Episode 101

Simulating Numb3rs: Pilot

Episode 1

Snapshot of the simlutaion:

• Ray casting algorithm
• Gamma distribution
• Uniform distribution

This edition of “Simulating Numb3rs” is dedicated to reconstructing the case from Episode 1 of the TV series “Numb3rs” by generating synthetic datasets using computational simulations and techniques used in geographic profiling. If you haven’t watched Numb3rs yet, then it a must watch for applied math enthusiasts, as it brilliantly focuses on breaking down the mathematical twists and investigative techniques to solve complex cases.

The episode opens with a tense investigation as FBI Agent Don Eppes and his team grapple with a series of escalating crimes across Southland. In their pursuit, Agent Eppes turns to his brother Charlie, a mathematical genius, and describes the serial perpetrator’s behaviour to him as being driven by his needs:

• He watches potential victims while avoiding detection, indicating a strategic approach to selecting targets.
• He covers a wide region but avoids committing crimes near his home, creating a “buffer zone.”
• There is a distance decay effect — the more intense his desire to commit the crime, the further he will travel to do so
• He has committed 13 sexual assaults in the Southland, with the most recent escalating to a murder.

With the above insights we can regenerate this crime scene by following these steps.

Step 1: Boundary generation

We will first obtain a polygon of the southland city using a bounding box tool and store it in a polygon class. To determine if the point lies within the city the class implements the ray casting algorithm. A ray casting algorithm calculates the number of times a ray, drawn from the point, intersects with the polygon’s edges. If the number of intersects is even, the point is outside the polygon; if it’s odd, the point lies inside.

class Point:
    def __init__(self, lat, long):

        self.lat = lat
        self.long = long

class Polygon:
    def __init__(self, point:List):
        """
        points: a list of Points in clockwise order.
        """…