This Demonstration shows the repeated subdivision of a triangle.
The barycenter of the triangle is determined using the classical dot product between the masses and the vectors of their positions:
The division into six triangles is done by using the barycenter as the common vertex and dividing the three edges according to the divider ratios .
A multitude of shapes can be achieved by iterating this process times and moving the sliders. This way, one creates triangles. The barycenter of each triangle can be moved by dragging the locators and varying the weight sliders. The shape of the triangles can be altered with the three divider sliders. Starting with a symmetric initial triangle gives a more balanced end result.