I was going through some old CDs today. On an album from 1993 I found this Mandelbrot fractal image. The authors were so proud of it that they gave a lot of details in the liner notes, which allowed me to recreate it and do some speed comparisons.
I was amazed.
Cover art generated by Lawrence S. Kroll, Professor of Computer Science at San Francisco State University. Dr. Kroll generated the fractal over a period of 4 1/2 hours on a Macintosh Il computer. This particular graphic image was rendered with a total of 640,000 points. Each point on the computer screen took up to 3500 computations to achieve high resolution. This comes to over 2 billon calculations for the one image. Typical times to generate this same image are: IBM PC or Mac Plus: about 4 days (day and night), CRAY X/MP Supercomputer: less than 10 seconds.
640,000 data points sounds like a lot, but it’s not. It’s only 800×800, or .64 megapixel. Your phone (depending on the age or model) is between 3 and 12 megapixel.
Likewise, 2 billion calculations sounds like a lot, but it’s not. CPUs are measured in MIPS (Millions of Instructions Per Second) and a modern Intel I7 CPU, like a typical gamer’s PC is rated at 317,900 MIPS – nearly 318 Billion instructions per second.
Yes, there is more than one “instruction” per “calculation”… But get real. The CRAY Supercomputer from 1993 doesn’t even make a good web browser these days.
For fun, I used a copy of XaoS software on my 2010-model MacBook to generate that same image today. I didn’t time it precisely, but it took around 1 second – on a 7-year-old laptop.
If you want to try it for yourself, fun fractal software is available for your iPhone, iPad, Windows and Mac. http://fractalfoundation.org/resources/fractal-software/
For anyone wanting to recreate this test, they listed the exact parameters of this fractal as:
The Fractal Location for this image is: center: x -0.7454286; center: y .11300881; magnify 2 x 10 times; Escape Radius- 2.5, Dwell 1000.