A teaching tape for BM-05, Random Steps to Diffusion
coin to bell
Open BM-05 with these settings
Where it starts
| Setting | Value |
|---|---|
| Per-step RMS (stepRms) | 5e-7 |
| Interval between steps (tau) | 0.1 |
| Walkers (walkers) | 2000 |
| Recorded steps per walker (runSteps) | 400 |
| Steps shown (n) | 0 |
| Asymmetric-deviation bias (bias) | 0.6 |
| Step distribution (kernel) | coin |
What it changes, and what to expect
Set Steps shown (n) to 4 changes how it is watched, not what happens
Set Steps shown (n) to 16 changes how it is watched, not what happens
Set Steps shown (n) to 64 changes how it is watched, not what happens
Set Steps shown (n) to 400 changes how it is watched, not what happens
Coin kernel, 400 steps: the predict prompt settles here
The histogram at 400 coin steps is the state that settles bm-05-predict-step-shape (same-bell-shape), read from this accepted snapshot's histogram and second-moment outputs, never from stored text.
Set Step distribution (kernel) to uniform changes what the run starts from
Set Step distribution (kernel) to gaussian changes what the run starts from
Gaussian kernel, same seed and step count: the same bell
Common random numbers: same seed, same step count, a different kernel. The second moment and histogram width agree with the coin-kernel checkpoint within the declared statistical band; the shapes differ at small n and agree at n = 400.
These are the values the tape's author recorded, not a result this page computed. Nothing here runs the instrument. Open BM-05 with these settings: the link puts them in its form, and it calculates when you apply them. Compare what it gives you with what is recorded here. The settings travel in the link and the laboratory reads them as it loads, so without JavaScript it opens at its worked example instead.
What these numbers were recorded under
| Identity | Recorded as |
|---|---|
| Model | bm05-host-preview-v1 version 1 |
| Seed | 1905 |
| Random-stream semantics | version 1 |