The Violence of Equilibrium
A simplified model of territorial formation
As part of the research for the project “This Land Is My Land” for the EMAP residency at Ars Electronica I became interested in the evolution of national borders in the context of a broader research into speculative map-making. [The full project link is at the end]
Before any line can be drawn, individual motivations and ambitions must interact and accumulate until they produce a shift in the existing order. Such shifts are often violently asserted and create only a temporary release before new pressures begin to accumulate.
I started thinking how can I reduce these complex conditions to a simple assumption: A border can be understood as the temporary spatial configuration produced by interacting fields of pressure.
After a series of iterations, I settled on a simple diffusion algorithm as the basis for territorial expansion. The simulation space is divided into cells, each storing a faction and a pressure value. The system operates through three main mechanics:
- Pressure continuously diffuses between neighbouring cells of the same faction, forming a pressure island with higher values toward the centre and lower values along its edges.
- At a border, this circulation encounters resistance from another territory. When the local pressure of one region exceeds that resistance, the border advances.
- Expansion continues until the difference in pressure is reduced and a temporary equilibrium is reached.
In other words, once a territory is created or given new energy, it expands along the path of least resistance. Differences in resistance determine the direction of this growth, making neutral areas easier to occupy than established territories.
I chose a hexagonal grid because each cell has six equidistant neighbours. This gives the simulation a more isotropic local structure, reducing the directional bias introduced by the underlying grid. As a result, diffusion and territorial expansion are less strongly aligned to horizontal and vertical axes.
The system is computed through custom CUDA kernels. Every cell reads its neighbors and updates at the same time, allowing pressure to diffuse and borders to shift across thousands of cells in real time. This parallel structure also mattered conceptually, because the territory is expressed as a field of pressure. Its shape is not decided from above. It emerges from many small local interactions happening at once.
The model can be reduced to a few simple rules.
- Every cell belongs to a faction and stores a pressure value.
- Pressure spreads between neighboring cells of the same faction, moving from higher pressure toward lower pressure.
- When a cell touches another faction, pressure becomes a competing force rather than simple diffusion. The neighboring faction with the strongest pressure makes the capture attempt.
- If that pressure overcomes the resistance of the cell, the cell changes faction. Its new pressure then allows the front to continue moving.
Pressure is exchanged only between neighbouring cells that belong to the same faction. Each cell gains or loses a small amount depending on the pressure difference with those neighbours. These exchanges are combined into a diffusion delta, which determines how the cell’s pressure changes at each step.
Once all six neighbors have been checked, the cell updates its pressure. Then it compares the strongest foreign offer against its local resistance. If that offer is strong enough, the cell changes faction. This same cycle is repeated across the whole grid, so the border keeps adjusting one local interaction at a time.
The result begins to resemble a density field. Pressure radiates outward from each faction, strongest near the points where it is introduced and gradually relaxing as it spreads through the territory. Where these fields meet, the gradients begin to shape the border.
In that sense, the system starts to echo other boundaries found in nature, such as competing bacterial colonies, where a visible edge appears from the interaction between two growing fields rather than from a line drawn in advance.
Once people can choose where to place a new faction, or add pressure to an existing one, the model becomes a form of gameplay. The choice is simple: claim territory for yourself or strengthen someone else. Their decisions enter the field as pressure and gradually reshape the borders around them.
What interests me here is how such a limited mechanic can start to reveal something about the individual. Faced with the same map, one person may expand their own claim while another chooses to reinforce someone else. The interaction becomes less about winning and more about making visible the kind of territorial instinct each person brings into the system.
In the next article, I will show how I used this pressure system to generate the structure of a map. The simulation defines the territories and their borders, which then become the basis for the visual landscape.
LINK - NEXT ARTICLE - TBA
LINK - PROJECT - TBA
Project developed as part of the European Media Art Platform Residency 2026. Hosted by Ars Electronica.
Scientific advisor: Prof. Dr. Cristian Axenie
