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Animation 15
The complex value rotates while its length stays fixed.
symmetry-complex-plane-wave-v2.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 × 900 · 30 fps · 12 s · 360 frames · 12 samples
MP4 SHA-256 e407d6199cc5539ba3a33469fd1a417d21023bef7461f1acad2ecd11fa903892
Frame manifest · Context markdown · Download complete review packet
Chapter context
Section: Primer - Complex exponentials and Wave Packets. Excerpts are verbatim; line numbers refer to the included chapter markdown.
Caption
The complex value rotates while its length stays fixed.
Image description
A complex plane wave, its two components, and the rotating value at a fixed position
Before the animation
Chapter lines 775–775
Here $A$ is the wave's amplitude, $\lambda$ is its wavelength, $k=2\pi/\lambda$ is its wave number, and $\omega$ sets how quickly the phase changes with time.
Chapter lines 777–777
In the animation, position runs along the helix. The other two directions show the real and imaginary parts of the complex value at each position. As time advances, these values rotate and the wave pattern travels along $x$.
After the animation
Chapter lines 785–785
The two components are $A\cos\theta$ and $A\sin\theta$. Their values oscillate, while the length of the complex value stays fixed:
Chapter lines 787–789
Generation source
Main script --render draws the complex plane-wave frames and encodes them directly. --check and --encoded-check produce the companion mathematical and decoded-video reports. It has no local Python imports or input movie.
Mapping evidence and limits
The script's NAME and output match the linked movie. Matching validation and encoded-validation JSON record 1440 x 900, 30 fps, 360 frames, 12 s. The reports contain no movie hash, so this is source/output-name attribution rather than a hash-attested build.
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_complex_plane_wave_v2.py · GitHub at 974f9de35254
SHA-256 6dc77c751f396bdc8d8a8d78ff7606b9331a5e0a31dc0aa9d2b556a0bbee6fd8
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-complex-plane-wave-v2-validation.json
SHA-256 482c1bdae6e380e4796007acf9c50dbcb46ab0540efa25539400407f25e65cb7 - symmetry-complex-plane-wave-v2-encoded-validation.json
SHA-256 aad970dd9e74c8f246b365431c9db9c8ab767f338f43a90e1983392284911b6a
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
