Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
```                    CHARLIE
Exactly.  My aggregation model will
filter through the characteristics
of the victims searching for the
strongest attributes in order to
determine their most likely choice
of seat.
```

# Random Tree Aggregation »

In random tree aggregation, a new branch can be added anywhere. Each new branch placement is selected randomly from among the nodes already present.
```                    LARRY
-- speaking of rearranging
molecules... did you see where
Professor Eric Kolokoff has
developed a new kind of graphene-
based digital paper...

They back against the table. Larry stares at the screen.
```

# Rolling Up a Sheet of Graphene »

A planar hexagonal lattice is rolled up into a cylinder. This can be an illustration of how a graphene sheet forms a nanotube of "armchair" geometry.
```                    CHARLIE
My program analyzed the DVD's...
(then)
We're cool, it's all legit.  I'm
under instructions from the LAPD to
info share with the FBI.
(then)
I got results by using a Hidden
Markov Model...
```

# Finite-State, Discrete-Time Markov Chains »

Consider a system that is always in one of n states, numbered 1 through n. Every time a clock ticks, the system updates itself according to an n×n matrix of transition probabilities, the (i,j)th entry of which gives the probability that the system moves from state i to state j at any clock tick. A Markov chain is a system like this, in which the next state depends only on the current state and not on previous states. Powers of the transition matrix approach a matrix with constant columns as the power increases. The number to which the entries in the ith column converge is the asymptotic fraction of time the system spends in state i.
```                    CHARLIE (cont'd)
-- similarly, the data you
presented appears to be an average
distribution of police work.

ON SCREEN - data appears...

CHARLIE (cont'd)
Until, like the stereogram, you
continue to stare or look at the
same data over and over again...
(data changes)
And a hidden pattern emerges.
```

# Floating Disk Stereogram »

When this stereogram is stereo-viewed, a disk floats above or below a background rectangle.