## Monday, September 06, 2021

### Expanding a program from the past

I will start with a disclaimer: this post might be of interest to only two other people,
neither of which read my blog
(as far as I know).
But it's my blog,
and I don't care.
*I* find it interesting.
Anyway,
on with the post.

I was playing around with an old program that plots a chaotic attractor. I won't pretent to know what the chaotic attractor is supposed to represent, but I find it fun to poke around the program from time to time. It revolves around two equations that interact with each other:

x_{i+1} = (Ay_{i} + B) x_{i} (1 - x_{i})

y_{i+1} = (Cx_{i} + D) y_{i} (1 - y_{i})

with the resulting image x and y values plotted on the graph between 0,0 and 1,1:

But then I got wondering—*why the unit square?*
Thirty years ago I never questioned that.
It should be easy enough to find out—just change the output range a bit:

Cool! I now have the range from -1,-1 to 1,1 working. So whereas before, I would have seen:

I can now see the full extent of this particular result:

And otherwise dull plots in the 0,0 to 1,1 range are now full of detail:

I am now left to wonder if this would have affected the research this program supported?