Fixed-radius simulations

If the r parameter for each cell is fixed in advance, only cell position varies during the simulation. In this case, the r parameter could be interpreted as the size of a chemorepellant field. Two simple sets of experiments have been performed.

Effect of changing density

The radius r for each cell was taken from a uniform distribution of 5-7 um. Simulations were run using different numbers of cells in the network (100, 200, 300, 400, 500). For each simulation I calculated the regularity index (CR - conformity ratio) and the number of cells that moved (proportion of movers = number of cells that moved/ number of cells in the network). Like the dmin rule, regularity increased with density. I also found that as cell density increased, so did the proportion of cells that moved.

Examples of final mosaics: Postscript PDF.

Development movies (red cells are those that moved during the simulation) (animated GIF format): 200 cells 500 cells (movies loop).

Conformity ratio and proportion of cell movement as a function of cell number (10 simulations for each value of N, number of cells in network): Postscript or PDF.

Effect of changing radius

A different set of simulations was run where the number of cells in the network was fixed (at 100), but the extent of the radius varied.

Examples of final mosaics: Postscript PDF.

We find that mosaic regularity increases rapidly with increasing r (corresponding to a bigger exclusion radius). Once the mean radius is bigger than around 20um we find that all cells moved during the simulation. Note however as r continues to increase we see a boundary effect: more and more cells are pushed to the edge of the surface (the last plot, number of rejects, shows how more cells are pushed to the border with increasing r). There is also a (suprising) drop in the nearest neighbour distance (NND) for mid-range values of r, but again this could be due to border effects.

Conformity ratio, proportion of cell movement, number of rejects and NND as a function of cell number (5 simulations for each mean value of r): Postscript or PDF.