Preset
Inversion — 1/z
lines → circles through origin
Cayley — (z−i)/(z+i)
upper half-plane → unit disk
Disk Map — (z−½)/(1−½z)
automorphism of unit disk
Rotation — e^(iπ/4)z
45° rotation, no fixed pts in ℂ
Parabolic — (3z−2)/(2z−1)
one fixed point, pole at z=½
Loxodromic — (2+i)z+1)/(z+1)
spiral: rotation + dilation
Morph t
0.00
▶ Animate
⊞ Source
● Fixed pts
○ Circles
Every circle (and line) maps
to a circle or straight line.
● Gold: fixed points f(z) = z.
× Magenta: pole → ∞.
a =
0+0i
b =
1+0i
c =
1+0i
d =
0+0i
Type:
—
t =
0.00
f(z) = (az + b) / (cz + d)
Space
— animate / pause
S
— toggle source grid
F
— toggle fixed points