Workshop report: Generative design with Clojure

2-day introduction to fundamental generative design techniques

Without wanting to sound generalizing, my impression sometimes is that for some coders, generative design is often still relegated as only lightweight application (and skills) of programming to create fancy imagery. In the traditional designer’s camp, generative design is often still looked upon either as a weird & wonderful magic tool to quickly spew out endless variations of specific aesthetics (e.g. the ever popular randomized, “organic”/biological routes many clients so often like to ask for) or is simply used as an automation tool without ever fully wanting to embrace or deeply engage with the underlying nature of the approach — that of building a complete design system from scratch, with all that entails, incl. developing sensibilities and taking responsibility over any aspect and detail of that system. The emergence & popularity of open source creative computing frameworks has helped to shift understandings for the better, but in some ways also slowly raised a copy & paste culture to simply achieve certain clichéd generative design aesthetics faster / cheaper — merely using a form of sampling or association by cultural/aesthetic proximity, but at the same time avoid a deeper conceptual engagement with the true possibilities offered.

For many years, to myself, generative design has been providing an ever varied and expanding work context to learn about topics, which in the end any cross-disciplinary designer and/or programmer should care about: System thinking (& System questioning), tool making, UI/UX, process research, abstraction, transposing & layering concepts and processes from one domain to another, iterative development & refinement, determine ways to parameterize approaches and exercise both systematic & serendipitous exploration of existing processes (i.e. mapping & hacking), learning to make and judge creative decisions as systemic trade offs etc. In terms of programming it often too requires one to learn about and master many different, often not-so-mainstream language features, data structures, algorithms and embrace the idea of constant refactoring — sometimes to actually implement a certain idea in the first place, other times to allow for more configuration options and hence greater expressive potential (incl. to enable output in different formats/media) or to make a generation process just run faster (and thereby sometimes making it realistic to achieve). The latter can quickly become important, since much of the work in this field often times requires fairly large numbers of inputs, actors, iterations and long simulation times etc.

Over the two days of this sold-out workshop I wanted to introduce people to several fundamental patterns, tools & techniques useful for this kind of work and at the same time show how to implement these idiomatically with Clojure (though we typically also talked about other languages in contrast).

Traces of a star polygon rotating around a point with a constantly modulated radius (using sine waves).

The first examples dealt with the basic approach of replacing thinking in terms of shapes/objects/nouns with thinking in terms of processes/functions/verbs. This is not just required by the more or less functional nature of Clojure, but also a fundamental approach for the generally bottom-up nature of generative design. Therefore, I believe Clojure is actually a superb fit for this field.

A circle is a shape, but it becomes so much more useful and malleable if understood as the process of a point rotating around another. This immediately leads to questions like: What is rotation? What is space? How to define it, how to work with it and how to map from one space to another (e.g. polar vs. cartesian). When is it better to solve a problem in one or the other, how do the same ideas exist in other domains (e.g. color spaces). It also leads us to question how this all can be controlled and manipulated, through the introduction of parameters and other processes to control their values over time. What happens if we rotate a set of points instead of a single point around the center, what happens if we connect these points? How can existing process metrics be used to form new relationships and drive other parts of the design? E.g. What happens if we make the radius itself a function of the rotation angle?

Whereas Clojure already offers an interactive workflow out of the box, working on visual generative systems, we also want to naturally visualize the results, straight from the REPL and as a way of unit testing, using our eye to judge the correctness and aesthetic potential of the system. All examples in this workshop are largely using vanilla Clojure, though we also extensively used the, & libraries to help us with vector algebra, SVG generation, geometry data types & export and to simplify working with color (in multiple color spaces & formats).

Polygons, polymorphism & graphs

We talked about various fundamental geometry data types, abstractions and polymorphic operations provided by These types could be considered classes (in the OOP sense), but they too can act as configurable point, line and shape generators and provide dozens of other useful operations: analysis of dimensions, bounds, area, volume, intersections with other types, conversions to other types, point classifications, spatial transforms, interior & boundary sampling, extrusions, subdivisions, tessellations etc. Many types also provide a kind of graph access, e.g. to extract the vertices, edges, cycles (i.e. mesh faces), find vertex valence, split/join edges etc. Much like many of the functions in clojure.core, all of the 50+ operations defined in the namespace are protocols and implemented to varying extents by the currently 20+ shape types, thus keeping the main API surface area small and easy to learn.

As a variation of these first examples, we put some of the above operations to use and learned how to create polygons from a circle, first by sampling the circle with a given resolution (e.g. resolution = 6 produces a hexagon) and then continued re-sampling the edges of the resulting polygon perimeter at a fixed distance to produce a sequence of uniformly spaced points.

A simple transformation like that can yield a quite major change in the resulting output of an otherwise unchanged process (this one inspired by my childhood hobby of taking hundreds of long exposure photos of a torch hanging in a dark room, though here we’re not using Lissajous curves).

Variation of the same process shown in the first image, but this time only using vertices obtained by sampling the perimeter of the polygon at a uniform distance.

Iterative systems

Many generative processes are iterative by nature, i.e. in math speak:

f(x+1) = f(f(x))

In Clojure this can be elegantly achieved by using iterate, reduce or loop.

Strange Attractors are some of the simplest iterative systems. We chose the famous Peter de Jong attractor and visualized it first using SVG, then as bitmap graphics and introduced color, by mapping spatial coordinates to points in RGB space.

The de Jong Strange Attractor (3 million iterations). XY coordinates used as interpolation factors for color blending.


