

2

There are thousands of species of butterfly, each with their unique egg design. 3A truncated icosahedron for a frame, the opposite of a football. Instead of panels pushed out, they are pulled in.

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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.

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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.

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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.

Interior

—Tia

Thursday 14th May Cross-Crit and Future Cities

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!

Eva Ciocyte - Aral City - As the earth gets too polluted to allow the growth of any edible crop, Aral City attempts to purify the soil progressively by building giant evaporative and inhabitable greenhouses.
Eva Ciocyte – Aral City – As the earth gets too polluted to allow the growth of any edible crop, Aral City attempts to purify the soil progressively by building giant evaporative and inhabitable greenhouses.
Alex Berciu, The Algorithmic City, In the presented scenario, the natural environment in which human beings live today will no longer exist, having been replaced by fully computer generated habitation. As the Earth’s surface will have been largely damaged by pollution and natural disasters, the only  solution for living pushed human society upwards in suspended structures developed through the  technique of extruding concrete and drone assembly. Based on a growth algorithm that evolves with  relation to continuous feedback gathered from climate data, structural qualities and population needs,  the system can perform in any given location. in the generated structure, the algorithm places accordingly a selection of 8 typologies considered  suitable for the needs of the future human society. These are: aliment production/farming, aliment  storage, housing, education hubs, culture hubs, spiritual hubs, places of sin and production  laboratories. Each typology is designed to fit within the modular grid and is placed according to  density and distance rules. The ratio between the 8 typologies is also adaptable, responding to  possible changes in societal needs.
Alex Berciu, The Algorithmic City, In the presented scenario, the natural environment in which human beings live today will no longer exist, having been replaced by fully computer generated habitation. As the Earth’s surface will have been largely damaged by pollution and natural disasters, the only solution for living pushed human society upwards in suspended structures developed through the technique of extruding concrete and drone assembly. Based on a growth algorithm that evolves with relation to continuous feedback gathered from climate data, structural qualities and population needs, the system can perform in any given location. in the generated structure, the algorithm places accordingly a selection of 8 typologies considered suitable for the needs of the future human society. These are: aliment production/farming, aliment storage, housing, education hubs, culture hubs, spiritual hubs, places of sin and production laboratories. Each typology is designed to fit within the modular grid and is placed according to density and distance rules. The ratio between the 8 typologies is also adaptable, responding to possible changes in societal needs.
Marine Pollution has become a growing plaque as plastics are accumulated into patches within the gyres around the world, damaging the marine ecosystem and entering the marine food web. As these plastics are not biodegradable, they continue to pose a threat to the marine wildlife as well as humanity. Centuries into the future, people have begun to seek for ocean colonization in an attempt to tackle marine pollution and the rising sea level. The Fluas is a self-sufficient city that realises the potential of ocean plastics as a source of reusable material. Situated within the North Pacific Gyre and consisting of clusters of floating platforms, the city is centred on the collection and recycling of these materials into elements of the city - in the form of pneumatic structures. As plastics are salvaged from the gyre, the inflated city continues to grow while its inhabitants live a seaborne lifestyle.
Garis Iu – The Inflated City – Marine Pollution has become a growing plaque as plastics are accumulated into patches within the gyres around the world, damaging the marine ecosystem and entering the marine food web. As these plastics are not biodegradable, they continue to pose a threat to the marine wildlife as well as humanity. Centuries into the future, people have begun to seek for ocean colonization in an attempt to tackle marine pollution and the rising sea level. The Fluas is a self-sufficient city that realises the potential of ocean plastics as a source of reusable material. Situated within the North Pacific Gyre and consisting of clusters of floating platforms, the city is centred on the collection and recycling of these materials into elements of the city – in the form of pneumatic structures. As plastics are salvaged from the gyre, the inflated city continues to grow while its inhabitants live a seaborne lifestyle.
Garis Iu The Inflated City
Cidade de Árvores The Atlantic Forest in southern Brazil has long been viewed as a vast quilt of rain forest interspersed by small river outposts. The surging population growth has seen these remote settlements transform this ancient rural vision to an expansive city scale. Cidade de Árvores (City of Trees) envisions an environment where both the city’s infrastructure and its inhabitants maintain a symbiotic relationship with the surrounding natural environment.  Built entirely from locally grown timber, the Cidade de Árvores exists as a network of steam bent beams, joined to form a structural space frame.  Like the forest, the frame is allowed to grow and develop organically over time with inhabitants adding to structure to meet their requirements. The city is powered through the use of micro wind turbine electricity generation which manifests as a series of towers scattered throughout the forest. For the city and the environment to function in harmony, the city access routes manifest as elevated walkways around large courtyards, allowing light to penetrate to the forest floor.
