George believed that his most original work lay in the future. He felt as if his own sensibility, that deep feeling of musical connection to the damndest things—which some people who had investigated his work called synesthesia—was growing in intensity, ripening and mellowing and expanding all the time. One organizing system that fascinated him, and he knew it would lead to at least one ambitious symphonic composition, was the way Fibonacci numbers and their forms are found in nature (although he was worried that art inspired by Fibonacci numbers had suddenly started appearing everywhere, a great deal of it fuzzy-headed and second-rate, which made him mistrust his own attraction to the form). There was also something that clicked about the proportions of the golden rectangle that called out to him, maybe just for one concise little concerto. Beyond that, in another year or two, once his understanding had deepened, the most exciting thing of all lay on the horizon—the infinity of possibilities in fractals and Sierpinski triangles. In a deeply significant way, as a competitive runner might look years ahead to an Olympic race, he felt that he was training, saving up, building up his abilities for this challenge.

Sierpinski triangles appealed to George especially because there was something exquisite about them and also because hardly anyone outside mathematics was messing around with them, as far as he could tell. They weren’t all the rage like Fibonacci numbers. Only one or two people seemed to be applying these calculations to music, and those individuals tended to be heavily into theory rather than composition. Did anyone care what music actually sounded like anymore? So much post-tonal composition. Too much.

And then there were the aleatory composers. George didn’t understand what drew them to music at all. They wrote a kind of music by a process of random selection, either by the composer or by the performer at the moment of performance. Every decision, including key, dynamics, tempo, sometimes even the order of the movements, depended on the outcome of thrown dice, drawn playing cards, or computed mathematical laws of chance. Some people called this “chance music” and compared some of George’s work to the best of the Boulez aleatory creations. But this was wrong—George left nothing to chance. And he found most of these contemporary compositions ugly and misshapen, devoid of musicality, music only by definition. Yet he was slotted into this category of new music just about every time his work was reviewed. It was rather discouraging to be so misunderstood; it was never a good sign when references to aleatory music crept into critical writing about a Botkin composition, as this tended to reveal the mind of an unpassionate critic whose head was too easily turned by theory, no matter what the music actually sounded like.

Which was not to say that theory didn’t interest George. Some new form or system would inevitably provide the starting point for something rich and strange. He was always searching for the next grain of sand to grow a pearl. Though found mostly in nature, once you know where to look for the forms (most ferns, the subcontinent of India), one way to locate a Sierpinski triangle is to play the “chaos game.” In this game, any three points are chosen on a plane. The points don’t have to be equidistant. Any point x may be chosen in the same plane, inside or outside the figure. With the roll of a die, a point is made halfway between x and the vertex indicated by the die. This process is repeated endlessly, each time from the most recent point. Although you might expect, after a while, to see a randomly dispersed field of points, what you see instead, inevitably, is a Sierpinski triangle.