Fractals vs Digital Fabrication

Since the last post on the 23rd October our students have been exploring how to materialise their research into fractals (which they generated with Mandelbulb3D). The conflict between endless geometry and finite material world creates a creative tension that pushes innovation in digital design and fabrication. From parametric equations to parametric design, students have explored fractals as self-generating computer images and attempted to control them, first through changing their variables and then by extracting the most appealing fragments and recreating them using Grasshopper3D . From pure voxel-based images to NURBS or meshes and to 3D printing, laser-cutting, thermo-forming, casting..etc… students are confronted to the limitation of the computer’s memory and processing power as well as materials and numerical control (NC) programming language such as Gcode.

Navigating through fractals, exploring their recursive unpredictability to create more finite prototypes is like walking through the forest and noticing a beautiful flower to design your next building – it helps to let go of a fully top-down approach to architecture, it encourages a collaborations with your computer and a deep understanding of machines and materials. It anticipates a world in which the computers will have an intelligence of their own, where the architect will guide it onto a learning path instead of giving him instructions.  Using infinite fractals to inspire designs helps instill infinity within the finite world – bringing a spiritual dimension to our everyday life. 

Below is a selection of our students Brief01 journey so far:

Manveer Sembi's  Aexion Fractal imported from Mandelbulb3D to Rhino and 3D Printed
Manveer Sembi’s Aexion Fractal imported from Mandelbulb3D to Rhino and 3D Printed
Alexandra Goulds' MIXPINSKI4EX fractal
Alexandra Goulds’ MIXPINSKI4EX fractal
Michael Armfield's parametric exploration of the Amazing Surf Fractal
Michael Armfield’s parametric exploration of the Amazing Surf Fractal
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Michael Armfield’s parametric exploration of the Amazing Surf Fractal
Michael Armfield's parametric exploration of the Amazing Surf Fractal
Michael Armfield’s parametric exploration of the Amazing Surf Fractal
Henry McNeil's Fibreglass modelling of the Apollonian Gasket.
Henry McNeil’s Fibreglass modelling of the Apollonian Gasket.
Henry McNeil's 3D printed support for his fractal
Henry McNeil’s 3D printed support for his fractal
Henry McNeil's 3D printed fractal imported from Mandelbulb3d to Rhino
Henry McNeil’s 3D printed fractal imported from Mandelbulb3d to Rhino
Henry McNeil's Fibreglass prototype from Ping-Pong and tennis balls
Henry McNeil’s Fibreglass Fractal prototype from Ping-Pong and tennis balls
Ed Mack's laser-cut Fractal Dodecahedron.
Ed Mack’s laser-cut Fractal Dodecahedron.

 

Ben Street's auxetic double curved paper models
Ben Street’s auxetic double curved paper models
Ben Street's single curved paper models
Ben Street’s single curved paper models
Lewis Toghill's composite shells with Jesmonite, plaster, wax and fibre glass
Lewis Toghill’s composite shells with Jesmonite, plaster, wax and fibre glass

20171109_114548Alexandra Goulds' flexible timber node

Alexandra Goulds' flexible timber node
Alexandra Goulds’ flexible timber node
Manveer Sembi's paper cutting for double curved paper sphere
Manveer Sembi’s paper cutting for double curved paper sphere
James Marr's single curved wood node with rotational geometry for subdivided mesh geometry
James Marr’s single curved wood node with rotational geometry for subdivided mesh geometry
Nick Leung's 3D prints of the different recursive steps of a space-filling curve
Nick Leung’s 3D prints of the different recursive steps of a space-filling curve

 

Rebecca Cooper's Fractal truss study on parametric structural analysis tool Karamba3D
Rebecca Cooper’s Fractal truss study on parametric structural analysis tool Karamba3D
Manon Vajou's burnt polypropelene studies
Manon Vajou’s burnt polypropelene studies

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The Curves of Life

“An organism is so complex a thing, and growth so complex a phenomenon, that for growth to be so uniform and constant in all the parts as to keep the whole shape unchanged would indeed be an unlikely and an unusual circumstance. Rates vary, proportions change, and the whole configuration alters accordingly.” – D’Arcy Wentworth Thompson

“This is the classic reference on how the golden ratio applies to spirals and helices in nature.” – Martin Gardner

The Curves Of Life

What makes this book particularly enjoyable to flip through is an abundance of beautiful hand drawings and diagrams. Sir Theodore Andrea Cook explores, in great detail, the nature of spirals in the structure of plants, animals, physiology, the periodic table, galaxies etc. – from tusks, to rare seashells, to exquisite architecture.

