An ecomorphic theatre as a case study for embodied design*


Alasdair Turner, MA, MSc

Bartlett School of Graduate Studies, University College London, London WC1E 6BT






In this paper we examine the ecomorphic design of a ‘theatre’.  The theatre is defined through the relationships of the players and audience.  The players occupy a fixed area, and the audience may sit around them.  Each member of the audience must be able to access their seating position, and, once seated, each is given score based on how well they may view the players.  After the conditions have been set down, we attempt to evolve the theatre to make a good fit for the audience and players.  The idea is to create an embodied system which captures the interplay between visibility and accessibility.  We compare several different generative techniques to create the theatre.  In the first place, we attempt a continuous process whereby each audience member themselves may raise or lower a column in order to view the play.  Then we allow the theatre itself to evolve, based on live cell growth from its edges, so it becomes a cellular automata system guided by the visibility and accessibility of its growth.  We also apply basic forms of diffusion-limited aggregation, genetic algorithms and genetic programs.  We find that the cellular growth model provides the best solutions in terms of number of accessible seating positions and the best visibility for each audience member, whilst also creating the most interesting design outcomes.  We suggest that this is because the cellular growth model naturally suits ecomorphic principles of design through continuous adjustment of the environment around its occupation to meet a natural interaction between audience and players.

1. Introduction

Ecomorphic design was introduced by the author in 2002 [1], in order to tie together a number of concepts centered around embodiment, situatedness and generative design.  It might best be expressed as the process of structural coupling as described by Maturana and Varela [2].  Originally, Maturana and Varela presented the idea of structural coupling in the domain of cell biology and within the domain of their theory of autopoiesis.  They considered cells as autopoietic, that is, cell maintaining within the environment.  Varela et al went on to extend these ideas into the domain of cognitive science, and specifically embodiment [3].  To Varela, following Heidegger, the mind is embodied, and its actions and reactions may take place only in the context of its environment.  To Varela et al, embodiment is the middle path between the Cartesian dualist mind body split, and the Liebnizian view of a single monadology.  Varela et al at once see the mind-body unit as separate from its environment, but simultaneously, as only possibly existing within that environment (that is, the being is meaningful only in relation to environment).  Returning to Maturana and Varela’s original conception, structural coupling occurs when the environment and the cell mould their physical form to each other.  Varela et al’s being would also be structurally coupled through physical interaction with it (we might compare Thompson’s model of bone growth, where the being creates bone in response to the physical demands of the environment [4], or patterns of stigmergy, where the environment is shaped through its occupation by beings [5]). 

Ecomorphism builds on this theoretical basis primarily through Luhmann [6].  Rather than considering directly the coupling of environment and a single being, ecomorphism considers the coupling of a social process and the environment.  Luhmann suggests that the ongoing process of the being and the ongoing process of the social phenomena are both autopoietic in nature, and can be considered simply in terms of whether they are psychic (concerning the individual) or social (a collection of individuals).  Thus ecomorphism is still concerned with the coupling of the environment to a being, albeit a distributed social process being.

In this paper, we examine the case of an ecomorphic theatre.  The social process to be engaged in is a performance.  We shall use a relatively standard interpretation of this process, with the audience engaged in viewing the actors, rather than some further interaction between them.  The process will concern the growth of the environment to support this activity.  For ease of presentation, the seating area will be defined outside the actors’ stage space, and it is this seating area that will be modified.  Strictly speaking, the ecomorphic environment should have no predefined distinction between stage and auditorium such as this: the actors and audicence should be free to arrange themselves within the environment, and the environment should evolve around this activity.  If this means the actor stands atop a mountain and the audience look up to her or him, then this is a valid outcome.  However, we should be clear that the action of looking and the ability to move to a place so as to view are fundamental to the ecomorphic process and cannot be excluded.  In considering these factors, we set up an interplay between accessibility of a space and visibility to and from that space.  This reflects the theory of space syntax [7], which examines how these variables may interact to structure space and the social process within it.  However, whereas space syntax is primarily analytic, in this paper, we will try to examine this interplay through generation of a space.

