I touched earlier on the aspect of self-similarity on smaller and smaller scales in fractals. I find the ones that are exactly the same on smaller and smaller scales a bit boring – like the Koch snowflake or the Sierpinski arrowhead or the Menger sponge (though it has a nice surprise). It’s the fractals that take on the slightly chaotic characteristics of nature that are the most interesting, and which stimulate the most thought about how this whole complex universe of ours developed.
The series I am presenting to you here does not really look like something you would find in nature, strictly speaking, (except for the parts that look like peacock feathers) but I thought it lent itself well to the illustration of self-similarity while emphasizing the variation. And because it already included elements of a human game, why not present it as a game?
The series is called “The Ball Went Over the Fence”.
Up until this point, you have probably looked at the fractal images on this site and you’ve detected the self-similarity, but what you maybe haven’t seen is what happens when you travel into a fractal. You can’t properly zoom in on a fractal without the equipment to do so – i.e., the software which allows you to make the fractal in the first place, or a video or .gif someone has prepared that takes you through it. When I say travel into a fractal, I mean precisely that – it resembles exploring a new realm. You enter the realm, you set your sights on a distant object, and when you get there, your surroundings have changed – you know you’re in the same realm, because it all looks familiar, but that which was tiny is now large and detailed, and you can see off into a new distance. You set your sights on that, and continue on your journey…. and you can keep doing this over and over again for a long time, depending on how many iterations of the formula you’ve rendered.
So I travelled into this fractal I created, and I stopped along the way and saved some images. The game is for you to try to figure out where I zoomed in to get to the next image. Give it a shot. In a couple of days, I’ll edit this post with the key at the end so you can have the answers. Hint 1: the orientation of the image doesn’t change. Hint 2: Some of these are a lot easier to find than others. Also, the first two images will open larger if you click on them, but the rest are locked at their size. (They are all scaled relative to their actual artwork size). The key at the end will open larger so you can see more clearly.
All images are watermarked and copyrighted.
If you are having trouble with the first two, try looking at #2 and #3, this is the easiest solution of all of them.
And now, as promised, the key to where the zooms took place – a map through the series: