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Email from Frank Odds August, 2003 Dear Bob, It's a few years since I did a Google search on 'spirolateral'. At that time the name brought up about 5 hits, all with little more than very basic descriptions. Now the word pulls up hundreds of hits, and your pages feature very prominently among them. Thank you very much for turning what began life as a simple set of figures into such beautiful creations. Allow me to explain. Like many sites, yours all describe spirolaterals in terms of 'what seems to be the first description by a British biochemist, Frank Odds'. Well, this mystery figure is me, and with so much current interest in spirolaterals on the web, I feel it's time I indulged in a bit of self-publicity to provide an accurate record and dispel the anonymity. The birth of the spirolateral concept occurred when I was doodling on graph paper during a not-very-interesting high school chemistry class. I drew a 1-2-3 square spiral and wondered what happened if I kept on turning and repeating. It soon became apparent that this 'rule' approach for repeating square spiral elements generated an infinite set of 90-degree figures. None of my mathematics teachers had ever heard of such things when I showed them what neat figures could be generated from square spirals. I put the figures on my mental back burner and moved on to university, to graduate in biochemistry. For 1970 till 1972 I was a postdoctoral research fellow at the Centers for Disease Control in Atlanta. In my desk I inherited a pad of triangular graph paper and returned to the spirolateral idea - I had not though of using angles other than 90° before. To my delight I discovered you can do spirolaterals at 60° too. (By now you'll realize I'm not exactly Albert Einstein when it comes to geometry!) The name "spirolateral" and the notion of rules with left and right turns and the use of any angle that's an integral divisor of 360° followed swiftly. I couldn't sit on my discovery any longer. It seemed to me the obvious person to write to about spirolaterals was the Martin Gardner, whose remarkable "Mathematical Games" column had already run for many years in Scientific American. He was keen to write a column about the figures, but - to ensure I received due credit for something that was entirely my own brainchild - he generously advised me first to write up a formal publication and suggested The Mathematics Teacher as an ideal journal. My paper on spirolaterals is a wonderfully obscure publication, and it was Gardner's column in Scientific American (and its republication in the Knotted Doughnuts book) that brought the figures to general attention. For the record, I had never heard of or seen Abelson's book, nor did I realize my figures were related to 'worm paths' till I saw Gardner's published column. My first (high school) spiros were drawn in 1962, and my correspondence with Martin Gardner was in 1971. My career has moved away from pure biochemistry - I'm now pretty well known internationally as an expert on fungal infections! I've never completely lost interest in spirolaterals, however (to be honest, I'm more proud of those figures than of any of my other possible achievements). I have occasionally given talks on them at the schools my children have attended, and made a Powerpoint explanatory file and Excel-based (not bug free!) program for generating the figures, which I hand out on CD-ROM to folks who show interest. What you have done with spirolateral art is impressive, amazing and very beautiful. It is indescribably rewarding to see a concept that started life as a doodle become the basis for such magnificent figures. I hope you don't mind my touching base with you. Kind regards.
Frank C. Odds, PhD, FRCPath
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