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Animation 27
Three trials accumulate a quarter turn at the longer wavelength while the shorter wavelength produces many rotations
symmetry-phase-remainder-spinners.mp4
These are sparse samples decoded from the current MP4, not newly rendered illustrations. They can support checks of the sampled states and labels, but cannot establish continuous motion, timing, transitions, or the absence of problems between samples. Use the full MP4 when judging those properties.
1440 × 870 · 60 fps · 17 s · 1020 frames · 12 samples
MP4 SHA-256 bb3a49c2b2cb17d33c7a5e67dd057eb1efa4c07e4f7d06390caad1214601360a
Frame manifest · Context markdown · Download complete review packet
Chapter context
Section: Wave Propagation and Interference. Excerpts are verbatim; line numbers refer to the included chapter markdown.
Caption
No separate caption in the chapter.
Image description
Three trials accumulate a quarter turn at the longer wavelength while the shorter wavelength produces many rotations
Before the animation
Chapter lines 1209–1212
Chapter lines 1214–1214
Away from a stationary path, the phase winds through many cycles over a small range of paths, leaving an effectively random phase remainder so that contributions away from stationary paths largely cancel, while those near stationary paths dominate the sum.
After the animation
Chapter lines 1220–1220
In this limit, waves passing through slits behave as rays. A narrow beam through one opening reaches a small region of the screen, much as a thrown ball does.
Chapter lines 1222–1222
Each path shares its color with its contribution to the tip-to-tail sum. As the wavelength shrinks, an increasingly narrow range of paths around the straight path carries the sum forward.
Generation source
Use the current main script --render, with --check and --encoded-check for validation. It imports general drawing/encoding helpers from two_tip_to_tail_limits. Archived phase-remainder v1/v2 scripts and movies are earlier variants; the current generator shows left endpoints at 30,60,90 degrees.
Mapping evidence and limits
Matching validation records lengths 1,2,3, wavelengths 12 and 5/47, right remainders 144,288,72 degrees, 1020 frames at 60 fps, 1440 x 870, 17 s. Matching encoded-validation.json confirms all 1020 frames. notes/worked/phase-remainder-spinners.md identifies the current generator and explicitly distinguishes the archived v1/v2 variants.
Source SHA-256 values identify the exact downloadable bytes in this packet. The source mapping and recorded checks explain the likely generation pipeline; they do not prove that these exact source bytes produced the movie. A GitHub link pinned to a commit is provided only when the delivered source bytes exactly match that path at the build's Git HEAD.
- scripts/generate_symmetry_phase_remainder_spinners.py · GitHub at 974f9de35254
SHA-256 ab2938d03e2a08d4e00e7294e353ba38d863d74b3ec27fef0d77c3ec5c0fdd42 - scripts/generate_symmetry_two_tip_to_tail_limits.py · GitHub at 974f9de35254
SHA-256 9a7e8081dc0333b30ba0d85cd49552af8cc9377a65b2bae582b7d1c5043bae12
Existing generator checks (2 reports)
These are existing author-produced generator reports, copied without changes. Their checks were not rerun for this packet and are not independent certification. A report may describe an earlier generation run; inspect its contents before applying its claims to the current movie.
- symmetry-phase-remainder-spinners-validation.json
SHA-256 8112603c8770b320ff3f83bfab3c4fe8119cbd6fe082d1cc6e7f3e874872cf61 - symmetry-phase-remainder-spinners-encoded-validation.json
SHA-256 5ab818c503620129176f021755901d3af0b68b490ae46f5669ba1acb8e55eab4
Decoded contact sheet
Extraction method: Twelve evenly spaced decoded frame indices, including first and last. Native-resolution JPEGs from the encoded MP4; timestamps read from FFmpeg showinfo. No source rerendering. Frame indices are zero-based. Sparse samples do not establish continuous motion or capture every transition.. Frame indices are zero-based.
Full-size sampled frames
