Category: Scientific Visualization

• Centroid Subdivision of a Triangle: A Simple Recursion Creating a Complex Pattern

  

  Michael Emmerich, 12 July 2025 1. Introduction A single, easily stated geometric rule—“draw the centroid of a triangle, connect it to the three vertices, and repeat recursively on the new sub-triangles”—produces a surprisingly intricate picture. This short exposition introduces the construction, shows how recursion drives the emergence of symmetry and complexity, and points out why…

  Michael Emmerich

  July 12, 2025

  Mathematical Playground, Scientific Visualization, Small Python Math Examples

  algorithms, fractal geometry, fractals, geometry, math, mathematics, python, recursion, space filling designs

• Multiobjective Heatmaps: Landscape Visualization via ε-Dominance

  Michael Emmerich, January 16th, 2025(inspired by a discussion of an application problem with Jonas Schwaab, ETH Zurich) In single-objective optimization, it is easy to visualize a function that depends on only two continuous or integer input variables by means of a heatmap plot, where the lightness indicates the achievement in the objective function, say F(x1,…

  Michael Emmerich

  January 16, 2025

  Computational Science, Multiobjective Optimization, Scientific Visualization

  data-science, Epsilon Dominance, math, Multiobjective Landscape, Multiobjective Multimodal Optimization, Nonlinear Multiobjective Optimization, python, Visualization