Joe Leach – Cidade de Árvores
The Atlantic Forest in southern Brazil has long been viewed as a vast quilt of rain forest interspersed by small river outposts. The surging population growth has seen these remote settlements transform this ancient rural vision to an expansive city scale. Cidade de Árvores (City of Trees) envisions an environment where both the city’s infrastructure and its inhabitants maintain a symbiotic relationship with the surrounding natural environment. Built entirely from locally grown timber, the Cidade de Árvores exists as a network of steam bent beams, joined to form a structural space frame. Like the forest, the frame is allowed to grow and develop organically over time with inhabitants adding to structure to meet their requirements. The city is powered through the use of micro wind turbine electricity generation which manifests as a series of towers scattered throughout the forest. For the city and the environment to function in harmony, the city access routes manifest as elevated walkways around large courtyards, allowing light to penetrate to the forest floor.
Tobias Power's Infinity Tree for Burning Man development
Tobias Power’s Infinity Tree for Burning Man development
The Infinity Tree - Updated structure with the help of Format Engineers and Ramboll
The Infinity Tree – Updated structure with the help of Format Engineers and Ramboll
This project seeks to develop a response to the combined challenges of natural disasters, the aging population and  over-fishing. All three are closely connected in Japan. In Japan, where life expectancy is one of the highest in the  world, 1 in 3 people will be over 60 by 2050. Unfortunately, Japan is also a country that has been hit by major natural  disasters such as tsunamis, during which the vulnerable elderly suffered the most. Finally, in Japan fish is the main  food source and over fishing may become a major issue in the future. Moreover, Japan has one of the highest  percentages of labour force of people aged 60 and over within the fishing industry. I am proposing a self-sufficient,  resilient city for the super-aging Japanese fishing community along the coast, as a response to these future scenarios.  The structure of the proposal would not only act as a vertical evacuation point, and accommodation for the elderly and  their families, but would also be used as sustainable fish-farming.
The Origami City – Naomi Danos – This project seeks to develop a response to the combined challenges of natural disasters, the aging population and over-fishing. All three are closely connected in Japan. In Japan, where life expectancy is one of the highest in the world, 1 in 3 people will be over 60 by 2050. Unfortunately, Japan is also a country that has been hit by major natural disasters such as tsunamis, during which the vulnerable elderly suffered the most. Finally, in Japan fish is the main food source and over fishing may become a major issue in the future. Moreover, Japan has one of the highest percentages of labour force of people aged 60 and over within the fishing industry. I am proposing a self-sufficient, resilient city for the super-aging Japanese fishing community along the coast, as a response to these future scenarios. The structure of the proposal would not only act as a vertical evacuation point, and accommodation for the elderly and their families, but would also be used as sustainable fish-farming.
Naomi Danos, The Origami City
Naomi Danos, The Origami City
Lorna Jackson presenting her Burning Man proposal and future city for women only.
Lorna Jackson presenting her Burning Man proposal and future city for women only.
Fractal BreakCity will act as defence and breakwater structures against tsunamis and floods.  Benefiting of internalised creation of food, resources and objects, a trade based economy will  emerge, while the cult of product marketing will shrink to its essential.  The city is based on recursive aggregation: one geometry is repeated in a self-similar way to create a  complex looking aggregation, following a fractal pattern. The system consists of one module, with structures of different scales according to their function, so that the bathroom will be the smallest box unit, the bedroom slightly larger and so on. The largest box unit at the center of an aggregated module, will consist of the communal and production based spaces. Cellulose mixed with water, can be 3D printed to create structures stronger than steel and will become structural elements for the city, while aerogel wall components (made of silica, which is found in sand, across the world) will clad each unit’s sides.
Diana Raican – Fractal BreakCity will act as defence and breakwater structures against tsunamis and floods. Benefiting of internalised creation of food, resources and objects, a trade based economy will emerge, while the cult of product marketing will shrink to its essential. The city is based on recursive aggregation: one geometry is repeated in a self-similar way to create a complex looking aggregation, following a fractal pattern. The system consists of one module, with structures of different scales according to their function, so that the bathroom will be the smallest box unit, the bedroom slightly larger and so on. The largest box unit at the center of an aggregated module, will consist of the communal and production based spaces. Cellulose mixed with water, can be 3D printed to create structures stronger than steel and will become structural elements for the city, while aerogel wall components (made of silica, which is found in sand, across the world) will clad each unit’s sides.
Jon Leung's developments on the Bismuth Bivouac for Burning Man
Jon Leung’s developments on the Bismuth Bivouac for Burning Man
Jon Leung's Bismuth Bivouac updated render with latest development with the help of format engineers.
Jon Leung’s Bismuth Bivouac updated render with latest development with the help of format engineers.
John Koning's power generating Ron Resch origami city
John Koning’s power generating Ron Resch origami city
Irina Ghuizan's flying city
Irina Ghuizan’s flying city
Toby Plunket's Silent City in China
Toby Plunket’s Silent City in China

