# 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.