The Graceful Goodies flow Markov chains

The owners keep reacting to one week's sales — 80% truffles last week, panic production, 30% this week. What they actually need is the flow: given what a customer bought last, what do they buy next? Put your class survey's own percentages into the table below — every cell starts at 0.25, which is a guess and nothing more — then step the mix forward and watch where it settles.

Your survey, as a matrix

Row = what they bought last. Column = what they buy next. Each row must total 1.00, because a customer buys something. Nothing is corrected for you.

The starting mix v⁰ — a row vector. This one must total 1.00 too.

Step it forward

Each circle is a candy; its size is the share of customers buying it right now. Each arc carries the probability of moving that way.

oldernow

One bar per week, oldest at the top and palest. Left to right inside a bar, the four candies always sit in the same order; the numbers under the newest bar are the current shares.

t = 0

Try: run it once with every cell still at 0.25, then type your survey's real numbers and run it again. Then start somewhere else entirely and run it a third time.