Deeper

Lab · c22.s05.L1

Sampling walk

A generated sample is a random starting point carried along a fixed path: the randomness is in the start, and the model supplies the motion.

Question: How do you draw a new sample?

Sampling walkA square panel shows a loose cloud of dots near the centre, each trailing a thin navy spiral out to a russet ring of radius 1.0. Hollow rings mark the starts; filled gold dots mark the current samples. Play runs the forty-step walk, stepping moves one checkpoint, and another seed scatters only the starts. Every dot lands on the same ring at a new angle, so the randomness is in where a walk begins.Sampling walkRandom starts, one fixed flow onto a ringtrailring, radius 1.0random startsample now0 of 4032 samples, seed 1start mean distance 0.5532final mean distance 0.0263first sample's final angle 79°All 32 samples begin as draws from a standard-normalcloud in the plane. Their mean distance from the ringis 0.5532. Nothing has moved yet, so the starts arethe whole source of randomness.
Synthetic Synthetic: a hand-built toy flow, not a trained model and not measured data, carries standard-normal starts onto a ring of radius 1.0 in 40 Euler steps of dt 0.025. At 32 samples and seed 1 the mean distance to the ring falls from 0.5532 to 0.0263; the first sample ends at 79° and the largest final radial error is 0.0813. The script data/scripts/c22.s05.L1.py computes every path, and the same seed and count reproduce the same picture.
Lab controls
32

Left/Down and Right/Up move by 4; Page Up/Down by 12; Home sets 4; End sets 60

seed 1

Left/Right move one option; Home selects seed 1; End selects seed 5

Frame 1 of 7: 0 of 40All 32 samples begin as draws from a standard-normal cloud in the plane. Their mean distance from the ring is 0.5532. Nothing has moved yet, so the starts are the whole source of randomness.

Keyboard: Space plays or pauses, Left and Right step, Home goes to the first frame, End goes to the last frame.

Text description of this lab

A square panel shows a loose cloud of dots near the centre, each trailing a thin navy spiral out to a russet ring of radius 1.0. Hollow rings mark the starts; filled gold dots mark the current samples. Play runs the forty-step walk, stepping moves one checkpoint, and another seed scatters only the starts. Every dot lands on the same ring at a new angle, so the randomness is in where a walk begins.

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Caption status: synthetic. Every lab declares one of published, re-simulated, schematic, synthetic or interpolated.