I had been following the MOOC “Scientific Computing with Fortran” for a week and currently doing the exercises. This is one of the assignments which has piqued my interests  Logistic map. Here’s a neat animation from Wikimedia for the same.
As Wikipedia states it, “The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations”. It is given by the equation, $$ x_{n+1} = rx_n(1x_n) $$ where,
 $x_n \in (0, 1)$
 $r \in [2,4]$ (just to keep the final $x_n$ values bound to $[0.5, 1.5]$)
I have written the following Fortran code (along with a simple GnuPlot script) to generate the plot.


And the following is store in the logisticmap2.plt file.


I have generated the plot for various initial r values,which pertains to different zoom levels.
I like how such chaotic behaviour rises out of seemingly simple equation and that too in just 3 iterations! Just to put in perspective, this is how the initial conditions looked like.
:)