A remarkably large number of artists had no vocabulary to express their grasp of the nature of fractals, yet such an understanding comes through very clearly in their work.

By doing ‘one’s best’, one can do amazing things. I have a thousand plans at the same time. My extremely complicated life has allowed two choices. One consists in setting priorities, staying committed to them, and doing everything possible to ensure that things are realized, in the order of priorities. The alternative policy judges, according to the circumstances, what is feasible and what is not, and then improvises with the means at one’s disposal at a given moment… I did not give a thought to seeking perfect, optimal conditions for seeing a plan through. I always concentrated on doing ‘sufficiently well’ here and now.

A primitive man or woman sees very few, simple, smooth shapes. For example, the full moon is a simple shape, a circle. The pupil and the iris of the eye are circles. Some berries are spherical. But in the wild, almost all the shapes are extremely rough and complicated; there is a sharp distinction between the smooth/simple and the rough/complicated. Historically, geometers concentrated on the properties of a very few smooth shapes and physicists were also significantly devoted to smooth, regular behavior, with perhaps sometimes a complication of the kind that the French mathematician René Thom theorises as “catastrophe”. But trees are not smooth at all, neither are mountains and clouds.

I have very strong connections with composers, who inhabit an entirely different world. In particular, György Ligeti came to me and confided that, until he saw my pictures, he had not understood an important aspect of music: it is not free to do as it pleases, because it must be fractal…