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.
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:
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?
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