He writes, “a staircase whose form and construction so vividly recalled a natural growth would, it appeared to me, be more probably the work of a man to whom biology and architecture were equally familiar than that of a builder of less wide attainments. It would, in fact, be likely that the design had come from some great artist and architect who had studied Nature for the sake of his art, and had deeply investigated the secrets of the one in order to employ them as the principles of the other.

Cook especially believes in a hands-on approach, as oppose to mathematic nation or scientific nomenclature – seeing and drawing curves is far more revealing than formulas.

252264because I believe very strongly that if a man can make a thing and see what he has made, he will understand it much better than if he read a score of books about it or studied a hundred diagrams and formulae. And I have pursued this method here, in defiance of all modern mathematical technicalities, because my main object is not mathematics, but the growth of natural objects and the beauty (either in Nature or in art) which is inherent in vitality.

Despite this, it is clear that Theodore Cook has a deep love of mathematics. He describes it at the beautifully precise instrument that allows humans to satisfy their need to catalog, label and define the innumerable facts of life. This ultimately leads him into profoundly fascinating investigations into the geometry of the natural world.

 

Relevant Material

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“An organism is so complex a thing, and growth so complex a phenomenon, that for growth to be so uniform and constant in all the parts as to keep the whole shape unchanged would indeed be an unlikely and an unusual circumstance. Rates vary, proportions change, and the whole configuration alters accordingly.” – D’Arcy Wentworth Thompson

D’Arcy Wentworth Thompson wrote, on an extensive level, why living things and physical phenomena take the form that they do. By analysing mathematical and physical aspects of biological processes, he expresses correlations between biological forms and mechanical phenomena.

He puts emphasis on the roles of physical laws and mechanics as the fundamental determinants of form and structure of living organisms. D’Arcy describes how certain patterns of growth conform to the golden ratio, the Fibonacci sequence, as well as mathematics principles described by Vitruvius, Da Vinci, Dürer, Plato, Pythagoras, Archimedes, and more.

While his work does not reject natural selection, it holds ‘survival of the fittest’ as secondary to the origin of biological form. The shape of any structure is, to a large degree, imposed by what materials are used, and how. A simple analogy would be looking at it in terms of architects and engineers. They cannot create any shape building they want, they are confined by physical limits of the properties of the materials they use. The same is true to any living organism; the limits of what is possible are set by the laws of physics, and there can be no exception.

 

Further Reading:

Michael-Pawlyn-Biomimicry-A-new-paradigm-1
Biomimicry in Architecture by Michael Pawlyn

“You could look at nature as being like a catalogue of products, and all of those have benefited from a 3.8 billion year research and development period. And given that level of investment, it makes sense to use it.” – Michael Pawlyn

Michael Pawlyn, one of the leading advocates of biomimicry, describes nature as being a kind of source-book that will help facilitate our transition from the industrial age to the ecological age of mankind. He distinguishes three major aspects of the built environment that benefit from studying biological organisms:

The first being the quantity on resources that use, the second being the type of energy we consume and the third being how effectively we are using the energy that we are consuming.

Exemplary use of materials could often be seen in plants, as they use a minimal amount of material to create relatively large structures with high surface to material ratios. As observed by Julian Vincent, a professor in Biomimetics, “materials are expensive and shape is cheap” as opposed to technology where the inverse is often true.

Plants, and other organisms, are well know to use double curves, ribs, folding, vaulting, inflation, as well as a plethora of other techniques to create forms that demonstrate incredible efficiency.

Please Vote For The Magic Garden

We are finalist for the Architizer A+ award with The Magic Garden, a project that was designed and built with the help of DS10 students last year. We are 1% away from victory and the votes finish this Friday. Please help – Vote for The Magic Garden! Below are the instructions for the vote. It is very simple but requires to “CONFIRM” the vote which is an extra step.

VOTE HERE : http://awards.architizer.com/public/voting/?cid=11

Voting Instructions
Voting Instructions