Ever since their first use in the original Tron movie, Ken Perlin’s noise formulas have become a staple for many procedural design tasks (e.g. texture / terrain generation, volumetric clouds, flow fields). In many design situations, procedural noise is more desirable than pure randomness, since it preserves local smoothness and can be easier controlled and shaped. Because the functions are pure and deterministic, they describe a noise space (in any dimension) and can also be applied in a manner similar to additive sound synthesis, combining the results of harmonics in different octaves to form more complex signals. Adding secondary processes to distort input coordinates (e.g. turbulence) and/or filter outputs (e.g. biquad filters), we can create a large variety of visual characteristics.

The direct representation of 2D noise values as colors is just one way of many. In the bigger picture, procedural noise is a highly flexible & powerful driver to control any other scalar design parameters.

2D gradient noise w/ turbulence (also noise)
A regular grid of 100k lines (320 x 320). Each line’s rotation and color is controlled by the underlying 2D noise field. Color gradient created with
3D noise visualized as voxel iso surface mesh and draft-rendered with Luxrender (via

Poisson disk sampling (Blue noise)

Apart from Perlin noise, there are many other types of procedural noise, each with different characteristics: Simplex noise, Fractal noise, Gradient noise, Pink noise, Brown noise, Blue noise etc. The latter also goes under the name Poisson disk sampling and is especially useful to generate random samples with locally adjustable uniform distributions. The image below has been generated with this approach, using a quadtree as acceleration structure and one of the example programs bundled with the library.

Image based Poisson disk sampling with brightness controlled local noise densities (139k samples). See for build & usage instructions.

Grid based simulations, Cellular Automata

With a similar mindset as used for the noise discussion, we briefly looked at other means of grid based pattern generation — again not necessarily for direct visualization, but as means to control other parameters or processes within a larger system. These applications don’t even need to be visual in nature, e.g. CAs are also highly useful for music generation, where the grid would define notes over several octaves of a musical scale.

Cellular automata & reaction diffusion simulations are a fascinating topic and can produce a vast amount of different outcomes, especially if reconfiguring them from their textbook descriptions (e.g. by changing convolution kernel sizes, increasing the number of possible cell states, playing with rules, making them self-modifiable etc.). Like procedural noise, this class of generator can also be applied in different dimensions and we looked at 1D-3D examples.

Classic 1D Wolfram automata (Rule #105), grid size 256x256, random seeding (50%)
Extended 1D CA with kernel size 3 and max. cell age of 64
3D visualization of the evolution of a 2D CA, created during toxiclibs workshop @ SAC Städelschule, Frankfurt, 2013

Agent systems

Whereas the examples so far all dealt with a single uniform process, we often require a solution to be formed in a more indirect, or rather emergent, way. In these situations, the idea of using autonomous agents, entities with behavior(s) and knowledge of some design constraints, is a powerful approach to create & shape possible, and often more complex, outcomes.

Inspired by a project commission I worked on in 2009, the onedotzero festival identity, we implemented a simple agent simulation to visualize field lines in an environment populated with randomly charged di-poles. At first, a number of agents is created for each positively charged pole and these are then evaluated until all agents have either reached a negative pole or have left the simulation space. At each time step, an agent will travel in the weighted direction of all di-poles, implicitly taking into account that neighboring same-charged poles exercise a repellent force on the agent. Also, at each time step we record an agent’s current position and charge potential, information which is then used to visualize the field line curves and their colors.

Field line visualization of 80 randomly placed & charged di-poles. Each line represents the trace of a single agent, each one spawned at one of the positive charged poles and being attracted/repelled by other poles in the system.

Design grammars, recursion, L-Systems & basic interpreters

Keeping the idea of an agent, controlled by other constraints in the design space, we introduced the concept of design grammars and rule based systems. The possibly best known candidate in that field are L-Systems, named after Aristid Lindemayer, who developed the idea in the late 1960s to describe natural growth patterns.

An L-System consists of a number of symbols, each associated with an arbitrary length replacement for itself (incl. the option of extinction). Given such an rule set and an initial sequence of symbols (the so called “axiom”), each symbol is iteratively rewritten, often forming vastly longer and more complex sequences after even just a few iterations. Some symbols can have a fixed meaning and are used as commands, similar to controlling a turtle in the LOGO language: e.g. move forward, turn left/right, branch. These commands can be used to visualize the system, but are more or less optional (again, I’m taking a bigger picture view here, since L-Systems also can be trivially used for non-visual applications).

The code below implements a simple, yet easily extensible L-System interpreter, based on Clojure’s multimethod mechanism (without even a single conditional expression, unlike implementations in most other languages). At the end we define a sample rule set for the Dragon curve fractal (pictured further below). The agent and interpreter supports nesting by implementing a “call stack” to store & restore previous agent states, whilst always collecting any sub-paths generated by a branch back into the main path when popping (unwinding) the stack. We also talked about how this is similar to the way S-expressions are executed and the current setup & syntax could be easily changed to turn it into a Lisp interpreter, even with macro-expansion.

The images below demonstrate different L-Systems generated with the above interpreter. My favourite one is the rhomboidal Penrose tiling (rules from here), but I’m equally fascinated by the succinctness of the Dragon curve rule set.

Collection of L-Systems, clockwise from top left: Pentagon gasket, Penrose tiling, Dragon curve, Fractal tree. Color hue represents position in iteration sequence.

Update: L-System Twitter bot

After the workshop, I expanded the L-System example and combined it with my existing Twitter bot skeleton project. The repo for this is here:

There’s also @thingybot, where you can find some more outputs (and the bot is sporadically online).


Two days are barely sufficient to even scratch the surface of an entire discipline and design philosophy. There are many, many more topics we could & should have talked about and experimented with, but I hope the topics we did cover at least provided some important insights into how this field can be approached with the elegance of the Clojure language and I hope they too provided more stimulus to continue building up the (still) small community of fellow Clojurians interested in this field.

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Till next time.