Why do random dots turn into a shape?
The chaos game fixes a few vertices and then repeats one move: from the current point, step a fixed ratio r of the way toward a randomly chosen vertex. The rule is new point = current point + r x (chosen vertex - current point), and with 3 vertices and r=0.5 the shape known as the Sierpinski triangle appears. You can use 3 to 8 vertices, any ratio between 0 and 1, and up to 20,000 points.
Plotting starts at the center of the frame, and the first 20 iterations are discarded so the starting spot leaves no trace. Every vertex is equally likely on each step, and the choice uses the browser random number generator. The results panel echoes the point count, the move ratio, the vertex count and the iteration rule actually applied.
This page reports no fractal dimension, because that figure is not confirmed by an authoritative source. Downloading the coordinates and editing colors or zoom are not supported. Browser random numbers are not cryptographically secure, so they must not drive legally binding or money-related draws, and the picture differs slightly on every run even with identical settings. Study use as of October 2026.
Frequently Asked Questions
The vertex is chosen with the browser random number generator, so the order and placement of the dots differ on every run. With many points the overall outline looks similar, but the exact picture never repeats.
No. This page only generates coordinates and draws them. Dimension values and area estimates are not confirmed by an authoritative source, so they are not shown.
Each point becomes its own shape element in the drawing, so the time grows with the count. On a phone it is easier to start near 3,000 points and raise the number from there.