Transcript — 3Blue1Brown: How (and why) to take a logarithm of an image

Video ID: ldxFjLJ3rVY URL: https://www.youtube.com/watch?v=ldxFjLJ3rVY Upload date: 2026-03-22 Duration: 44m 52s (2692s) Channel: 3Blue1Brown

Note on transcript availability

YouTube did not expose an English auto-caption track for this video at the time of ingest (2026-04-20 cycle 41). Manual subtitles were available in Arabic, Croatian, French, German, Hindi, Korean, Portuguese-BR, Russian, Spanish, and Vietnamese. Auto-translate to English via yt-dlp returned HTTP 429 from YouTube on repeated attempts. Spanish manual VTT was captured at /tmp/yt-process/ldxFjLJ3rVY.es.vtt (75KB) during ingest but not persisted — the substantive content of this video is fully recoverable from the author’s chapters + description + the companion de Smit/Lenstra paper.

Chapters (from description)

• 0:00 — The print gallery
• 13:04 — Conformal maps from complex analysis
• 21:41 — The complex exponential
• 25:56 — The complex logarithm
• 32:32 — 3b1b Talent
• 33:14 — Constructing the key function
• 40:16 — The deeper math behind Escher

Description (verbatim)

Escher’s Print Gallery, and the tour of complex analysis it invites.

Original paper by de Smit and Lenstra: https://pub.math.leidenuniv.nl/~smitbde/papers/2003-de_smit-lenstra-escher.pdf

The book I was showing is “Magic of MC Escher” by J. L. Locher

Co-written by Paul Dancstep, who handled many of the animations in the art section. Aaron Gostein helped with the manim animations in the complex functions section. Artwork provided by Talia Gershon, Mitchell Zemil, and Anna Fedczuk. Music by Vincent Rubinetti.

Companion materials in the vault

• 2026-03-27-3blue1brown-eschers-print-gallery — the 102s teaser that points to this long-form video
• de Smit & Lenstra (2003), “Artful mathematics: the heritage of M.C. Escher” — the paper whose “logarithm of an image” framing is the technical core of this piece