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Animation 26
Huygens–Fresnel principle
symmetry-schematic-screens-v3-concise.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 · 24 s · 576 frames · 12 samples
MP4 SHA-256 66887f22e7e0dae166c0e097a20ef5256c28be0e9192eb803e6af168e0d0a24b
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Chapter context
Section: Wave Propagation and Interference. Excerpts are verbatim; line numbers refer to the included chapter markdown.
Caption
Huygens–Fresnel principle
Image description
Huygens wavelets and their coherent sum as slits and screens are added
Before the animation
Chapter lines 1199–1199
We can extend this procedure to its limit and include infinitely many screens with infinitely many slits, and recover unobstructed propagation. In the following animation, we start with a plane wave and recover that same wave. This construction, which provides a bridge to Feynman’s path integral formulation of quantum mechanics, has its roots in Huygens’ wavelets from the late 1600s, extended by Fresnel to include interference in the early 1800s.
After the animation
Chapter lines 1207–1207
Let us now ask one more question. What happens to our tip-to-tail diagram of the path contributions when we vary the wavelength relative to the slit? As the wavelength becomes small, even a slight change in path length can produce a large phase change:
Chapter lines 1209–1212
Generation source
Final entrypoint is retime_symmetry_schematic_screens.py, which consumes content/drafts/animations/symmetry-schematic-screens-v3.mp4. Generate that 52-second source with generate_symmetry_schematic_screens_v3.py --render; its listed local imports supply construction state, field model, and drawing helpers. The final script applies whole-frame monotone FFmpeg setpts/fps retiming to 24 seconds, without recomputing fields or interpolating frames. Source-to-output knots are 0:0, 2:1, 22:7, 42:17, 48:21, 52:24 seconds.
Mapping evidence and limits
The concise validation explicitly names the v3 input and retiming method and records 576 frames, 24 fps, 1280 x 720, 24 s. Both current movies match its source_sha256 and video_sha256 fields (source 4fca2f3e85cddef6ae2e85b0fbb400b157c807dfebdb86cc9df76be8cf298da2; final 66887f22e7e0dae166c0e097a20ef5256c28be0e9192eb803e6af168e0d0a24b).
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/retime_symmetry_schematic_screens.py · GitHub at 974f9de35254
SHA-256 d6801c0b61fb87e9e202633c31b0fc5853268614fef2db5ce5846f8365de4db9 - scripts/generate_symmetry_schematic_screens_v3.py · GitHub at 974f9de35254
SHA-256 fdba8977d904d4bea5de26b701e095c01e3a24e2fe79ab65251d7fcfa3d3d615 - scripts/schematic_screens_v3_model.py · GitHub at 974f9de35254
SHA-256 c094ccf24f356709e2ff2a103ecad4ae716c2bafbcbc7f2040c41c106bb3f7fa - scripts/generate_symmetry_schematic_screens_v2.py · GitHub at 974f9de35254
SHA-256 e5d7fa0d52eefbcfb839dbc48565299901d49914fc9f48fd1aaab548f842c2ba - scripts/generate_symmetry_schematic_screens.py · GitHub at 974f9de35254
SHA-256 6e31805fd5a4de5bd4b19ed3c2a6a035ca6458e2389dab5162a0567186b07977 - scripts/generate_symmetry_plane_wave_screens.py · GitHub at 974f9de35254
SHA-256 0085a1a626f9ba5bfb88cb22974b4c65692dddc7afcf97165b9751c320331381 - scripts/plane_wave_screens_model.py · GitHub at 974f9de35254
SHA-256 627e82993ba8de74005677c6dc5b5afafe8f3a801a8b0ebde7ffd368b51ea420
Existing generator checks (1 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-schematic-screens-v3-concise-validation.json
SHA-256 e1991adcb42c874b12663ad78e83e353d3e9eb8a4c5420d9454a8a236d647b55
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
