
Unity Fractal Type

formulas: unity


This Peterson variation began with curiosity about other "Newton-style"
approximation processes. A simple one,

   One = (x * x) + (y * y); y = (2 - One) * x;   x = (2 - One) * y

produces the fractal called Unity.

One of its interesting features is the "ghost lines." The iteration loop
bails out when it reaches the number 1 to within the resolution of a
screen pixel. When you zoom a section of the image, the bailout criterion
is adjusted, causing some lines to become thinner and others thicker.

Only one line in Unity that forms a perfect circle: the one at a radius of
1 from the origin. This line is actually infinitely thin. Zooming on it
reveals only a thinner line, up (down?) to the limit of accuracy for the
algorithm. The same thing happens with other lines in the fractal, such as
those around |x| = |y| = (1/2)^(1/2) = .7071

Try some other tortuous approximations using the 'test' stub and let us know
what you come up with!

