World of Fractals - Beauty of Recursion

In my computer programming adventures I tried many things.  Among them I've explored  iteration and recursion.

Iteration is simpler, because it's basically just a For loop used in all common languages. It handles a number of steps consecutively.  You go up or down, step by step, until you reach the top or the bottom.

Recursion is much more convoluted.  It's a way of thinking and solving problems, because there is more then iteration to it.  Steps are also repeated here, but you reduce the problem to a smaller tasks and handle them separately;  sort of divide-and-conquer strategy involving inheritance.  You define the value of your function, which has more than one variable, by using other values of the same function, i.e. you change only one variable and keep all others constant, until some endpoint is reached, and then change something else, reach another endpoint, and so forth.

Recursive algorithms take many forms.  It's the beauty of math, really, which shows up in many of those algorithms.  One example of recursion is fractals.  The whole art of fractals evolved in recent years.  Have a look at its beauty e.g. at this website.

I've just touched the recursion issue many years ago.  Sometimes it took several hours of my computer time to produce a complex picture, but it was quite satisfying to see the algorithm at work.

Here are some examples of what I was able to create in early 1990s. No special software.... All done using just Excel VBA procedures.