| In Space-time dynamics of video feedback, Crutchfield
models the several types of dynamical patterns arising in videofeedback. |
| The monochrome version of Crutchfield's model describes how In+1(x,y), the intensity of the
screen light at time n+1 and point (x,y), depends on In(x,y)
and on the intensity at nearby points. |
| The basic model is this |
| In+1(x,y) = L In(x,y) +
L' Av(In(x,y)) +
f In(bR(x,y)) |
| where |
In(x,y) is the internsity at time n, and
L denotes the image decay between time steps. |
Av(In(x,y)) is the average of the intensities at points
near (x,y), and L' denotes the amount of the intensity of nearby
points affects that of (x, y) |
R denotes rotation, b denotes
scaling (zoom), and f denotes f-stop. |
| (The last term of Crutchfield's model includes two additional features: inverting the image
(black pixels -> white pixels), and averaging over some time period. We drop these from
the current brief discussion.) |
| Simulations with this model have produced some of the simpler video feedback patterns,
including spirals. |
| Crutchfield points out that the bursts observed at high zoom result from the amplification
of noise in the system. |
| Among several variants to the basic videofeedback set up, he proposes using mirrors.
This is the direction we have pursued. |