Last week we went to the Sandia Heights Artist’s Studio Tour. Lots of great stuff but I really enjoyed seeing some computer generated “fractal” art by Collin Delker. Really nicely colored 3D stuff. I did some similar work back in early 1989 when I was a graduate student at the University of Minnesota and working at Honeywell’s Systems and Research Center.
I had read James Gleick’s Chaos and a few other articles in the area of nonlinear systems, but it was an article in The Communications of the ACM by Clifford Pickover called A Note on Chaos and Halley’s Method that got me to write some code.
Since I was at Honeywell in the group that designed the Ada language, that was what I used for the implementation. I did it all in one morning as I recall. I ran it on my Sun 3 workstation not realizing it would take a week to get the final result. I didn’t have any reason to think the code would work the first time (it never does). I ran some scripts to convert the raw data not a bitmap and was surprised by what came out.
I was calculating the convergence of the 7th roots using Halley’s Method and zoomed in on the turbulent area at the convergence boundaries. Since the data was only 256 colors I had to map the colors to the millions of possibilities. At first I just stole colormaps for other GIF bitmaps but it was hit and miss. I made a rainbow-like spectrum that was the most interesting.
Instead of waiting a week for my results I started splitting the work across several other desktop workstations and running the job in the evening when they were usually idle. I also parlayed this into a project for Sudha Yalamanchili‘s graduate class in Parallel Processing at UMN.
I did some more complicated polynomials which took even longer to run, but produced some great images, even when colored with a limited palette.
I added some load balancing since some parts were more complicated than others and were taking longer to finish. One morning I came in to work and found out my job was still running. But it had gone wild and drove up the load on nearly every workstation in the lab. Nobody could even log in. The sysadmin was waiting for me in my office. He had tried to kill it but it kept re-spawning work. He asked me how to kill it off. I told him I didn’t know. I was sure I would be looking for a new job by afternoon.
But it completed in a few minutes and it turns out Bob (the sysadmin) hadn’t told anyone I was the culprit. I showed him what I was doing. Soon the whole office wanted to see my pics. My boss never mentioned it to me and I remained employed at Honeywell. I even got an A in Yalamanchili’s class. But that was more or less the end of my work in this area, though I did continue to specialize in high performance commuting for the rest of my career.
Steven A. Guccione 