Remembering Ken Knowlton

A Portraitymology

 

Either the first or second time I attended a G4G conference (around G4G4), I found myself randomly sitting next to Ken Knowlton at a dinner event. We had never met before, but being a computer science guy trained in the 70s, and familiar with Bell Labs’ pioneers and computer graphics history, I had known who Ken was, and I was familiar with some of his early mosaic pictures.

 

During our getting-to-know-you dinner conversation, I explained that my little field of expertise was elementary space-filling curve constructions whose approximations were self-avoiding paths, and that I had drawn a few illustrations of geometric fractals for Benoît Mandelbrot’s seminal book <i>The Fractal Geometry of Nature</i>.

 

Ken immediately said that for a long time he had wanted to do a portrait using a space-filling curve of some sort. Would I be interested in providing one of my own constructions for him to do a self-referential portrait? he asked. I said “of course” (of course!).

 

I provided him the construction for the simple E Curve that I had found in 1978, but Ken preferred a perturbed variant of it that I had described in a chapter in the 1994 book <i>The Lighter Side of Mathematics</i>, the proceedings for an Escher-inspired recreational math conference. Ken’s excellent reason was because the variant hid the underlying square subdivision better.

 

He then asked me for a photo of myself, which he would boil down to a low resolution grid of pixels. When I got the email, I was visiting my friend Jef Raskin (who named the “Macintosh” computer project after his favorite apple!). Jef had a professional camera and studio backdrop in his office to use, so he took the black & white picture that I forwarded to Ken.

 

After some months, I received a draft of Ken’s portrait based on Jef’s picture, done with a white connected path on a black background. Ken’s idea was to use a full motif pattern for the whitest pixels, and then to reduce the number of line segments in motif copies (while maintaining connectivity with neighbors) for building darker areas of the image. So technically, it’s a partial space-filling curve.

 

It turned out pretty well!

 

Ken was an inspiration to many mathematical artists, including me. He used his mathematical knowledge and computer skills—during an amazing time when automated math exploded in myriad directions—to make unique and/or pioneering artworks whose worth will be long-lasting for many reasons including aesthetic, historic, and for their playful visual mystery with a touch of implicit humor.

 

I will always feel honored to have been in the right place at the right time, with my visage now found in a “luminarial” collection of self-referential portraits, up to all of whom I look. Over and over.

 

 

– Doug McKenna, Mathemaesthetics