Order in Chaos: Periodic Points give birth to The Most Irrational Number

The Logistic Map is widely known for its chaotic behavior arising from the quadratic recurrence equation x_(n+1)=r*x_n(1 - x_n). Investigation of new bifurcation diagrams and recurrence equations could give more insight into the nature of periodic points. I explored a bifurcation diagram that produced period-doubling that occurred a lot quicker than the traditional Logistic Map. Let us call this bifurcation diagram the “golden” map. Extracting the periodic points from this “golden” map and plotting them on a coordinate plane exposed interesting relationships with the Golden Ratio.