Ambiguity: Fractal LXVI

Sorry for the delay, folks... I’ve been bogged down with homework this past week, and now have a sick kid on my hands. So, the Friday Fractal was bumped to Saturday, and then Sunday. I’ve said it before; I ought to just call these the "Weekend Fractals".

When two people see the same thing, do they necessarily have the same experience? This is a problem which troubles philosophers, particularly philosophers of science. I just finished writing a paper on the subject, comparing the views of several scholars. I won’t post it until it has been graded, but in the meantime, I’m still stuck thinking about the question. It was enough that I decided to title this week’s fractal "Ambiguity" and leave it up to you, the reader, to decide what it is supposed to look like. (In a way, I was aiming for the Georgia O’Keefe look, as many of her paintings are quite ambiguous.)

As you decide what you are looking at, ask yourself if the way you are seeing it is influenced by who you are--your memories, your favorite things, your specialties, etc. Does anyone simply see what it is--a plot of complex numbers? How about if I explain it in mathematical terms?

Bear with me for a moment... we’ll simply start with two complex numbers, "f" and "g", which will define the coordinates of a particular pixel. Then, we call the coordinates of the pixel "z". ("z" is another complex number, which has two parts, a real part and an imaginary part, which become the x and y on the complex plane.) Our complex numbers will relate to one another like this:

z=pixel
f=z
g=f

In order to decide which "z" does what, we drop all these variables into the following set of algorithms (which adds all the strange loops and shapes) and repeat until we’ve filled up the screen:

z=z+sin(e)*0.2-f^g
f=tanh(f)
g=asinh(z)

Finally, we set an ajustable parameter (the bailout) which basically defines a threshold at which the pixels will be colored--and in this case, doubles it. This looks like this:

return(|z|<bailout)

And that’s it. Voila, a fractal. But has the way you look at the fractal changed? Does it actually appear any different now? Now, let’s play with the bailout parameter, and see how it varies. We started with a value of 3; that’s what you see above. In this animation, we start at 3 and raise it to 3000, and then back:

So now, I’ll ask again... what did you see? Did you watch the video simply in terms of mathematic expressions--which it is? Or was it still influenced by your previous knowledge, and your appreciation for aesthetics?

Fractal created by the author using ChaosPro.