Robert Spann
The behavior of dynamic systems -- be they mathematical, physical, or
financial—fascinates me. Where do they end up and how do they get
there? Do they reach an equilibrium or do they continue moving
randomly forever? Computer graphics allows one to see both the
numerical and aesthetic properties of these systems. For some time, I
have been interested in rational polynomials in the complex plane. I
have been exploring their mathematical properties and using those
properties to design images.
Sand Dollar is also produced by iterating the function
$f(z)=z^2/w(1-z^4)$ twice with $w=-.5i$. Similarly, I compute
$arg(z_{f})$ and use these values to color the image. The
differences between the two images result from using three colors
in Sand Dollar and nine colors in Chariot Wheel. In addition, I
apply a pixelation filter from Photoshop to Sand Dollar to create
the grain effect in that image.
Chariot Wheel is produced by iterating the function
$f(z)=z^2/w(1-z^4)$ twice with $w=-.5i$. This function has no
attracting fixed or periodic points other than a super attracting
fixed point at the origin. It does have the property that $f(z) =
f(-z)$. As such, it can be used to produce images that are
symmetric with respect to a 180 degree rotation. Letting $z_{f}$
be the value of $f(z)$ after two iterations, I compute
$arg(z_{f})$ and use these values to color the image. I use
commercial software (Circle Crop) to crop the image from a square
to a circle.