2. Background

The techniques used to generate morphology in this paper have generally been used extensively within the field of generative architecture [e.g.,8,9].  In the case of each algorithm, the same evaluation function will be used, described in section 2.2, either for the members of the audience as a whole, or for individuals seated within it, depending on the algorithm. 

2.1 Generative algorithms overview

We first implement an individual based algorithm: each audience member chooses a location, and may build on the location to obtain a better view.  This then leads on to a less individualistic interpretation, with the audience members being collectively rewarded for achieving the best view for everyone.  However, both these methods are restricted to a set number of audience members: we define a 20 x 20 grid of boxes, with a 5 x 5 area for the stage, leaving 375 places to sit.  If we want to increase the number of seats, we must allow the columns to grow outwards, into the space.  This rule thus becomes a form of 3D cellular automata system [10].  The rules for when to grow an adjoined structure depend on whether or not the population get a better view, or through adding more audience members, thus increasing the population numbers with any view at all.  We then moved on to test other forms of well know generative algorithm: diffusion limited aggregation [11], a straight-forward genetic algorithm using a direct translation from genotype to phenotype [12], and then a genetic program, allowing different types of cell to grow outwards from a seed [13].

Figure 1: a typical system evolved using the cellular growth model

2.2 The reward function

All the algorithms are evaluated using the same reward function, which combines accessibility and visibility.  A typical proposal to be evaluated is shown in figure 1.  To give an idea of the intended scale, each block is 75 x 75 x 75cm, with a growth space of 20 x 20 x 20 blocks (15m in all dimensions).  We first evaluate which locations are accessible.  These are discovered by starting with the location of the actor shown on the stage.  A location is accessible if it is adjacent to another accessible location, and if it is either at the same height as the accessible location, one block higher, or one block lower (either step up 75cm or down 75cm).  In addition, there must be a head-clearance of two blocks (1.5m) to allow transit between locations.  Once all the accessible locations have been discovered using a breadth-first search, we then assess the visibility from each of these locations.  An audience member may sit at the accessible location if she or he has an unobstructed view of the upper torso and head of the actor.  The visibility is assessed by pixelating the path from the viewer to the actor at the scale of the blocks.  The audience member is rewarded according to the number of other audience members obscuring the view of the actor.  There is a maximum reward of 20, with 1 deducted for each member of the audience in the (pixelated) line of vision to the upper torso and head of the actor.  Before any evolution of the system, this works out at an average of about 6.6 other audience members obscuring the view.

3. Experiments

As discussed above, we start with an individualistic algorithm.  Each audience member finds a location, and the block is raised according to whether she or he personally benefits from the change.  At the beginning of this process, the audience are evenly distributed over the grid of blocks, as shown in figure 2(a).

Figure 2: (a) Early growth of individualistic agents (b) Later growth: a few agents block other locations from seeing


However, as the system progresses, agents near the front block other agents from viewing, and as the system grows, raise up the blocks so that other locations within the system are no longer accessible (starting from the stage as discussing in section 2.2).  Figure 2(b) shows the converged end product of a run.  There are just 52 audience members remaining, from the 375 that started, although each has a completely unobscured view of the actor.  In order to overcome this problem, we moved to a second form of algorithm, where columns are raised, but only if the overall fitness of the system is increased by doing so.  As might be expected, the columns start rising from the back, so they do not block those at the front, as shown in figure 3(a).  As the system run progresses, the seats nearer the back rise higher to compensate for the angle of view, as shown in figure 3(b).  The end result is that all 375 audience members can view, mostly unobscured by others.

Figure 3: (a) Early growth of the social optimum system starts from the back (b) a later result, with seating rising faster to the rear


This system however lacks interest, and can only ever reach an optimum based on 375 audience members.  In order to increase the viewing audience, we allowed any accessible space to grow not only upwards, but outwards (in any direction), with the results shown in figure 4.  The growth starts as before, but after a while the higher cells start to grow towards the stage, allowing more audience members to view the stage.  The system is shown after about 30000 generations in figure 4, and run to completion, this run allowed 759 audience members to view the performance (over double the original capacity), each on average obscured by about one other audience member.  Note how upper tiers have formed above raked seating zones.  In addition, the system seems to evolve ‘staircases’.  Locations without a view are unoccupied, and looking at the figure from above, it is possible to see blocks winding up towards the higher reaches of the theatre, which once would have been occupied, themselves, but now merely serve for access.

