Description
Description-Separate-1The VI "Bifurcation Diagrams.vi" shows the bifurcation diagrams for two well-known fractal equations: Population Pn+1 = Pn.R(1-Pn) and Mandelbrot (Zn+1 = Zn^2 + C). The application plots the results of the selected equation for a range of R values for the population equation and for a range of C values for the Mandelbrot equation. The range is set by the values of the Min X and Max X controls.
For each of the X values within the range, the iterative equation is run 300 times. The output 250 last values (P or Z) are plotted in the diagram. The X range is divided into 2000 steps and the 250 values are plotted for each of the 2000 steps.
The plot shows that for some values of X, the output values converge to a single value. For some range of X values, the output values converge to two values (bifurcation) or more. For some other range of X values, the output become chaotic and does not converge to any specific value. However, it is interesting to note that within chaotic ranges, some pockets of stability can be observed. These pockets of stability show fractal behavior. As you zoom in those pockets, similar pockets of stability can be found.
Using the mouse, you can zoom around those pockets of stability to observe the fractal behavior.
Description-Separate-2How to Use
How-Separate-1The code is attached in a zip file. It is in LabVIEW 2016 format. You will also find an executable. This executable requires the LabVIEW 2016 Run-Time Engine.
The video below shows how the VI can be used.
How-Separate-2
