Friday Fractal VI

When I joined the crew here at ScienceBlogs, I was given a pledge name: Fractal. Now, you can see why: I'm in love with fractals. As a close friend of mine put it, a fractal is essentially "a tangent off on a tangent off on a tangent off on a tangent...," which described me rather well. It describes nature rather well, too. In living beings or solid rock, there are often many layers of complexity, each reliant on other layers.

I used this idea with today's fractal, by layering two separate Julia sets on top of one another. In the upper set, I used a formula which masked certain areas, determined by their distance from the calculated points. This lent well to the black spots you see below. In the lower set, I used the typical Julia set formula, but applied a transformation that trapped the patterns into polygonal shapes. (You can see the repetition of forms in the full set above.) Here's the result:

Now, while you may have already guessed the following photo, similar to the fractal above, I must warn you--nature can be a bit surprising:

The ladybugs, collectively known as the family Coccinellidae, aren't really bugs at all--they're beetles. In fact, most biologists prefer the term "lady beetle." Thanks to its bright colors and round shapes, this is one of the most well-loved arthopods known to humankind. Still, this lady is no lady. While gardeners usually know of the predacious tendencies of the lady beetle, few know that they can also be cannibals. Of course, many things in the animal kingdom will eat each other, or even eat their own young, but there's something about the cuteness of the lady beetle that makes it shocking.

The lady beetle I caught landing on my gneiss was introduced from Europe as organic pest control. They're rather common these days, hunting aphids across North America.
Of course, this doesn't mean that species native to America act like proper ladies. Not only are they as vicious as their European cousins, but they have large orgies as well. Convergent lady beetles(Hippodamia convergens) hibernate en masse, deep in canyons or on cool mountainsides--wherever they can find. (Sometimes, they simply find someones nice air-conditioned house.) Then, in the spring, millions of lady beetles awake and mate.

If you should happen to want a mass of horny, violent beetles (albeit, cute ones) for your garden, H. convergens are available online, from places such as this, but I would recommend finding local options. In 2001, John J. Obrycki and his colleagues compared groups of H. convergens from various corners of the Americas: Honduras, California, and Iowa. They discovered that while the groups could easily reproduce with one another, they showed considerable genetic variation. So, while, phenotypically, the lady beetles appeared to be the same species, their DNA was suggestive of increasing distinctiveness. By flying lady beetles across the continent and introducing them into our local gardens, we may be spoiling their shot at speciation.

Not only that, local lady beetles are probably the best for the job. Obrycki found that while the offspring of H. convergens crosses were successful predators of the aphid A. pisum, they were not necessarily suited to the local environment. In the end, he suggested such introductions weren't worth the trouble:

The observed interbreeding among California, Honduras, and Iowa beetles, in addition to the presence of parasitoids and pathogens in California adults, combined with the lack of substantial evidence of effectiveness,
suggest that the practice of augmentative releases of field collected H. convergens needs to be carefully examined for non-target effects.

Of course, if local lady beetles are tough to find, you could always try attracting them with gneiss... it worked for me.

A gneiss note: The rusty slabs in the photo above are microcline, a type of feldspar, while the white crystals are milky quartz, one of the most common forms of rock on earth. The rock was formed as magma hardened under the surface, then subjected to heat and pressure before being exposed by erosion in the doubly-uplifted Rocky Mountains.

Other notes: Photo of H. convergens converging via Arizona Highways. All other photographs taken by the author. All fractals were created by the author using ChaosPro.