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.

The Bifurcation GUI

The Input Dialog for a Logistic Mapping


Logistic Mapping


Quadratic Mapping




Sine Mapping