For those who are interested, I found those first Mandelbrot set images from Byte magazine September 1984. I added the picture to my Lambda map page ( http://www.mrob.com/pub/muency/lambdamap.html) and the figure itself is here: http://www.mrob.com/images/0-muency/byte-198409-p158.jpg Image by David Turk, the computer graphics researcher and professor at Georgia Tech, when he was still an undergrad. Based on the article text, the images were probably created on a VAX 11/750 at West Coast University. - Robert Munafo On Fri, Jul 29, 2011 at 02:14, Robert Munafo <mrob27@gmail.com> wrote:

The only "az^2+bz+c" variation I've seen is the "lambda map", f(z) = c z (1-z) = c z - c z^2. Here is an image:

mrob.com/images/0-muency/lambda.jpg

Notice the shape is different from the normal Mandelbrot shape, and they are related by "squaring" one to get the other.

This version of the Mandelbrot set was actually published in Byte magazine[1] some months earlier than the Scientific American[2] that is normally thought to be the popular introduction of the Mandelbrot set. The Byte article was about fractals and simply showed a few pictures of the Lambda fractal, without a formula or other explanation. The "interior" was white, as in my image above, not black as the Mandelbrot set is more commonly drawn. I immediately recognized the importance of this new fractal and wished I could find out how it was calculated. [...]

-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com