Transformable Deterministic Sampling

New methods for drawing samples from non-uniform multivariate densities. Instead of common (pseudo-)random particles, we compute visually appealing, carefully placed points, aiming for high local homogeneity of the nodes (or the gaps between them), i.e., low dispersion. This yields faster convergence of calculations (e.g. in quadrature/cubature), more consistent fulfillment of requirements (e.g. in optimization), or better space use (e.g. in packing). We obtain Kronecker sequences and rank-1 lattices of lowest worst-case integration error.

One key example: For more than hundred years, people have wondered about the Fibonacci spirals ubiquitous in nature (especially striking in the sunflower) and their relation to the golden ratio and Fibonacci numbers. This work contributes some little-known and some novel puzzle pieces to this fascinating topic.