Space

Space
[image of digits]

Space is important in cultural, social, biological and physical systems.
How do we represent space in simulations?

By its dimensionality.
By its texture.
By its granularity.

Space is represented dimensionally by: 0d - Point Dynamics 1d - Linear Dynamics 2d - Planar Dynamics 3d - Volumetric Dynamics Simulations may behave differently when using different representations of space...
We can represent it as a bounded plane Like a sheet of graph paper. The world is flat and has edges or boundaries. Typically we represent it as a plane on the computer screen. The world may be so small that agents will bump into its edges, giving rise to "edge effects," or the world may be large enough that agents will never reach its borders. If two agents continue to move away from one another, they get further and further apart on the screen, as they would in "real life." The farthest apart two agents can get from one another is to occupy the opposite corners.	We can represent it as a wrap-around torus Like a donut or an automobile inner tube. The world wraps-around and has no edges or borders. Consequently there are no "edge effects." Typically we represent a torus as a plane on the computer screen, but it will have peculiar properties that a plane does not have. When an agent exits from the top of the screen, it re-enters from the bottom. When an agent exits from the right it re-enters from the left. If two agents continue to move away from one another, they reach a point where they appear to be moving apart on the display but they are actually moving together on the torus. The farthest apart two agents can get from one another is half the dimension of the representation of the plane on the screen.





A toroidal world looks superficially like a bounded plane. But there is a difference. On a flat representation of a toroid if you move off the screen to the left, you return to the right. If you move below the bottom, you return to the top, etc. Consequenmtly, the neighborhoods in that space can be confusing as illustrated in the application below. The executable and source code are here.

Space is represented texturally by: Cells or Rasters - discrete dots Vectors - abstract shapes Simulations may behave differently when using different representations of space...
Cells or Rasters (Images) An example: Adobe Photoshop represents space by pixels arranged in grids called bitmaps. Pixels have no knowledge of any shapes they may be part of. Enlarged images are subject to the "jaggies" or "pixellation." Textures can be represented economically, but complex shapes are best left to vectors.	Vectors (Shapes) An example: Adobe Illustrator represents space as geometric shapes (lines, squares, circles, ellipses, etc). Shapes have no knowledge of any pixels which they may contain. Enlarged shapes preserve their sharpness. Shapes can be represented economically, but complex textures are best left to rasters.




Examples of each are shown below:
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Space is represented granularly by: The relative size of the units of space compared with the relative size of the units of time and agency.
Fine-grained simulations run more slowly but are more precise.	Coarse-grained simulations run more quickly but are less precise.