Beauty in the Math - Fractals #2

Hi again.

I’m continuing on from my previous post to talk more about fractals.
My very first attempts at fractal art were on a Commodore 64 computer.
With a CPU speed of around 1 MHz, some of the calculations were, to say the least, time consuming. Even now with PC’s running at GHz speeds, some fractals I have created still take hours to render/draw. The reason for this is not just the equations themselves but the magnification to which the equations are subjected. The fractals have minute detail which you can zoom in on. If it was a digital photo, you can zoom in to some extent but you eventually get to the point where you are just expanding pixels and getting a “blocky” image. With fractals you can rerun the equation on a selected area to expand the fine detail as much as you like. Essentially you are only limited by your computer’s processing power… although it’s a little more complicated than that.

Here are a few examples of zooming in.

I could have kept going but in this case the detail started to get repetitive. This is not always the case. Sometimes I have found amazing and unexpected detail by zooming in to the limits of my PC’s computing power. This one for example …..

Maybe you don’t find this one particularly appealing but I love it.
I always find it interesting how different people’s tastes can be. I have many fractal images that I don’t personally like and yet other people do. My wife often comments on how some of the ones I like are "Too out there!" Thanks Honey!
(Although she does like the one above.)

Bye for now.
Richard