LARRY Ah, Charles, my ambulatory reference book. Chaitin's Omega Constant...? CHARLIE Omega equals .00787499699. Why, what're you working on? (sees the file, reacts) Oh. FBI file.

Chaitin's constant measures the probability that
a Turing machine will halt.
The busy beaver game is a competition
to find an *n*-state Turing machine that either leaves the largest number of 1s on its tape or makes the largest
number of head movements before halting. A busy beaver is a Turing machine that, when provided with a blank tape,
does a lot of work.

Larry points. Colby grabs the remote, zooms in. In the corner of the driver's area, a shiny, CHROME HANDLE. On it, a WILDLY DISTORTED, fun-house mirror version of the Suspect. DAVID We see it. What're we supposed to do with it? It's too distorted... LARRY Certainly from the limited perspective of the human eye it isn't what we normally comprehend as a face... AMITA The image's been altered by the refracting nature of the surface, but the information is still there. It's called Non-Linear Warping.

The figure shows a nonlinear warp, which maps a regular grid onto a cylinder or hemisphere.
The effect is the same as wrapping a flat image around an object and viewing it from afar. The image transformation is a
function of the radius of the cylinder or hemisphere.

AMITA Contemplation, or second thoughts? LARRY (iffy) Working cell by cell will suffice, certainly, in producing Splines... But there must be a more elegant approach...

In the full Demonstration, each of the four control points can be moved to see the effect on the form of the spline curves. Either Bézier or cubic splines can be experimented with.

CHARLIE Belief Propagation. Algorithms that convert scattered information into a coherent picture, even if the information is incomplete. Charlie moves toward the living room FLAT SCREEN -- CHARLIE (cont'd) It's like... say you're a TV network on election night... AUDIENCE VISION - Charlie appears INSIDE the TV, with a flashy, Network-like chyron - 'Election 2008: America's Decision.' As Charlie moves to the TV -- CHARLIE (cont'd) You want to be first to predict a winner, so you collect information from all over the country...

The voter model shows how the views of neighbors can influence a neighborhood. On a given day, several voters
will abandon their current views and assume the position of one of their four neighbors. When run, strong
groupings appear almost immediately, with conflict at the borders. Eventually, some positions vanish entirely.