Fraxion supports the calculation of bifurcation diagrams for divergent fractals (main fractals, not dual ones). The bifurcation parameter of the system corresponds to the c value in the complex plane, which is bounded by a single straight line segment.
Bifurcation functionality is accessed via the following options in the Fractal menu:
Selecting the Show bifurcation diagram menu option triggers the calculation of the bifurcation diagram for the current fractal. Initially all bifurcation diagrams are shown for the range -2.0 + 0 i to 0.25 + 0 i. This results in the following image for the classic Mandelbrot set (with the red line indicating the bounds for the bifurcation parameter, and the intensity of the plot denoting points in the orbits that are visited more than others):
By selecting the Set general bifurcation axis menu option, you can draw an arbitrary bifurcation axis. Fraxion will ask you to select the axis' begin and end points in the complex plane (you right click at anytime to cancel). Note that when the bifurcation diagram is shown, you can move the mouse around the complex plane. Fraxion will automatically translate between a point on the bifurcation axis (shown as a small white box), and the corresponding location in the shown bifurcation diagram (shown as a transparent small vertical rectangle). An example of an arbitrary axis is shown in the following figure:
By selecting the Fix horizontal bifurcation axis menu option, you automatically set the bifurcation axis to the width of the screen, with a fixed imaginary component of zero. An example of a fixed horizontal axis is shown in the following figure:
Note that when a bifurcation diagram is shown, the following properties at the mouse cursor are fixed to a location on the bifurcation axis: the dual inset fractal, the orbit diagrams, and the current location. Activating the orbit diagrams shows how the number of fixed attracting points correspond to the lines in the bifurcation diagram, as shown in the following figures:
Selecting the Set number of bifurcation points per orbit opens a dialog box in which you can specify (1) the number of points in the orbit to discard (allowing the orbit to settle and remove initial transients), and (2) the number of points in the orbit to retain. The more points used, the smoother the bifurcation diagram will look in the chaotic regions. Additionally, the Set bifurcation outlier percentile offset allows to set a percentile to exclude some of the points in the bifurcation diagrams, thereby zooming in on more detail.
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