Conformal map graphics

Images of concentric circles around the origin

Images of concentric circles of radii between and around the origin under the (conformal) map . The curves of small radii concentrate around the point .

Images of the Riemann sphere of concentric circles of radii between and around the origin under the (conformal) map . The curves of small radii concentrate around the point on the equator.

Images in the ‐plane of concentric circles of radii between and around the origin under the (conformal) map . The curves of small radius concentrate around the point .

Images of radial rays originating from the origin

Images of rays from the origin under the (conformal) map .

Images on the Riemann sphere of rays from the origin under the (conformal) map .

Images of a square grid

Images of a square grid of size under the (conformal) map . The two accumulation points of curves are the points .

Images of the tessellated Riemann sphere

Images of triangles on the Riemann sphere under the (conformal) map .

Plane to plane map

Curves parametrized by . Points (where ) move smoothly into points .