creative coding

Here is a representation of some rational points on the projective plane. More precisely, the first cursor provides a value $B$ for the bound on the height

where $(x,y,z)\in {\mathbf{Z}}_{\mathrm{prim}}^3$ and we randomly and uniformly pick a certain number of points of height at most $B$. You can make this number of points vary with the third cursor.

The second cursor controls a certain value $B_{\mathrm{small}}⩽B$ and the script plots in red the points of height at most $B_{\mathrm{small}}$.

This script is inspired by E.Peyre’s beautiful illustrations.

You will find here a similar figure for the 3-dimensional projective space.