Uploaded December 2025 | Updated September 2026, 1 hour ago
This animation, created using MATLAB, illustrates an iterative game. Start with an initial point. Then randomly select a vertex (from a uniform distribution) and consider the line segment from the current point (iterate) to the selected vertex. Given a specified proportion, p, (and its complement 1-p) select the next point (iterate) with weights p and 1-p. Repeat this process and watch a pattern emerge.
The question we close with is, "Does this happen for other regular polygons?"
This animation, created using MATLAB, illustrates an iterative game. Start with an initial point. Then randomly select a vertex (from a uniform distribution) and consider the line segment from the current point (iterate) to the selected vertex. Given a specified proportion, p, (and its complement 1-p) select the next point (iterate) with weights p and 1-p. Repeat this process and watch a pattern emerge.
The question we close with is, "Does this happen for other regular polygons?"
