Having had a look at 2000-2015 sci-fi glimpses into the future, climate change remained a constant, unchanged factor of influence. This study investigates the basics of desertification, how dunes are formed and how they are shaped and moved by external forces.
A couple of experiments investigate the wind effects on sand formation and also an interesting method of solidifying the resulted dune with adhesive and heat.
The Inversion Principle is a mathematical formula that maps points from inside to outside a circle and vice versa, governed by the equation MQ = r2/MP where [MP] is the distance between the origin of the circle and a chosen point and [r] is the radius of the circle. The chosen point is then moved along motion vector [MP] at new distance [MQ].
Initial experiments explored inverting a series of two dimensional shapes through a circle. Each shape or series of curves was first divided into a series of points which were remapped using the inversion principle and then reconnected with the same relationship.
The same process can be applied to three dimensional objects, using a sphere as the inverting object as opposed to a circle. Below is the inversion of an Icosahedron, achieved by dividing the initial shape into a series of vertices defining the faces. These are remapped by the Inversion Principle and then reconnected with the same relationship to give new vertices and faces.
Exploration into the number of subdivisions showed that the more vertices a shape is divided into, the more it approaches its ‘true’ approximation. Less subdivisions leads to a more faceted output geometry.
These experiments were followed by a series of physical models which investigated modelling the interior volumes of the 3D object as a series of two dimensional planes using both spheres and cylinders as the inversion object. Below are the internal volumes of an inverted Dipyramid and four sided pyramid.
First developed in 1979 by Dániel Erdély the Spidron is created by recursively dividing a 2-dimensional hexagon into triangles, forming a pattern that consists of one equilateral followed by one isosceles triangle. The resulting form is of six Spidron legs that, when folded along their edges, deform to create a 3-dimensional Spidron.
Initial investigations into the Spidron system using paper resulted in irregular shapes that could not be predicted, and therefore replicated precisely. Progressing onto using rigid materials allowed the system to be broken down into six components, removing unnecessary triangulated fold lines, and developing latch folded Spidron that is precisely the same as that formed parametrically.
This relationship between parametric and physical tests of component based Spidrons in both regular and irregular hexagons, as well as various other equal-sided shapes, has enabled the development of large scale models concluding thus far in a 1:2 scale version being built which will continue to be developed as a pavilion for submission to the Burning Man festival.
In parallel there has been an investigation into the system at a smaller scale allowing for the Spidron nest to be made as one component. In order to achieve the 3-dimensional Spidron form lattice hinges, also known as kerf folds, have been employed. Rigorous testing into the best cutting pattern have resulted in a straight line cutting pattern that allows for bending on multiple axis at once.
Developing this smaller scale system for submission to Buro Happold the intention is to create an arrayed system that is a conglomeration of both regular and irregular spidrons with varying depths and apertures that are able to integrate various display models etc. within.
Here are couple inspiring pictures from our last tutorial. Students are now focusing on developing larger models. They will soon choose between submitting an installation for Buro Happold’s new HQ or the Burning Man festival.
Here are couple pictures from our last tutorials. DS10 is back with some exciting experiments, models and diagrams for Brief01:Systems. From Lorna’s spiralhedrons to Sarah’s pyritohedron, Maria’s stalagtites to Charlotte’s Jitterbug, Garis’ curved folding to Tobias’ Rheotomic surfaces, students are exploring the mathematical, natural or biological system of their choice, both with physical and digital parametric models.
A small selection of photos from DS10s unit trip to Southern Spain.
For more Images follow: http://issuu.com/josh-haywood/docs/bewk?e=10839685/7097420
A small script based on Hankin’s Method to generate nonperiodic plane tiling patterns. It includes a very crude method for applying colour, as well as a basic projection on a non euclidean space plus the appropriate Poincare disc. This is not an Archimedean tessellation in hyperbolic space, being just a projection of the flat Hankin tiling, .
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
Suppliers: Hess Precision (Plywood Laser Cutting), One-to-Metal, (Metal Punching and Folding), Safway (Scaffolding), West Coast Netting (Netting)
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.
The Story:
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.
On site:
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.
It was DS10’s Final crit yesterday which concludes our BRIEF03:TEMPLE. Wonderful day with a wide spectrum of temples showing the concerns and fascinations of a group of twenty-one architectural students in 2013. A myriad of political and spiritual statements on today’s society helped by parametric design tools and physical modelling. Here is the list of all the themes that emerged in the third term:
Thank you very much to all our external critiques: William Firebrace, Jeanne Sillett, Harri Lewis and Jack Munro. Two weeks more to go until the hand-in of portfolios (28th May). Here are couple pictures:
Arthur C. Clarke’s documentary on Fractals:
A basic set with fractal behaviour is the set of Complex numbers (C):
No matter how much one zooms in or out, the set is self-similar with infinite detail.
The typical fractal sets (Mandelbrot, Julia, Fatou) follow a pattern of 3 infinities: an infinite number of points is run an infinite number of times through a recursive polynomial and it will/will not reach infinity:
To make the step to 3d, the major issue is that the 2d rules cannot be generalized because there is no corresponding set of numbers for 3d space. 1d space has Real numbers, 2d space has Complex numbers, but there is no 3d equivalent. However, Quaternions (hypercomplex numbers) are a theoretical set of points corresponding to a 4d space. Therefore there are two possible approaches: a) Define a three dimensional set of points in polar coordinates and switch them back to a cartesian coordinates in order to build it in computer space. b) Build a theoretical 4d fractal using hypercomplex numbers and cast its 3d shadow in 3d.
Either way, results are similar:
Dealing with infinite numbers, infinite iterations and infinite sets of points, computation times become an issue. One way around this is to build ray-traced images estimating distances to a virtual fractal (not physically storing the points of the fractal in memory):
The image above is magnified ~3.10e13 times. In other words, presuming the size of the sectional model is 1m, it scaled up to roughly the size of the Solar System.
Building 3d models in computer space is slightly trickier because of the huge number of points involved to define even a limited section of a fractal. The issue is to define an algorithm for the correct order of the points in order to build a mesh. A rather neat solution is to ray-trace consecutive sections through a fractal (ray-tracing involves a Z-buffer anyway) and work from there. Here is an example (a 38,000,000 face-mesh obtained from 1,000 sections):
An important tool in exploring 3d fractals is building Julia sets (the only difference is that they use a constant increment at each iteration rather than the initial step):
Software used for my project: Processing, ImageJ FIJI, MeshLab, Netfabb Studio, Jesse’s MandelBulb 3D, Autodesk 3dS Max, Chaos Pro, Adobe Premiere.
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