A density-driven method for the placement of biological cells over two-dimensional manifolds
Copyright 2017 Nicolas P. Rougier, BSD License.

We introduce a graphical method originating from the computer graphics domain that is used for the arbitrary placement of cells over a two-dimensional manifold. Using a bitmap image whose luminance provides cell density, this method guarantees a discrete distribution of cell position re- specting the local density. is method scales to any number of cells, allows to specify arbitrary shapes and provides a scalable and versatile alternative to the more classical assumption of a non- uniform spatial distribution. e method is illustrated on a discrete homogeneous neural eld, on the distribution of cones and rods in the retina and on the neural density on a a ened piece of cortex.

Figure 1

Please go to https://github.com/ReScience-Archives/Rougier-2017

Figure 2

Before running figure-2.py, you'll need to run the stippler.py script on the gradient-1024x256.png image as follows:

$ ./stippler.py --n_iter 25 --n_point 1000 --channel red data/gradient-1024x256.png
$ mv data/gradient-1024x256-stipple-1000.npy output
$
$ ./stippler.py --n_iter 25 --n_point 2500 --channel red data/gradient-1024x256.png
$ mv data/gradient-1024x256-stipple-2500.npy output
$
$ ./stippler.py --n_iter 25 --n_point 5000 --channel red data/gradient-1024x256.png
$ mv data/gradient-1024x256-stipple-5000.npy output
$
$ ./stippler.py --n_iter 25 --n_point 10000 --channel red data/gradient-1024x256.png
$ mv data/gradient-1024x256-stipple-10000.npy output

Figure 3

Run the script figure-3.py.

Figure 5

Run the script figure-5.py.

Figure 6

Run the script figure-6.py.

Figure 7

Run the script figure-7.py.

Figure 8

Run scripts figure-8A.py, figure-8B.py and figure-8C.py.

Figure 9

Run the script figure-9AC.py, then run:

$ ./stippler.py --n_iter 25 --n_point 25000 --channel red output/galago-patch.png
$ ./stippler.py --n_iter 25 --n_point 25000 --channel red output/galago-inter.png

Then run the script figure-9BD.py.