Chaotic Utopia

Friday Fractal VIII

i-cbf9f092c3bd549fcff1cd6db8b116e3-swfwhole.jpgWhile crawling across the web this week, these stories of spiders just seemed to stick. So, when it came to making today’s fractal, I knew exactly where to turn. The shape seen at right is an example of a “loom” style fractal, originally described by Cliff Pickover in his book, the Keys to Infinity. He calls it a mygalomorph pattern (sounds like something from King of the Hill, doesn’t it?) or “Interactive Spider Geometry.”

His webpage, found here, provides a simple java applet for exploring the various shapes. (Read: fun little web toy.) He also explains the math behind the image with a cute and simple parable. (“One day, a rather intelligent Mygalomorph let a straight web piece amble around the circumference of the circle…”) Well, I took one of these mygalomorphs, sandwiched it between a layer of fractal Brownian motion noise and a couple of cropped-up Julia sets, and came out with this…


…which looks eerily like this photograph from today’s issue of Science:


An araneoid spider, Argiope trifasciata, in Palo Alto, Calif. (By Mark Chappell for Science)

Of course, the news this week hasn’t been so much about spiders, so much as their webs. Scientists this week revealed the a fossil of the world’s oldest web, new light on the evolution of webs, and advancements in web-silk-based nanomaterials.

First, we’ll look at the origins of the web-spinning abilities of the araneoid spiders (like the one shown above) and deinopoid spiders, highlighted in today’s issue of Science. (Click the link to view the abstract, the full article, unfortunately, requires a subscription.) Biologists used to assume that the two types of orb-weaving spiders were different enough to have evolved their similarities separately:

Araneoid and deinopoid orb weavers use nearly identical behavioral sequences and spinning apparatuses to produce architecturally similar webs. However, there are notable differences between the adhesive mechanisms of capture spirals spun by araneoids (aqueous glue) and deinopoids (dry fibrils) (2). Thus, the two types of orb webs were widely considered a dramatic example of convergent evolution (3).

Now they’re rethinking this. Following a trail of genes, all the way back to the Cretaceous age, Enrique Penalver of the American Museum of Natural History and his colleagues discovered the two spider groups shared a common origin:

The collective combination of Flag, MiSp, MaSp1, and MaSp2 in araneoid and deinopoid spiders implies that the orbicularian ancestor was equipped with the molecular elements necessary for orb-web construction. Based on fossil evidence, this ancestor minimally dates from the Lower Cretaceous, 136 million years ago (7).

This cool tree shows just how:


Deinopoid (purple) and araneoid (green) lineages (2), depicting inferred ancestral web and spidroins. Orb-web frame and radii composed of MaSp1 (blue) and MaSp2 (brown) are shown along with temporary spiral with MiSp (black) and capture spiral with Flag (red). (Peñalver’s description.)

i-6694034071cecfd0f0bc7a7728f5d0be-amber.jpgIn the same issue of Science, we find this piece of amber, containing the most ancient web ever found:

Reported here is an exceptional situation of insects trapped in part of a gummy aerial web preserved in a runnel of amber from Spain that is ~110 million years old (Early Cretaceous). This is the oldest direct evidence of a spider web made by Araneoidea and of its use for predation. Thus, the interception of flying insects by spiders has a minimum age coinciding with the explosive diversification of the angiosperms and of major pollinating groups of insects.

The article (which requires a subscription to view as well) goes into the gorey details of the various insects trapped inside, and the sizes of the spider silk. The best part, however, is the image of the amber itself, which is available for free here.

As if this isn’t enough web news to capture your attention, Scientific American reported this week on new innovations in bone replacement growth, using (you guessed it) spider webs. Combining the spider silk with the silica gives scientists the flexibility and strength they need:

Researchers have created a novel nanomaterial that combines the strength of spider silk with the rigidity of silica. The product could help pave the way for the fabrication of replacement bones.
Regrowing bone requires a scaffold that is stiff, long-lasting and safe. With that in mind, David Kaplan of Tufts University and his colleagues decided to marry the protein that constitutes the drag lines of golden silk orb weaver spiders with the protein that helps diatoms–a subset of plankton–make silica, a glasslike compound. The spider-silk protein alone “just doesn’t have the stiffness you want, that’s why you need the glass,” Kaplan says.

Since the spiders have a 110 million year head start on this structural engineering bit, it is nice to know we’re starting to catch up.

Image notes: Spider by Mark Chappell in Science, borrowed from the Boston Globe, Amber image by Penalver, et al, via Science,
web tree also from Science.
All fractals were designed by the author using ChaosPro.


  1. #1 Jack
    June 24, 2006

    This is really cool, I jsut found your blog, it looks mighty interesting!

  2. We need a proposal for internships progress. Because we can’t receive so many students for that. Maybe we will make a selection for that.