Riemann zeta spiral and plot up to 40k + "car hifi cd" rip
Автор: IJK
Загружено: 2026-02-06
Просмотров: 30
Описание:
Animation of the zeta spiral to a height of forty thousand units. It is also about the music found in "24k car hifi" Chinese bootleg CDs. For @3blue1brown.
A followup to my #SoME4 submission. The animation starts at height 0, and goes up by one imaginary unit per second. Will be remade.
See GitHub: https://github.com/mulliganaceous/Rie...
Legend:
Left bar: The critical strip and its immediate vicinity. The color palette is designed to highlight the contour where the value takes on a certain absolute value, or are purely real or imaginary. The center of the left bar indicates the current view of the zeta function.
White cross: Output of the zeta function at this frame
White curve: Path of the zeta function from the nearest multiple of 5 to this frame
Red curve: Path of the function at surrounding input values on the right half of the critical strip (up to Re s = 0.75).
Blue curve: Path of the function at surrounding input values on the left half of the critical strip (down to Re s = 0.25).
Green curve: Path of the zeta function at the same height, with real component of input from 0 to 2
Yellow curve: Path of the zeta function at the Basel line (defined as Re z = 2)
Gray lines and circle: Coordinate grid and unit circle of the complex plane
Rotating gray line segment: Segment from origin to the output, plus the segment from origin to the unit circle in the direction opposite to the output. If the output has absolute value less than the value of the Basel problem, the segment pointing in the direction of the output will have length of the Basel problem, givin the appearance of a circle with a stroke, with one side protruding.
Limitations:
From 3:20 to 5:00 the critical strip is either absent or misaligned. This will be fixed in the update.
The color palette may need to be revamped to make the gridlines more subtle. Also, I need to add transparency to ensure the marker is visible.
This spirals file is originally 283.3 long gigabytes (gibibytes), and the plot fil is 88 long gigabytes. The highest quality compression reduces it to 21.3 long gigabytes.
Currently, I have not implemented a way to count the number of zeros up to that point in a continous run, and then convert that into audio.
Music and Chapters:
00:00:00 - The first track is Zeta for @3blue1brown.
00:04:35 (275) - The next three tracks @incompetech_kmac's recordings of ragtime pieces (Fig Leaf, Maple Leaf).
00:11:16 (676) - The next three tracks are for @3blue1brown that are not composed by him in album order.
00:26:56 (1616) - The next track is another @incompetech_kmac's recordings of a ragtime piece (Frog Legs Rag), followed by the remaining tracks are for @3blue1brown in album order.
01:56:40 (7000) - The first Lehmer Pair will appear at height 7005.
For the next few hours, the music came directly from a "Car HiFi Music" 3CD set my father bought. These albums are notorious for making bootleg material; but this album seems to be original. This has been discussed on Discogs: https://www.discogs.com/forum/thread/...
02:35:02 (9302) - 梅蘭竹菊 A
03:51:30 (13890) - 梅蘭竹菊 B
05:03:51 (21231) - 梅蘭竹菊 C
06:21:51 (22911) - 四大鋼琴王子 A (alphabetical ordering)
07:39:22 (27562) - 四大鋼琴王子 B
08:51:37 (31897) - 四大鋼琴王子 C
The music for the final hour is an incomplete list of an older Chinese disk of mp3 collections.
10:05:30 (36330) - 15 of the 100 mp3s in some Chinese mp3 collection
11:00:18 (39618) - Moonstruck! (congrats for making it that far!
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