Fractals
chaoticutopia | June 23, 2006While 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…
chaoticutopia | June 16, 2006The phoenix is one of those enduring symbols from ancient mythology that occurs frequently in modern culture. Phoenix is a name for places and stars (Hollywood and constellations alike.) It shows up in movies and literature (including the Harry Potter series.) Most importantly (at least for the context used here) this name for a mighty bird, which perished in flame, is a type of fractal. A phoenix set seemed rather fitting for today's image, as we'll soon see.
This set (seen whole, at right) is a modification of the original phoenix sets, discovered byShigehiro Ushiki. Essentially, I began…
chaoticutopia | June 9, 2006When 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,…
sb admin | June 9, 2006With a click of your mouse, you find yourself in a chaotic utopia.
That click sent an electrical signal inside your computer,
passing through circuits, joined by a contact made of gold.
The gold, you may find, was mined from a mafic vein,
deep within the Rocky Mountains, surrounded by Precambrian gneiss.
The gneiss, disguised by the mountains for billions of years,
lays exposed to the north in a shaded canyon.
The canyon, still being carved by the creek below,
crumbles with age, loosening a piece of milky quartz.
The quartz, lured by gravity, tumbles from the canyon wall,
and lands with a…