Local Colour: Smaller World Network

Back in September I showed a little work called Local Colour at ISEA 2011. This project continues my thinking about generative systems, materiality and fabrication. It's a work in two parts: the first is a group of laser-cut cardboard bowls, made from reclaimed produce boxes - you can see more on Flickr, and read the theoretical back-story in the ISEA paper. Here I want to briefly document the second element, a sort of network diagram realised as a vinyl-cut transfer. The diagram was created using a simple generative system, initially coded Processing - it's embedded below in Processing.js form (reload the page to generate a new diagram).

Network diagrams are one of the most powerful visual tropes in contemporary digital culture. Drawing on the credibility of network science they promise a paradigm that can be used to visualise everything from social networks to transport and biological systems. I love how they oscillate between expansive significance and diagrammatic emptiness. In this work I was curious to play with some of the conventions of small world or scale-free networks. A leading theory about how these networks forms involves preferential attachment: put simply it states that nodes entering a network will prefer to connect to those nodes that already have the most connections. In visualising the resulting networks, graph layout processes (such as force direction) use the connectivity between nodes to reposition the nodes themselves; location is determined by the network topology.



This process takes the standard small-world-network model and changes a few basic things. First, it assigns nodes a fixed position in space. Second, it uses that position to shape the connection process: here, as in the standard model, nodes prefer to connect to those with lots of existing connections. But distance also matters: connecting to a close node is "cheaper" than connecting to a distant one. And nodes have a "budget" - an upper limit on how far their connection can reach. These hacks result in a network which has some small world attributes - "hubs" and "clusters" of high connectivity - but where connectivity is moderated by proximity. Finally, this diagram visualises a change in one parameter of the model, as the distance budget decreases steadily from left to right. It could be a utopian progression towards a relocalised future, or the breakdown or dissolution of the networks we inhabit (networks in which distance remains, for the time being, cheap enough to neglect).

The process running here generates the diagram through a gradual process of optimisation. Beginning with 600 nodes placed randomly (but not too close to any other), each node is initially assigned a random partner to link to. Then they begin randomly choosing new partners, looking for one with a lower cost - and cost is a factor of both distance and connectivity. The Processing source code is here.

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Uniform Diversity: Space-Filling and the Voronoi diagram

This post is a short excerpt from a paper recently published in Architectural Theory Review 15(2) - a special issue on architecture and geometry with lots of good (Australian) stuff. My paper (pdf) is a critical look at space-filling geometry in generative design. It touches on several things already blogged - the Water Cube and ideal foams, and some generative projects that use self-limiting growth. This excerpt looks at the Voronoi diagram as a space-filling process.

The Voronoi diagram has become a ubiquitous motif in recent generative architecture and design. It, too, can be usefully read as a space-filling model. In formal terms, a Voronoi diagram is a way of dividing up space into regions so that, for a given set of sites within that space, each region contains all points in the space that are closer to one site than any other. The result is also foam-like, but as a model the Voronoi diagram has attributes quite different to the ideal Kelvin or Weaire Phelan foams.

Firstly, while the formal model is again based on a strict set of conditions (in this case proximity) it works with an arbitrary input — the given sites —rather than defining a regular structure. The Voronoi is thus a procedural geometric structure in a way that the ideal foams are not: its structure emerges through the application of a specific process or algorithm to a given set of inputs. In this way, the specific spatial relations between neighbouring cells depend on, and emerge locally from, the given spatial relations of the specified sites. This trait also gives the Voronoi model a kind of malleability; sites can be added, removed, or moved, and the spatial structure readily adapts

Again we can read off the attributes of the Voronoi as a model in this way. It is multiplicitous, but in a different way to the grid-like uniformity of the foam models. In this case, the multiplicity can, in fact, be irregular: the sites can be positioned anywhere within a given space. However, this does not amount to much, in terms of heterogeneity: while the sites can be positioned arbitrarily, the procedure, and the relation between sites that it encodes, is entirely uniform. Each site, taken as a formal entity, is identical to every other; this is a kind of uniform diversity. Like the foam models, the Voronoi diagram treats space as indefinite and extensive: it can go on forever; its only practical limit being the computational resources required to calculate the diagram. The model itself has no way of defining an edge or bound. Finally, the variability of the Voronoi can be phrased another way, as arbitrariness; in other words, that there is no inherent reason for a given site to be where it is. There is nothing internal to the model that can generate that differentiation.

