I played with drawing ferns and trees with Aza Raskin's Algorithm Ink, a client-side recursive drawing tool. Then I got some ideas about a different kind of spiral.
Morse Code Forever rendered in Algorithm Ink 
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The program offers three alternatives for "dit", a circle, a rectangle or a space. The spiral grows inward laying these dits down randomly.
The general spiral shape comes from recursively drawing dits while turning two degrees and shrinking by a fraction of a percent each time around.
A dash is normally three times longer than a dot in Morse code. I found a shorter dash much more pleasing.
startshape frame rule frame { shape {s .07 y -2} } rule shape{ dit {r 2 s .9997} } rule dit { CIRCLE {x .5 s .8} shape {x 1} } rule dit { SQUARE {x 1 s 1.6 .8} shape {x 2 r 2} } rule dit .7 { shape {x 1} }
I met Aza for the first time years later at a Wikipedia 10th Anniversary party. He told me he had been taken by the quality of my work in his tool. Aza is a ham and would get the irony in the title.