This note answers one question in math.PR/0505668, concerning the connected allocation for the Poisson process in R2. The proposed solution makes use of the Riemann map from the plane minus the minimal spanning forest of the Poisson point process to the halfplane. A picture of a numerically simulated example is included.
The picture:
(full size: .png, .svg)
Software used for simulation: coformal.tgz
It should run on any linux machine, not tested on other platforms.
You'll need R, python and tripack installed;
check README for detailed instructions.
More pictures / references
- http://www.math.ubc.ca/~holroyd/stable/
- http://www.stat.berkeley.edu/users/manju/pictures.html
- http://www.math.huji.ac.il/~romik/Site/Allocations.html
The zoo: few typical shapes from the picture above
