Infinite Beauty

My post on perfect numbers generated some interesting discussion, so at the risk of being labelled a geek again, I thought I would continue for one more post on the amazing beauty and infinate detail that exists in God's creation, not just in the details without (the vastness of the Cosmos) but also the infinite details within, and in particular in numbers. What's so beautiful about numbers, I hear you say? How can a number have infinate detail?

Consider the snowflake; though it is tiny, it has beautiful detail, and were you to magnify these details, you would see just as much beauty on the finer details that exist upon these details. There are details on details, and further details on these details, right the way down to the atomic level. Not quite infinate detail, but these types of shapes are known as fractals, and can be represented by mathematical equations which do indeed, theoretically at least, have infinate detail. There is as much beauty and detail, no matter how much you zoom in: infinity enclosed within a finite space. Incredible!

One of the simplest of these mathematical equations (Z_n+1 = Z_n² + C) is also one of the most beautiful. It's called the Mandelbot Set, after its discoverer, but the infinate beauty of this equation was crafted by God, just waiting for man to discover it.

Here's another Java Applet I wrote so you can try it out for yourself:





To explore the infinite (within the limits of the computer's arithmetic) detail in this fractal, drag a box around the area you wish to explore and then click in this box. You can repeat this as often as you like, increasing the magnification each time. When the screen stays blank, your computer has run out of decimal places to perform the calculations . Press the 'Reset' button and start again!