In the last paragraph, it was noted that we only allowed the accessible locations to grow.  What would happen if any location were allowed to grow regardless of location?  As the system must improve fitness through any growth, we do not see uncontrolled increase in blocks, but in fact observe the situation shown in figure 1.  Although this looks very similar to figure 4, careful inspection of figure 1 shows that the lower tiers are flattened, without the raking observed in figure 4.  This is due to the fact that outward growth can occur at any time, not just when a cell is at the top level, and thus will often trigger to add another audience member, at the cost of restricting the view of those already present.

Figure 4: Four views of the cellular growth model after about 30000 generations


One problem of the cell growth method above is that it is an additive process.  Although it could be adapted to also remove blocks, it is difficult to do so and maintain structural integrity.  Therefore, we turned to a few other well known techniques to attempt sparser or more regular growth.  Firstly, we implemented a diffusion-limited aggregation method.  Cells were allowed drop from above, or fly in along one of the cardinal axes, sticking if they collided with another block.  The results were less good than the cellular block growth, although, by ensuring the same rule of only allowing a change if the added block improved the fitness, the actual mechanics of the two algorithms are fairly similar: the aggregation differs in that places in the middle tend to blocked by towers to the sides collecting material, but otherwise the growth method tends to be based on cells sticking to other accessible (and therefore exposed) locations.

The final two experiments were conducted using evolutionary algorithms.  These followed standard genetic algorithm operators for mutation, crossover and selection [14], although we also implemented a mutation only GA, essentially equivalent to simulated annealing.  The genotype for the first evolutionary algorithm contained a string of 8000 bits – one for every location in the 20x20x20 grid.  The bit represented block or no block, but only if the block was reachable through others from the ground, ensuring some structure to the form.  Crossover, where used, was uniform.  Figure 5 shows the result of evolution using the mutation only method, after approximately 40000 generations.  As can be seen, although structure is enforced, it can be in a snake-like pattern.  The results were not good generally, with most experiments producing around 480 seats with an average of three intervening people.  This appeared to mainly be due to the non-structural parts, previously unseen in the aether being ‘linked’ in through mutation, suddenly accruing a connected chain, but having no real optimisation of the floor plain into raked seating.

Figure 5: Standard genetic algorithm evolution


In order to overcome the problem of unstructured seating, we applied a genetic program, evolved using similar operators to the genetic algorithm.  In this case, each genotype consisted of 16 genes.  Each gene coded a pointer to another gene to grow in each dimension (up, down, left, right, front, back), and a timeout, after which the gene would deactivate, in terms of the recursion depth from the seed.  The seed was placed at 0,0,0 (the furthest corner from the stage).  It quickly became apparent that the order of applying identical genes drastically affected the outcome, and ultimately, a fixed order of application was adopted (i.e., left then right then up, etc), despite the fact that this would tend to skew systems to right-handedness or left-handedness.  The results near the beginning of a run are shown in figure 6(a), and at the end in figure 6(b).  Despite the regularity of the solutions and seemingly many seats, the performance of the system was at best around 500 places, with each audience member on average obscured by approximately 2 others.

Figure 6: (a) Early run results from the genetic program experiment (b) the same run after about 20000 generations


The genetic program suffered considerably from early convergence, perhaps because minor gene changes make such drastic differences to the final structure.  Despite the often tantalising range of structures shown early in the runs [see figure 6(a)] the outcome was usually very similar: a pyramidal type object towards the rear and no other structure.  Figure 6(b) shows about the most interesting result from the run.  The genetic program often seemed stunted by its own regularity: the requirement for accessibility necessitates single steps upwards, that often need offsets from one row to the next.  Features such as the ‘staircases’ observed in the cellular growth models did not occur.

