a mapping carrying the upper complex half plane conformally into the interior of an equilateral triangle

From the 2023 Maple Conference Art Gallery

The picture shows the image of a grating in the upper half plane under this Schwarz-Christoffel mapping.
We note that all grid lines meet at 90°. (They met at 90° in the upper half-plane and conformal mappings
preserve angles.) The tear-drop pattern at the top is caused by the image of the uppermost grid line
(parallel to the real axis but with a large imaginary value). It can be shown that the radius of curvature
at the bottom of this tear-drop is asymptotically equal to one quarter of the remaining distance to the
apex of the triangle. The vertical grid lines near the imaginary axis squeeze together proportionally to
the fourth power of the remaining distance to the apex, making the central spike.

Full write-up https://www.maplesoft.com/mapleconference/2023/art/PDFs/MCAG23-Ross-Triangle.pdf