Generator
walk
A generator in the probability library, called 6 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.
walk is one function. Everything below came out of it during this
build, at parameters taken from the essays rather than invented for this page — so a figure
here is the same figure a reader meets in an essay, and if the generator changes, this page
changes with it.
At its defaults
show: "spread"
show: "lattice"
show: "return"
What it checks while it draws
Collected by running the family and listening to lib/verify.js, not written
here. The count is how many separate times this build put that claim to the test.
- a walk in space escapes, and the simulation sees it ×1
- a walk on a line comes back, and the horizon barely hides it ×1
- a walk on a plane comes back too, but more slowly ×1
- an endpoint has the parity of the step count ×1
- and their spread is the square root of the number of steps ×1
- each step moves one place along one axis ×1
- every step is drawn ×1
- every step is one place, either way ×1
- every walk is counted once ×1
- some walk goes outside the envelope, because √n is typical and not maximal ×1
- the position has the parity of the step count ×1
- the quoted constant is Pólya's ×1
- the spread of the endpoints is of the order of the square root of the steps ×1
- the walk comes back to where it started at least once ×1
- the walks are centred on where they started ×1
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.