quantum random walks

Amplitudes of planar quantum random walks. The connection matrix is a one-parametric (circular) deformation of the Hadamard matrix. The family is presented in an animated loop.


More deformations (seeded at different matrices).

catch an intruder

In the 40-by-40 array of sensors, a running intruder is represented as a black dot. Can you spot her? The catch: the sensors are prone to spontaneous signals ("false positives"). These signals are rare (just 2.5% probability), but what a mess they make!

self-organized alarms

Here (1.3MB) the intruder desiring to remain unnoticed is squeezed away by the wave of activated sensor. These waves are propagating in the dense field of mostly sleeping nodes activated according to a variant of Greenberg-Hastings cellular automaton (in our setting though, the nodes are located randomly over the plane).

The "old movie" jitter is a surprising side effect of converting a series of .eps files into the animated .gif. In much wisdom...

spies in the fog

Here we see a few spies conspiring in groups and then disappearing in the fog. You see just vague shadows of them; how many (at least) of them are there? Note that at any time there are at most three shadows! A convenient model for counting targets in such situations involves sheaves and cohomologies...


...just before running aground

perspective (courtesy of A.S.)

family politics

shades of blue

Up [ Math Center | Bell Laboratories | Mothership ]

Last modified: October 25, 2007