2.22 Unity
(type=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 (p. 64) and
let us know what you come up with!