The Mandelbrot set in a certain sense is a **** of a dream I had and an uncle of mine had since I was about 20. I was a student of mathematics, but not happy with mathematics that I was taught in France. Therefore, looking for other topics, an uncle of mine, who was a very well-known pure mathematician, wanted me to study a certain theory which was then many years old, 30 years old or something, but had in a way stopped developing. When he was young he had tried to get this theory out of a rut and he didn’t succeed, nobody succeeded. So, there was a case of two men, Julia, a teacher of mine, and Fatu, who had died, had a very good year in 1910 and then nothing was happening. My uncle was telling me, if you look at that, if you find something new, it would be a wonderful thing because I couldn’t – nobody could.
I looked at it and found it too difficult. I just could see nothing I could do. Then over the years, I put that a bit in the back of my mind until one day I read an obituary. It is an interesting story that I was motivated by an obituary, an obituary of a great man named Poincaré, and in that obituary this question was raised again. At that time, I had a computer and I had become quite an expert in the use of the computer for mathematics, for physics, and for many sciences. So, I decided, perhaps the time has come to please my uncle; 35 years later, or something. To please my uncle and do what my uncle had been pushing me to do so strongly.
But I approached this topic in a very different fashion than my uncle. My uncle was trying to think of something, a new idea, a new problem, a new way of developing the theory of Fatu and Julia. I did something else. I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics. I was at IBM, I had the run of computers which then were called very big and powerful, but in fact were less powerful than a handheld machine today. But I had them and I could make the experiments. The conditions were very, very difficult, but I knew how to look at pictures. In fact, the reason I did not go into pure mathematics earlier was that I was dominated by visual. I tried to combine the visual beauty and the mathematics.