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Animation 5
Continuous symmetries
symmetry-continuous-so2-translation.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.
1280 × 620 · 24 fps · 5 s · 120 frames · 12 samples
MP4 SHA-256 63f62f9a684091f29dea57b738da51ac054b51f81acf29a63aa83a4b1b346381
Frame manifest · Context markdown · Download complete review packet
Chapter context
Section: Continuous symmetries. Excerpts are verbatim; line numbers refer to the included chapter markdown.
Caption
Continuous symmetries
Image description
Continuous rotation and translation symmetries
Before the animation
Chapter lines 171–171
What rotations return a circle to itself? All of them! Similarly, all translations return a line to itself. The symmetries of space and time are continuous and can therefore be represented as transformations that depend on continuously varying parameters.
After the animation
Generation source
Run the main script without arguments. It draws and encodes the movie directly, then calls make_contact_sheet from _make_contact_sheets to sample the encoded output. The helper does not supply an earlier input movie.
Mapping evidence and limits
main() explicitly writes symmetry-continuous-so2-translation.mp4; constants specify 1280 x 620, 24 fps, 120 frames. No matching validation JSON is present. Attribution is by source/output name and pipeline, not a recorded movie hash.
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_continuous_so2_translation_animation.py · GitHub at 974f9de35254
SHA-256 217746be53dc44cb1ded70680fa654bc660f39e594789bdd0807255fb2d2c721 - scripts/_make_contact_sheets.py · GitHub at 974f9de35254
SHA-256 9084b8285991d44dcba3ba937cc55ac76d7bc761c9c9cf048d2735cc1f6eadb9
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
