Home: Vignettes: The First Friday Fractal
I’ve found many images in fractals which are reminiscent of forms in nature. Both the precise mathematical displays and the delicate shapes of life have an essence of intricate beauty, provoking strong feelings of awe—especially when they are strikingly similar.
Each week, I’d like to share one of these comparisons, along with some of the science behind the beauty. If you’re the puzzle-loving type, take a good look at the fractal, and try to guess the following image before clicking before the fold.
For the first Friday Fractal image, here is a section taken from the Mandelbrot set:
And its corresponding form in nature:
An ammonite fossil, Discoscaphites conradi, from the upper Cretaceous age, found in the Pierre Shale Formation here in Colorado.
This animal lived somewhere between 100 million and 65 million years ago, when the dinosaurs went extinct. Ammonites went extinct at that time, as well. Ammonites were cephalopods, distantly related to the Nautilus, which shares the distinct spiral formation, but even more closely related to the modern squid and octopus.
The average daily life for this ammonite probably consisted of swimming through the ocean, grabbing fish with tentacles for an occasional snack. Ammonites were sometimes snacks, themselves, as they shared the oceans with a variety of carnivorous reptiles.
Ray Troll, an artist who has received some recent recognition for his Tiktaalik images, depicted the life of ammonites in this gorgeous poster (available for purchase here.)
The inner chambers of the ammonite are called camerae, collectively, the phragmocone. The largest camera contained the body of the animal; other camerae were previously occupied, and left vacant as the creature grew. (Kind of like Walmart, eh?) The chambers of the ammonite helped control propulsion—water could be pumped out of a chamber through a thin tube called a sipuncle. This affected the buoyancy of the creature, allowing it to rise and lower through the water. The Nautilus today propels itself in the same fashion, with the sipuncle in a slightly different location.
Ammonites can be found in jewelry today—their iridescent shells, like pearls, were formed from the mineral aragonite, (CaCO3) a form of calcite that forms pseudohexagonal crystals. (I like to call it “Tolkien stone.”) When some ammonite fossils were formed, the aragonite in the shell was preserved. This remaining mineral is a rare organic gemstone called ammolite. Ammolite typically contains trace impurities which give the stone a colorful, iridescent glow. When combined with the elegant spiral of the shell, the beauty of ammolite is unsurpassed.