Friday Fractal LVII: A Tribute to Aphrodite

How do you mimic a classic rendition of mollusk, sea, naked flesh, and love with a computer? Stop... I know what you’re thinking. I suppose there are some sites out there that specialize in such a thing, but today, we’re just going to stick with fractals. Oh, don’t look so disappointed. What if I throw in a little 4D action? (We’ll get to the raging sea part in a bit.)

If you look at the fractal below, you’ll see one of my layered fractals. If you casually ignore the morphed Julia set in the background, you’ll notice an odd shape in the middle. This unique form is called a quaternion, a fractal I don’t attempt to use very often. They’re a little awkward to draw. See, most fractals are defined by a single pair of complex numbers (each also defined by a pair of numbers and an imaginary part: a+bi) which are used as the x and y parameters in a given formula. A quaternion, in contrast, is defined by four complex numbers. So you have an x and a y, plus another z and... shoot, we’re out of letters, lets say "q". The fractal object defined by all these complex numbers would have enough sides to be considered a 4D object. Since our screens can only display 2D objects, however, we have to draw the object from a number of angles to get a sense of what we are looking at. Using the coloring formulas to create a sense of light and shadow, a 4D object is displayed as a 3Dish strange object.

I have very little practice with these, so I had to be satisfied with an abstract look. As strange as it is, the rippled, twisting effect was just what I was looking for. It reminds me of flowing fabric, perhaps one disguising a gentle metamorphosis.

Chaos Rising: An Abstract Fractal

It may not be recognizable, but this is my fractal tribute to Sandro Botticelli’s iconic painting:

Venus Rising by Sandro Botechelli

I’ve wondered if this painting looked so kitschy when it was originally painted. It certainly is now. It’s a fun sort of kitsch, at least. Perhaps the way this image has been portrayed in those surreal holes of our pop culture. I can’t look at the painting without thinking of this scene with Uma Thurman in Terry Gilliam’s The Adventures of Baron Munchausen:

Or maybe it isn’t that Monty-Pythonesqe joviality that does it. Perhaps Venus herself was kitschy even before Botticelli. After all, we are talking about the Goddess of Love. Venus, or Aphrodite, if we go by her Greek name, was the icon of romance in her day, despite a few, er, shall we say, scandals.

She had numerous lovers, including a number of the gods on Olympus, and a mortal born of questionable circumstances. (That is to say, Aphrodite bribed a young lady to sleep with her father, who happened to be the King of Assyria. From that incestuous encounter came Adonis. He wasn’t around long before other Goddesses tried to steal him away, and finally Ares (one of the gods she’d been seeing) killed him in a jealous rage. While Aphrodite might sound a bit promiscuous, it may be that Zeus married her off to Hephaestus, the grouchy god of smithing. Hephaestus was about as jealous as Ares, however (as proves by the rest of the scene from The Adventures of Baron Munchausen) and didn’t prove to be much company.

Aphrodite amused herself by causing, or to be fair, helping others fall in love. This includes a statue that she brought to life for one lonely lad. (Remember Mannequin?) Then, of course, there was that incident, where fueled by an apple casually tossed by Chaos, she threatens, I mean, helps Helen to fall in love with her enemy, the King of Troy. Look at the mess that caused. (Homer wrote a book about it. No, not Simpson, Iliad.)

So, where did all this scandalous behavior originate? We could examine her genetics... if we could be certain what they were. The circumstances behind her birth are somewhat questionable. The best record we have comes from Hesiod, who wrote the sort of Who’s Who on Olympus, also known as the Theogony. According to Hesiod, the story begins with Earth, who was very upset with the children she’d recently borne. (The ungrateful, careless brats were just tearing the place up.) She had another son, Chronos, who always had some spare time, to take action against her husband, Heaven. Proudly, he swore to take revenge, saying "Mother, I will undertake to do this deed, for I reverence not our father of evil name, for he first thought of doing shameful things." And so he hid out till his father returned. I’ll let Hesiod explain what happened next:

And Heaven came, bringing on night and longing for love, and he lay about Earth spreading himself full upon her. Then the son from his ambush stretched forth his left hand and in his right took the great long sickle with jagged teeth, and swiftly lopped off his own father’s members and cast them away to fall behind him.

Er... that’s right. He basically flung Heaven’s penis in the sea.

And so soon as he had cut off the members with flint and cast them from the land into the surging sea, they were swept away over the main a long time: and a white foam spread around them from the immortal flesh, and in it there grew a maiden.

And well, from the sea and foam, rose Aphrodite... Talk about a metamorphosis. Think Botticelli got the look just right?

Image of Bottecelli’s Venus Rising via the Art 1 Projects page at Henrico County Public Schools. Fractal by the author using ChaosPro.