The shape extends less than 2 units in any direction from the center of the plane (0,0) but the boundary that encloses this finite area has infinite length. It manages this seemingly impossible feat by having an edge that is infinitely wrinkled. You can zoom in on any part of the edge and it displays more and more detail the further you go, deeper, deeper... forever. It is a fractal.
However the article was less about this than about the extraordinary, scintillating beauty of the shapes to be found and the ease with which they can be created.
To this day I have never found a more accessible and easy to understand description of how to generate your own mandelbrot set and how to embark on your own journeys deep within it.
I remember feverishly making notes during work that day (I must have been a much worse employee than usual), then on closing time rushing home, eager to try out my rudimentary program on my computer. At less than 1 MHz speed, my lovely little computer was thousands of times slower than even a cheap, crappy computer from nowadays, and the images took overnight to grow on my screen. I was over the moon.
I want to digitise many of the documents that had great impact on me while growing up. This one is now done and uploaded to my website:
I don't know if Mr Dewdney's wonderful columns are collected in book form. I certainly hope so, because I'd love to buy it. If I'm able to find it online (probably on Amazon) I'll link to it below.
Edit: The article I so painstakingly digitised [groan] is available for free download from Scientific American at: http://www.scientificamerican.com/media/inline/blog/File/Dewdney_Mandelbrot.pdf
Edit 2: I found it. A K Dewdney's book The Armchair Universe is a collection of his columns from Scientific American. Unfortunately it is only available in dead-tree format, not ebook. A pity.
(Crossposted from http://miriam-e.dreamwidth.org/326311.html at my Dreamwidth account. Number of comments there so far: )