Getting Airborne

By rising up off the ground, we can get a much better view of the surrounding landscape. From this vantage point, a calm blue river is visible, the vegetation-covered hills are all around and, in the distance, some snow dusted on the higher peaks. It's an overcast day, but still plenty of light to enjoy the view (see thumbnail picture at right). The air is brisk, yet invigorating. Anyone care to guess where on Earth this scene is located?

Fractal IslandsWhile you are thinking about it, let's move off the coast to check out some islands. With a little more altitude, and looking straight down, we can see the entirety of several islands in an archipelago, surrounded by crystal clear blue water (see picture at left). In this climate, the vegetation doesn't grow too tall, but the beach areas are clearly defined and the coastlines vividly displayed. Were you to descend to ground level and look into the water, you could see the submerged rock formations quite clearly. I'd suggest a light coat or sweater if you choose to walk along one of these beaches! Still don't know what part of the world is depicted in these images?

Fractal snow valleyNow, let's zoom up to those snow-dusted peaks and see what we can see there. Bundle up because the temps are quite nippy, plus you'll find a strong breeze in those mountain canyons as well. Bring along a thermos full of hot tea or other warming drink because you'll need it.

Now that we're here, I see there's more snow than was apparent from our first distant view near the river. I'm guessing more than a foot in the valley there (see picture at right). Let's just stay here inside our craft where it is warm because I don't think we brought the right gear to go walking around down there! I've been here before, so I can tell you there are a lot of hidden canyons and interesting places down there to explore. Unfortunately, we don't have the time right now to look around more thoroughly. Wait, did I just see a deer duck behind the foliage there near the snow line? I wonder if you are ready to guess where we are now.

An Unexpected Surprise

OK, ready to move on now? Then I'll just . . .what, you say? What's that button with a face that looks like a gambling die? It's for . . . No, don't push it! Stop . . .oh, well, now you've done it. (A flash of light and a deep humming noise, then silence.) No, I can't tell you where we've ended up. Just don't try opening the door and getting out. I don't think there is any breathable air out there. So let's hope we can find our way back home. . .

Unknown moon and planetIn case you haven't guessed already, every image in this article is an example of what fractalic computations can produce. Everything from clouds to snow, mountains, valleys, islands, coastlines, even outer space planets and a moon, are all possible with the right fractalic formulae. It's been my pleasure to share with you this brief journey into the wondrous world of fractal geometry and the expression of that geometry in natural forms.

Image Credit: LariAnn Garner

(Editor's Note: This article was originally published on December 17, 2008. Your comments are welcome, but please be aware that authors of previously published articles may not be able to promptly respond to new questions or comments.)