O-Matrix User Stories

Exploring Bifurcation Diagrams with O-Matrix

Bifurcation diagrams, also known as Feigenbaum plots, are an excellent way of demonstrating the nature of chaos. They can show how an iterative function for certain values of a constant converge to a steady state over time, while for other values it may oscillate between a number of different states, and for yet others, vary without settling into a pattern. Dr. Charles Sadler, an orthopedic surgeon and advisor for the California Workers' Compensation system used O-Matrix to quickly build a GUI-based system for exploring the mathematics and plots of bifurcation diagrams. Using this prototype Dr. Sadler was more easily able to create a quantitative logistic regression method to replace the previous subjective techniques used by the California Compensation system.

Using the O-Matrix GUI Building Tools displays a simple GUI for selecting a diagram mapping type.

Bifurcation GUI
The Bifurcation GUI

Depending on the mapping type, the bifurcation GUI displays an appropriate dialog for specifying parameters.

Logistic Mapping Dialog
The Input Dialog for a Logistic Mapping

Logistic Mapping
Logistic Mapping

Quadratic Mapping
Quadratic Mapping

Sine Mapping
Sine Mapping

Download/View Bifurcation Source Code

This user story was contributed by Charles Sadler, M.E.E., M.D., F.A.A.O.S.
Sadler Medical Group, Inc.

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