In Marc Newson's Voronoi Shelf, for example (above), we see a characteristically organic variety: a range of cell sizes and shapes, different wall thicknesses, all in an agreeable state of harmony. The form gives an impression of inherent logic. It is as if the harmony of the relationships between the cell sites assures us that there must be a reason for them to be as they are. This is unsurprising, given our familiarity with, and aesthetic attunement to, naturally occurring structures that resemble these cells. The visual signature carries an association of organic logic: but in formal fact the cell sites are arbitrary, that is to say, designed. There is no necessary relation of one to another, only (we can but assume) a designer's choice, which is concealed by an appearance, much as the surface of the Water Cube conceals the regularity of its foam model.


Conversely, some designers directly address the arbitrary input to the Voronoi diagram, treating it as an opportunity and exploiting the malleability of the model. As Dimitris Gourdoukis writes, "the problem of deciding on the initial set of points is, I think, one of the most interesting in relation to voronoi diagrams." In Gourdoukis' Algorithmic Body project (above), the locations of the Voronoi sites are specified by a second generative system, a cellular automaton; here the Voronoi acts as a geometric filter, interpreting and interpolating one set of spatial data into another. In Marc Fornes' POLYTOP, the designer proposes a mass-customised product in which customers can design the point cloud that drives the Voronoi geometry; here a problem of arbitrary choice is turned into a feature, towards uniqueness and specificity.

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The Self-Made Tapestry - Philip Ball

I'm currently in Melbourne, working with the CEMA group at Monash Uni. Among other things, we've been talking about artificial ecosystems, growth, morphogenesis and self-organisation - and I've been working on a generative art piece that has had me casting around for models and mechanisms. Jon McCormack passed me Philip Ball's 2001 book, The Self-Made Tapestry: Pattern Formation in Nature.

The book looks at morphogenesis - the self-creation of form - in physical and biological systems, and computational models. It updates the work of D'Arcy Thompson, whose 1917 book On Growth and Form showed that natural forms could often be explained as products of dynamic physical interactions as much as adaptation or evolution; for example, a seashell spiral emerges as a result of the growth rate of the organism living inside it. Ball takes a similar approach to morphogenesis, in that he treats physical systems and living systems as fundamentally interlinked, often examining the material mechanisms in biological form. Unlike Thompson though, he has a modern reservoir of complex-systems science, biology and physics to draw on. In a great piece of pop-science writing, Ball knits together a wide range of work under a useful set of headings, and the text is full of enticing illustrations. The image below is by Eshel Ben-Jacob, whose bacterial growth work is featured extensively in the book.


It's a treasure trove for the generative artist/designer; flick through until you find an illustration that catches your eye - maybe a bacterial growth form, a reaction-diffusion system, or fracture patterns - and then read up on the morphogenetic models involved. Generative clip art? Not quite; Ball's text explains the principles and processes clearly, but links them organically to each other through systemic properties: symmetry breaking, bifurcation, fractal dimension and so on. While there are verbal descriptions of plenty of generative algorithms, understanding them really requires coming to grips with the underlying models and their shared characteristics.

Ball also talks explicitly about the use of computational models, which play an important role in the book. This is especially important for anyone using the models as (generative) ends in themselves, rather than empirical devices. Ball clarifies the scientific sense of "model" as something selective and partial, rather than representational or exhaustive: there are plenty of things that such models omit, either because it's too hard to include them, or they don't seem to influence the outcome. Along the same lines, some (maybe all) phenomena can be modelled effectively in several different ways, using different assumptions and techniques. Conversely, the interrelations between morphogenetic systems often come down to shared models, cases where pattern formation in different domains (say, fracture patterns and plant growth) can be modelled using similar, often very simple, techniques.

I've been critical in the past of the simplistic models used by generative artists - but also argued that generative art's ability to play with models (creatively and intelligently) is what makes it interesting. So my recommendation here is half creative and half critical; in other words it's got eye-candy (bacterial eye candy even) as well as substantial model-y goodness.

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