Recreational math buffs were introduced to fractals, shapes that repeat themselves at ever-smaller scales ad infinitum, in the August 1985 issue of Scientific American.  This was back when Scientific American was a thick, high-quality magazine that respected the intelligence of reasonably-educated persons — and when I was a subscriber.

Anyway, French mathematician Benoit Mandelbrot (1924-2010) coined the term fractal for the dimension-rich contours of such natural formations as coastlines and fern leaves.  He was responsible for advancing and popularizing the science of fractals, most notably in his work The Fractal Geometry of Nature, published August 15, 1982, 37 years ago today.  I prize my hardcover copy.

Perhaps the most well-known fractal shape is the bulbous and prickly Mandelbrot Set which featured prominently in his book.  For some reason — probably that small indentation — this figure always reminded me of the 20th-century comic strip character Nancy, who was created and drawn by Ernie Bushmiller.

By odd coincidence, August 15, 1982, the day Mandelbrot’s masterwork was published, was also the day Ernie Bushmiller died, a week before his 77th birthday.  I don’t quite know what to make of this but I’m sure it holds some cosmic (or comic) significance.

So to properly commemorate this day, I created a visual portmanteau of the signature works of both men, which I call The Nancy Set.  Although Mandelbrot and Bushmiller sat on opposite ends of the intellectual spectrum, their respective creations seem to belong to the same dimensionally-ambiguous world.

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For an intriguing foretaste of fractals in Nancy’s world, here is the Nancy strip published on May 19, 1948, as Mandelbrot was about to receive his masters degree from Cal Tech:

Note how Fritzi is looking right past Nancy, back to the infinite regress in the first panel.  Is this a second way that the strip plays with endless repetition?  Or would that premise give Bushmiller too much credit?  I suspect the latter but we will never know.

Dream in peace, Benoit and Ernie.