Pulp Librarian
Complex numbers are based on the number i, defined as the square root of -1. Now this square root doesn’t actually exist, but 16th Century Italian mathematicians discovered that if you *pretend* it exists you can solve some quite complex equations. Which is fun. Better still you can create a two-dimensional space – the complex plane – that has real numbers along the x axis and imaginary numbers (computed using i) on the y axis. Any point on the plane represents a complex number, i.e. it has a real and an imaginary component to it. You can use complex numbers in a number of formulae; if you feed the answer back into the formula and repeat many thousands of times you’ll get a range of answers (including infinite ones – ignore them!) which you can map onto the complex plane. Benoît Mandelbrot used IBM computers to work on the simplest of complex equations: Z goes to Z squared plus C (where Z is a complex number and C a complex constant). He ran this several thousand times, feeding the result back into the equation. Then he mapped it on the complex plane. The result, first visualised on 1 March 1980, was a bug-shaped image. But at the edges the patterns seem to be repeated, they were more complex and seemingly never-ending. The more cycles of the equation you ran, the more of this detail you revealed.