In 1953 at Los Alamos, Metropolis and colleagues found a way to explore a probability landscape you can only evaluate, never integrate: stand somewhere, propose a nearby step, compare the two heights, and accept the move with probability min(1, π(θ*)/π(θ)).
Only the ratio of heights appears — so the unknown normalizing constant cancels and never has to be computed. Your painted terrain is a raw, unnormalized posterior, and that is all the prospector ever needs.
The step size is everything. Too small and he accepts almost everything but crawls, exploring one hillside forever; too large and nearly every proposal lands off a cliff and is rejected. The comfortable band accepts roughly a fifth to a half of moves — a rule of thumb near 0.234 for high dimensions.
A well-mixing chain draws a fuzzy caterpillar trace. Beware the tidy one: a chain stuck on a single peak produces a confident, clean histogram that is lying by omission about every mode it never reached.
The prospector's survey instrument jammed mid-expedition. The lesson continues without it — everything you have learned so far is safe.