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.
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...
