The floor is a 2D feature space (two made-up measurements, plotted as X and Z). Every small sphere is a labelled training example — green for Class A, orange for Class B — scattered along two interleaving crescents that a straight line could never separate. A decision tree learns a sequence of "is this feature above or below a threshold?" questions that slice this space into rectangles, one class prediction per rectangle.
Leo Breiman formalized random forests in 2001, but the core idea — bootstrap aggregating ("bagging") many high-variance models to cancel out their individual errors — dates back to his 1996 bagging paper. A forest of trees that individually overfit can still generalize well, because their mistakes are mostly uncorrelated.
A 2D feature space rendered as a 3D meadow, carved into class-colored regions by a decision tree — or smoothed into a stable boundary by a growing forest of trees standing beside it.
Each rectangle on the floor is a real leaf of the trained tree, split by whichever feature and threshold most reduces class impurity. Deeper trees carve smaller, jagged, overfit shards; a forest of bootstrap-resampled trees averages its votes into a smoother, more reliable boundary.
Switch between a single tree and a random forest, raise the max depth to watch overfitting appear, grow the number of trees to watch the boundary smooth out, and adjust label noise to see how much harder overlapping classes are to separate.
Random forests work because each tree, trained on a different bootstrap sample with randomized splits, makes largely uncorrelated errors — averaging cancels out the noise even though every individual tree still overfits its own sample.