Diving into the Mandelbrot Set - 1:

The Mandelbrot set can be defined as the set of all points c in the complex plane for which the sequence

c -> c² + c -> (c² + c)² + c -> . . .

is bounded. This set has strange properties that are only partly understood. As we dive into the set, we see smaller Mandelbrot worlds unfolding before us. Little buds seem to grow, but we pass them by on our way closer and closer to the infinitely convoluted edge of the set. Finally, we reach the limits of computation -- the computer image loses its detail at the end, although the true Mandelbrot set has ongoing complexity at smaller and smaller scales.