The picture shown above is an image given by the Mandelbrot equation z_{n+1 }= z_{n}^{2} + p and is similar to what Benoit Mandelbrot showed the mathematics world in 1980. The old black and white image vividly reveals a simple but probably the most important fact about the M set (Mandelbrot set): The pattern in a neighborhood of a point outside of the M set grows more and more complex without bound as the point gets nearer the boundary of the M set.
In fact, the M set conceals infinitely many intricate fractal patterns near its boundary. We show several of them here painted by the "true color" technology that became available in the 1990s.
