The user may select from 4 basic equation classes, manipulating them through the use of a constant modifier, and the initial x0 value. One can experiment with the various different constants, intial points, and number of iterations to explore various results. Some formulas, such as the locistic function, bifurcates to chaos, when given a constant value of 4. WIth other constants, the values of x repeat through several different values, in a circular cycle. Some of the other formulas end up converging on a given value.
Iteration is one of the most common methods to study chaos.
This function oscillates very quickly as it approaches the origin, creating a unique, interesting effect. Clicking on the second, teal colored window at the bottom will zoom in on the origin. A left click zooms closer by changing the dimensions to make the window size .2 units smaller. A right click enlarges the window size .2 units. While the function is graphing, the color changes slightly in a gradient manner, from medium-green to medium blue.