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:
xi+1 = (Ayi + B) xi (1 - xi)
yi+1 = (Cxi + D) yi (1 - yi)
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?