4. Conclusion

In this paper we examined several algorithms to generate an ecomorphic environment around the notion of ‘theatre’.  An ecomorphic environment is one that is structurally coupled to the activities of its occupants. In this case, the activity is a play, where both actors and audience are engaged in an ongoing process about their various roles in the performance, be it participant or observer, or a combination of the two.  We started with an individualistic approach to growth of form which failed due to the avarice of the individuals within the audience.  Each individual optimised their own visibility, whilst blocking the accessibility for other agents.  In a sense this is unsurprising, as the building growth is not about the activity in general, but in relation to individuals within it.  Thus we modified the rules to create a cellular growth model, evaluated according to the accessibility to the population and visibility of the stage at every accessible location. The evaluation ultimately should also contain structural analysis of the results, although by its very nature the cellular growth algorithm ensures constructability.  The algorithm, while limited to additive growth without pruning or rejuvenation, performed better for the numbers of audience members satisfied than more sophisticated diffusion-limited aggregation and genetic algorithm approaches.  Its aesthetic seemingly followed the ecomorphic intention as a randomised yet consistent growth of a multi-tiered theatre with raked seating.  The algorithm embodies a natural evolution around the activity within the environment from step to step.  As such it can of course only hillclimb towards a goal.  If there are local maxima then the algorithm may halt suboptimally.  However, this is not as restrictive as it may sound.  It conforms with precepts of evolutionary growth: that an intermediate step must be a viable individual, and it does not necessarily imply a fixed output form.  An analogy can be made with scaffolding, where the structure is advantageous to get a certain amount of the way, but may then be removed later to reveal a more appropriate form.  This seems in fact to occur, with previous seating turning to ‘staircases’ out of view of the stage when further seating is added.  Indeed, we might ask could local optima even exist for this problem?  The complex nature of the evaluation function allows for many different approaches to the building of form whilst still evolving a better outcome.  The interdependent constraints allow an offset of costs, so that a move that lowers fitness in one area may raise it in another.  As an exploration, therefore, the system offers a creative process which adapts to its occupation through a natural progression of design evolution.

5. References

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2.                  Maturana, H.R. and Varela, F.J., 1979: Autopoiesis and Cognition: The Realization of the Living, Kluwer Academic Publishers

3.                  Varela, F.J., Thompson, E. and Rosch, E. 1993: The Embodied Mind: Cognitive Science and Human Experience, MIT Press

4.                  Thompson, D’A. W., 1961: On Growth and Form (Abridged Edition), Cambridge University Press

5.                  Grassé, P.-P. 1959: La Reconstruction du nid et les coordinations interindividuelles. La théorie de la stigmergie, Insectes Sociaux 6: 41-84.

6.                  Luhmann, N. 1996: Social Systems, Stanford University Press

7.                  Hillier, B. and Hanson, J. 1984: The Social Logic of Space, Cambridge University Press, Cambridge.

8.                  Soddu, C. 2004: “Generative Design / Visionary Variations - Morphogenetic processes for Complex Future Identities” in P. Van Looke & Y. Joye Aesthetics and Generative Methods in Architectural Design, Communication & Cognition 36

9.                  Coates, P.S., Broughton, T. and Jackson, H. 1999: “Exploring Three-dimensional Design Worlds using Lindenmayer systems and Genetic Programming” in P. Bentley (ed) Evolutionary Design by Computers

10.             Coates, P., Healy, N., Lamb, C. and Voon, W.L. 1996: “The use of cellular automata to explore bottom-up architectonic rules.” Eurographics UK Chapter 14th Annual Conference, Imperial College, London.

11.             Witten, T.A. and Sander, L.M. 1981: Diffusion-limited aggregation, a kinetic critical phenomenon.” Physical Review Letters 47 1400-1403.

12.             Holland, J.H. 1975: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence, University of Michigan Press

13.             Koza, J.R. 1993: Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press

14.             Goldberg, D.E. 1989: Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley




* This paper is based on an original idea by Christian Derix