Select the various functions and try to find regions of gain where attractors exist. See if you can identify regions of gain where the functions display two, four and eight-fold attractors. This doubling phenomena is called "bifurcation". perhaps we will hear more of this in another article.

Just to get another look at a situation we have already explored, set the function to quadratic and the gain to 3.5. Then place the mouse cursor above the x-axis at 0.25, or as close to it as you can conveniently get, and click on that location. This has the effect of changing the initial value of x to 0.25. Next, click on the action button 35 or more times and change color. Add a few more iterations and notice that the you have settled on an attractor that cycles among four values. Use the mouse cursor to estimate the values by placing the cursor on each of the four horizontal lines in the attractor. These will be the same four values we found back in the Next x by Feedback display where we also iterated the quadratic function starting at 0.25 on the x-axis.