# The Boston Diaries

The ongoing saga of a programmer who doesn't live in Boston, nor does he even like Boston, but yet named his weblog/journal “The Boston Diaries.”

Go figure.

## 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?

## Obligatory Miscellaneous

You have my permission to link freely to any entry here. Go ahead, I won't bite. I promise.

The dates are the permanent links to that day's entries (or entry, if there is only one entry). The titles are the permanent links to that entry only. The format for the links are simple: Start with the base link for this site: https://boston.conman.org/, then add the date you are interested in, say 2000/08/01, so that would make the final URL:

https://boston.conman.org/2000/08/01

You can also specify the entire month by leaving off the day portion. You can even select an arbitrary portion of time.

You may also note subtle shading of the links and that's intentional: the “closer” the link is (relative to the page) the “brighter” it appears. It's an experiment in using color shading to denote the distance a link is from here. If you don't notice it, don't worry; it's not all that important.

It is assumed that every brand name, slogan, corporate name, symbol, design element, et cetera mentioned in these pages is a protected and/or trademarked entity, the sole property of its owner(s), and acknowledgement of this status is implied.