2014 End of Year Portfolio Review

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.

Joe Leach's Reciprocal Seed Temple for Burning Man
Joe Leach’s Reciprocal Seed Temple for Burning Man
Andrei Jipa's incredible 3D printed collection
Andrei Jipa’s incredible 3D printed collection
Garis Iu's Chanting Bridge for Mont St-Michel
Garis Iu’s Chanting Bridge for Mont St-Michel
Georgia Rose Collard-Watson's tent structure for the Burlesque Festival
Georgia Rose Collard-Watson’s tent structure for the Burlesque Festival
Our beautiful messy studio space full of 1:1 Prototype
Our beautiful DS10 studio space full of 1:1 Prototype
Our beautiful messy studio space full of 1:1 Prototype
Our beautiful  DS10 studio space full of 1:1 Prototype
William Garforth-Bless, Charlotte Yates and Andrei Jipa showing their models in the Diploma Studio 10 space
William Garforth-Bless, Charlotte Yates and Andrei Jipa showing their models in the Diploma Studio 10 space
Solanopolis - Andrei Jipa's 3D printed potato fractal city
Solanopolis – Andrei Jipa’s 3D printed potato fractal city
Solanopolis - Andrei Jipa's 3D printed potato fractal city
Solanopolis – Andrei Jipa’s 3D printed potato fractal city
Solanopolis - Andrei Jipa's 3D printed potato fractal city
Solanopolis – Andrei Jipa’s 3D printed potato fractal city
Solanopolis - Andrei Jipa's 3D printed potato fractal city
Solanopolis – Andrei Jipa’s 3D printed potato fractal city
Solanopolis - Andrei Jipa's 3D printed potato fractal city
Solanopolis – Andrei Jipa’s 3D printed potato fractal city
Solanopolis - Andrei Jipa's 3D printed potato fractal city
Solanopolis – Andrei Jipa’s 3D printed potato fractal city
Solanopolis - Andrei Jipa's 3D printed potato fractal city
Solanopolis – Andrei Jipa’s 3D printed potato fractal city
Solanopolis - Andrei Jipa's 3D printed potato fractal city
Solanopolis – Andrei Jipa’s 3D printed potato fractal city
Solanopolis - Andrei Jipa's 3D printed potato fractal city
Solanopolis – Andrei Jipa’s 3D printed potato fractal city
Solanopolis - Andrei Jipa's 3D printed potato fractal city
Solanopolis – Andrei Jipa’s 3D printed potato fractal city
Solanopolis - Andrei Jipa's 3D printed potato fractal city
Solanopolis – Andrei Jipa’s 3D printed potato fractal city
Josh Haywood's Hayam and Pop-Up Mosque for Trafalgar Square
Josh Haywood’s Hayam and Pop-Up Mosque for Trafalgar Square
Josh Haywood's Hayam and Pop-Up Mosque for Trafalgar Square
Josh Haywood’s Hayam and Pop-Up Mosque for Trafalgar Square
Joe Leach's Reciprocal Seed Temple for Burning Man
Joe Leach’s Reciprocal Seed Temple for Burning Man
Lorna Jackson's Surreal Dali Museum
Lorna Jackson’s Surreal Dali Museum
Mark Simpson's Synthetic Diamond Crematorium
Mark Simpson’s Synthetic Diamond Crematorium
Jessica Beagleman's Kabbalah Centre
Jessica Beagleman’s Kabbalah Centre
Jessica Beagleman's Kabbalah Centre
Jessica Beagleman’s Kabbalah Centre