Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
```                    ALAN
(re: blackboard)
'Fuzzy C-Means Cluster Analysis.'
Hard to believe there was a time when
I considered myself math literate...```

# Cluster Analysis for 2D Points »

Cluster analysis groups data elements according to a similarity function.
```                    ALAN
(re: blackboard)
'Fuzzy C-Means Cluster Analysis.'
Hard to believe there was a time when
I considered myself math literate...

CHARLIE
The process can get complex, but the
concept is fairly simple -- David and
Blakely are throwing off two
coinciding heat signatures...

ENTER AUDIENCE VISION --

Of a SCHOOL OF FISH -- think coral reef, colorful,
beautiful...

CHARLIE (V.O.) (cont'd)
... like two schools of fish, passing
through each other... looking to the
naked eye like a single group...

... a SECOND SCHOOL OF FISH swimming into the first... it
becomes a writhing mass of color and motion... data on each
fish flying away from them...

CHARLIE (V.O.) (cont'd)
... but if you analyze the data
discretely -- check the movement and
behavior of the individual fish --

... the math separating the TWO SCHOOLS to opposite sides of
the screen...

CHARLIE (V.O.) (cont'd)
-- you can separate the two
groupings.```

# Merging Schools of Fish »

Imagine two schools of fish passing through each other, looking to the naked eye like a single group.
```ENTER AUDIENCE VISION --
Of FIREFLIES in the night...

CHARLIE (V.O.) (cont'd)
-- much like fireflies, flickering
off and on during a summer night;
apparently random blinks of light in
the darkness ...

... MATH following their trails backward --

CHARLIE (V.O.) (cont'd)
... but math reveals their path and
purpose, tells us which trees they've
laid eggs beneath, where they've gone
to mate; bringing rhythm and pattern
to the light show.```

# Model of a Firefly Swarm »

Using techniques of swarm modeling, it is possible to make a somewhat unrealistic model of firefly behavior.
```                    CHARLIE
Chaos Theory holds that outcome is
sensitive to initial conditions. We
must restore the decision making
process to the man who started it.```

# Sensitive Dependence in Iterated Maps »

A classic result in chaos theory is that small perturbations in "chaotic" iterated maps grow roughly exponentially.