Fractal Analysis of Southern California Lagoons

Andrew J. Schatz
Torrey Pines High School
Grade 11
San Diego County
Ms. Victoria Coordt

Summary Statement
This project demonstrates the corrolation between fractal mathmatics and lagoons, and it realizes the effects of man's intrusion into the flood plains on the fractional statistics.

Objective: The purpose of my project was to resolve two issues. Currently, we know of no procedure to accurately measure the fractal statistics of a lagoon. Also, no one knows what effect man has had on the fractal characteristics of the lagoons in Southern California. Knowing what effects he has had could lead to many other conclusions about man's interaction with nature.

Materials and Methods: I created a computer program called FracFlow 2.0 designed to measure the fractal statistics of a lagoon obtained from scanned arial photography (including the fractal dimension and the standard deviation.) It can find the statistics at many different levels of detail and allows the user to alter the flood plain and flow path to analyze the effects of man's intrusion into the flood plains of the lagoons.

Results: The mid-point recursion method for measuring fractal statistics successfully found the characteristics of several different lagoons. One effect that man's intrusion usually has on lagoons is the complete loss of their fractal characteristics. Unrestricted flood plains allow the flow path to remain fractal, while constriction removes the natural characteristics. Also, an unrestricted, fractal lagoon will tend to retain the same fractal dimension over time.

Discussion: Knowing the fractal dimension of a lagoon allows us to predict future flow paths. Since the paths will have the same fractal dimension, factors within the lagoon such as sand flow, erosion, and wildlife habitat remain fairly constant. In a lagoon that is not fractal, these factors act unpredictably. A lagoon that is constricted will tend to follow the same path over a long period of time, thus removing its self-similarity. Also, when a lagoon is constricted, the direction of the slope will change. The slope change is due to sand buildup in constricted areas. Although constricted lagoons have higher water velocities, and therefore mechanically more efficient sand flows, they have a much smaller source of replenishable sand. Fractal lagoons have more natural environments, so it follows that they supply more sand to the beaches.

Help Received:
Mother helped glue backboard. Father supplied equipment and technical information.

CSSF / Projects / CalifSF@usc.edu