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Animation 6
Symmetry flows provide a rich picture of symmetry transformations
symmetry-so2-vector-field-flow.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 × 720 · 24 fps · 8.75 s · 210 frames · 12 samples
MP4 SHA-256 8eb47d9c4cc2c5949c9c02c0ae622fc244ea9203c9fe3aa880f1e64e5e51057a
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Chapter context
Section: Symmetry Flows. Excerpts are verbatim; line numbers refer to the included chapter markdown.
Caption
Symmetry flows provide a rich picture of symmetry transformations
Image description
Rotation generator as a vector field
Before the animation
Chapter lines 330–330
We can think of a symmetry transform as a "uniform looking" vector field, as illustrated below:
After the animation
Chapter lines 338–338
Here we ask not what happens when the transformation is applied to a single set of starting conditions, but what the transformation does to all starting conditions. This view lends itself to seeing the structure in the evolution of a collection of nearby states.
Generation source
Run the main script without arguments. It draws the vector-field-flow frames with Pillow and encodes them with FFmpeg. It has no local Python imports or input movie.
Mapping evidence and limits
main() explicitly writes symmetry-so2-vector-field-flow.mp4; constants specify 1280 x 720, 24 fps, 210 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_so2_vector_field_flow_animation.py · GitHub at 974f9de35254
SHA-256 a966dd1533d8aa529a7412b9a72cf12d3a118d5cf54fc5e1f80c348e82b8054c
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
