This is a question about probability. The Galton box (or quincunx) uses the physical process of shot moving down a pin-board, to demonstrate central limit theorem, eg:
So I am interested in events with converging probabilities (like a coin toss @ 1/2, or card-guessing @ 1/5) and have found this matrix from a paper by E.G. Boring (Boring, E. G. (1941). Statistical frequencies as dynamic equilibria. Psychological Review, 48(4), 279):
And have a stackoverflow question plotting a related graphic in R:
If we think of the heatmap as depicting the shape of a gradient, it seems to me that it is possible to imagine a physical board that contains the same gradient, such that shot put on it would follow the same path.
So my question is, is there an equivalent of the Galton-box, that would allow a physical demonstration of this (and similar) Boring matrices?
Update: I have found this graphic of a quincunx which reminds me very much of the heatmap: