Remove the central third of each side and replace it with two sides of an equilateral triangle pointing out of the original triangle. Repeat this process on all sides of the new figure. Repeat this process forever. The shape you have generated is the von Koch snowflake. The von Koch snowflake is an example of a fractal.
Fractals are a good example of convergent infinite processes.
Top Convergence is an important mathematical idea. Convergent sequences may enable us to approximate answers to calculations which would otherwise be very difficult if not impossible. Mathematicians through the ages have been using convergent iterative processes to solve problems.