Logistic Bifurcation Diagram

Generate an image of the bifurcation diagram of the logistic equation

x1 = r * x0 * (1 - x0)

This is about as cheap and dirty as I could get. I use gnuplot to draw the image, I didn't even bother to have the Go image package involved. My program outputs text representations of floating point numbers.

Algorithm

0. For values of r from 2.8 to 4.0 (step 0.0002):
1. Set x = 0.5
2. Run 100 iterations of x = r * x * (1.0 - x)
3. Run 100 more iterations of x = r * x * (1.0 - x), this time keeping all (floating point!) values of x
4. Print out r and the unique values of x from step 3

Things that could change the diagram:

• Initial value of x
• Step size of r
• Number of "settling" iterations
• Number of iterations done to find unique values of x

My diagram has bulkier bifuration points than the Wikipedia diagrams. I could not make it as graceful as other people got.

References

• Wikipedia
• Python code
• Logistic map