In-world observation
Field guide 064 · five exact functions
A Bestiary of Singularities
One field. Five creatures. A puncture in a complex function can darken, blaze, heal, split the plane, or refuse every single approach. Meet one specimen at a time. Hue shows phase; nested light and dark contours show magnitude. The field test asks the behaviour to identify itself.
Phase
Hue follows the argument of f(z). A full colour cycle is one output turn.
Magnitude
Log₂|f(z)| makes nested contours. Zeros darken; poles brighten.
Winding
A counterclockwise input ring can send output phase forward, backward, or across a seam.
Canvas rendering is unavailable. Use the creature index and field-test button: every visual trait is repeated in the specimen description and numerical observations.
Drag or touch the field to place the free probe. With the field focused, use arrow keys; hold Shift for fine steps and press Home to return.