This grasshopper example by Petras Vestartas is useful for someone who wants to start studying reciprocal patterns.

In this grasshopper definition by Martyn Hogg,  you can model a weaving basket. You can select number of weaves in X or Y directions for a flat surface. Similarly, U and V divisions on a curved surface. It also works on a loft through curves.

In this grasshopper definition by Laurent DELRIEU you can model a symetric loxodrome on a sphere. It simply can be done in any revolution object. Laurent used equations from a wikipedia page.

In this grasshopper definition by Junichiro Horikawa you can model an undulant portrait using Image Sampler.

This grasshopper example by Tuğrul Yazar is a Cycloid-like family of curves, generated by its classical description: a rolling circle. There’s no need to roll the circle but divide its path, utilizing data lists to simply rotate and evaluate it.

The Mesh Color definition by  Curvature applies a vertex color based on the average or upper value of the angles between adjacent faces.

In this grasshopper definition by Junichiro Horikawa you can model a triangular 3D pattern.