Gecko takes a rather literal geometric approach to topology (Figure 1 and Figure 2). Agents are spheres projected onto a plane as circles. They have ungridded movement on the plane and real-valued size, expressed as radius. An agent's radius defines the limit of its world at any timestep. An agent's neighbors are not adjacent to, but within this radius. As an agent grows, its opportunities and liabilities grow. Agents must intersect to interact.
Agents also intersect the plane of the landscape, as their circular representation on the plane. An agent's rate of resource uptake is a function of this circular area, minus any area lost to competition (intersection with other agents vying for this resource). In the ecosystems presented here, only plants acquire resources from the landscape.
All action takes place on the landscape plane. The simulator
displays the agents as
circles, and resource-producing areas as rectangles. However,
the implicit third dimension plays a key role: an
agent's biomass is its spherical volume, specified by the radius.
As a sphere has volume
, and area 
, an agent's radius
is proportional to 
, while its ability to
gather resources is proportional to its area, or 
.
Metabolic costs of
self-maintenance default to the allometric norm of
. This results in a natural curb to growth,
as volume-based costs of self-maintenance grow somewhat faster than the
area-based ability to procure food.
The agent sphere can be thought of as its space-time extent, or its range over one timestep. This is like a probability sphere---with probability 1.0, the agent is in here over this time period. This is as specific as ``here'' gets in Gecko, as the agent's ``true'' location is its entire spatiotemporal extent. If two agents overlap, that may imply for example that one is above the other, or they miss each other in time by less than a simulator timestep, or their roots and leaves intermingle. Or, of course, one may be eating the other.
Movement range, perceptual range, perceivability range (the range at which other agents can perceive this one), and offspring spacing, are concentric spheres, of radius equal to a multiple of the biomass-tied radius. In the models shown here, all these ranges are identical with the biomass radius unless otherwise noted.
The remainder of this section describes the simulator from the bottom up.