Infinite Barnsley Fern Iterated System

This simulator runs the real Barnsley fern chaos game: four affine transformations with their true probabilities (0.01, 0.85, 0.07, 0.07) are applied to a single wandering point, one randomly chosen map per step, and every resulting position is plotted. There is no drawn outline anywhere — the frond shape you see is entirely an emergent statistical pattern, the attractor that this random process converges to no matter where it starts. Points are held in a fixed-size instanced buffer that keeps overwriting itself once full, so the fern regrows forever rather than settling into a static image. Adjust the iteration rate, point size and the stem transform's probability to see how each piece of the system shapes the final form.