Organisational logic, digital growth

As part of the initiating workshop, a series of different algorithmic methods were developed and discussed. The thesis outlines only one method, which has also subsequently been further developed.

This method is based on a generic DLA algorithm, implemented by David Andreen for the workshop. The algorithm is based on the DLA model, developed by Witten and Sander. By using a basic DLA model, the idea was to gain the basic open, branching character known from DLA, and to simultaneously be able to incorporate additional specific growth-controlling parameters. Having the scope of the experiment in consideration, it was decided to work with only one additional parameter, namely sun radiation. By linking the form generation with an environmental parameter, the method could be extended with a type of contextual relation, or even a form of optimisation. Moreover, it would be possible to establish some form of negotiation between the inner logic of the algorithm and the optimisation parameters. The virtual environment for the DLA growth was defined as a three-dimensional lattice. This made it possible to record the position of the cells both as a position vector and as an index in the three-dimensional array of points in the grid. The random particle that finds the random growth directions by randomly searching through the grid does not need to analyse the position of all cells in the existing structure, but only needs to test if the current random particle position and its immediate neighbours are occupied by a cell.

The solar radiation simulation was set up in a way, where the challenge is to protect a number of precisely identified points, later referred to as attractor points, from sun radiation. However, the goal was not to provide a solution for a specific problem, but rather to investigate possible implications of embedding a simulation

Figure 5: The intensity of the irra-diation was in the simulation directly linked to the angle of the sun. Top:

Relative irradiation levels , used in the simulation. Note that the diagram shows the months from January to June. Above: Irradiation diagram for Copenhagen in April.

Figure 6: The lattice underlying the DLA growth. The spatial lattice was a grid with a depth of 6 layers of cells.

The image shows a wall with 100%

density.

method in the form generating process. Eventually it is possible that the system could be used for generating sun protection as part of a façade system or perhaps for covering an outside space. In this case it would typically be relevant to specify a whole array of points that needs protection. A property of the system would then be its capability of adapt to a large variety of both local conditions in the structure and differentiation due to orientation. A couple of illustrations indicate the use in architecture. The calculation of sun angles is based on a Java library implemented by Klaus Brunner², and uses latitude, longitude, date and time as input parameters.

The irradiance value is then calculated directly from the sun angle, meaning that the higher the inclination of the sun is, the higher irradiation value. Despite the simplicity of the irradiance calculation, it seems sufficient for the method. An example of a precise calculation for Copenhagen in April is shown, and when compared to the diagram used in the simulation, there is a similarity in the relative increase in irradiance during the day. The irradiance values in the simulation were not quantified. In the cases where the simulation was used for generating a sun protection wall, the sun angle in plan also has importance. In the experiment, the sun protection wall was facing south. This means that in positions, where the sun was not precisely positioned in south, the radiation hitting the façade was reduced, and therefore the orientation was part of the calculation, similar to the sun inclination.

The cell growth was controlled by adjustment of some essential variables. Mainly it was important to be able to control the balance between random growth and solar protection. When the solar protection setting was set to zero, the growth was fully controlled by the DLA logic. When the solar protection setting was increased, the growth was intensified in areas where the protective values for the cells were calculated as high. If the solar protection setting was set to 100%, and random growth was set to 0, it meant that only cells with a protective value above zero could be added to the structure. The question was whether it was possible to generate a compromise between inner logic and solar protection, and it seemed that a setting where solar protection was set to 20% resulted in a formation still appearing as a DLA structure, but also with increased solar protection properties.

The growth process can be described as follows: The

‘random particle’ performs its search through the lattice until it ‘bumps into’ the existing cells. The chance of a new cell being added at the position is a stochastic decision, where the essential

2. The Java library used for calculating the sun angle is developed by Klaus A.

Brunner, and based on the paper: Blanco-Muriel et al., ‘Computing the Solar Vector’, Solar Energy Vol 70 No 5, pages 431-441.

Figure 7: Generation of solar protec-tion wall. The solar protecprotec-tion pa-rameter is set to 0, which results in a pattern, completely reflecting the DLA  growth logic. Still, the attractor points are protected from solar radiation to some extent. The protection percent-ages range from 16 to 94.

Figure 8: Generation of solar pro-tection wall. The solar propro-tection parameter is set to 100%, and random growth is set to 1%. This results in a pattern entirely formed to protect the attractor points. DLA is still the driving principle, but the character of the pat-tern is blurred. The protection ranges from 80% to 97%.

Figure 9: Generation of solar pro-tection wall. The solar propro-tection parameter is set to 100%, and random growth is set to 20%. The pattern still appears as a characteristic DLA pat-tern. The attractor points are protected from solar radiation with values rang-ing from 71% to 94%.

Figure 10: Rendering of the DLA solar protection pattern generated from 100% random growth.

Figure 11: Rendering of the DLA solar protection pattern generated from 1%

random growth and 100% tendency for solar protection.

Figure 12: Rendering of the DLA solar protection pattern generated from 20%

random growth and 100% tendency for solar protection.

parameters define the probabilities. It can be compared to the adjustment of stickiness in the generic DLA algorithm, but in this case the probabilities depend on the protective values of the cells.

If the cell is added, the protective value of the cell is calculated.

A simulation is run, where a number of sun positions with defined intervals are tested throughout a period. In this case, the simulation covers a year, where one day in each month is calculated with hours from 5.00 to 19.00, divided into intervals of 5 minutes. The days that are not included are in some cases readable in the growth, but this is countered in adjustments in the settings. Each cell has a protection value, reflecting the accumulated irradiance values, that the cell can prevent from hitting the attractor points during the simulation period, in this case a year. If the cell is placed in a position where it can block sunrays hitting one of the attractor points with high irradiance value at some time during the year, the cell gets a high protection value, and is showed with a bright yellow colour. If it does not block any rays it gets a protection value equal to zero, and is shown with a blue colour. If the cell only blocks sunrays with low irradiation value, the protection value is low, and the cell is shown with a graded dark yellow.

In order to address an architectural context more directly it was decided to produce examples, where the solar protection

Figure 13: Rendering of the DLA solar protection pattern generated from 20%

random growth and 100% tendency for solar protection.

Figure 14: Agent Construction. Physi-cal structure after completed growth process

structure is organised as a wall. As described in the general explanation of the DLA model, the system can work, both in two and three dimensions, so the example could have been developed as a two-dimensional pattern. However, when developing the sun-protection wall method, the idea was to establish a formation of three-dimensional appearance and to use the spatial depth as part of the protection strategy.