Lecture 19 · Mathematics
Build your own de Bruijn deck
Video in production
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Meanwhile, read the outlineWhat you will learn
Construct, verify and export an order-four de Bruijn card stack and matching decoder.
Before this lecture
Ideas you will use
- Graph correspondence and Euler proof
In this lecture
An outline of the lecture, scene by scene, with the statements that appear on screen. It follows the draft script, so details may change in production.
Define an executable construction task
- Target: order 4,16 windows
- Outputs: cycle +stack +decoder
- Extend or finish; never jump
Specify algorithm data and operation
- Unused edge: mark and push
- No unused edge: pop to finished list
- Reverse finished list to read tour
Show small cycle splicing before large run
- Stack implements cycle splicing
- Used edges never reset
- Two views, one construction
Run a verified order 4 tour and spell it
- Linear spelling has 16+3 symbols
- Discard repeated closing context
- Cycle 0000100110101111
Convert bit cycle into physical identities
- 0→next unused club
- 1→next unused heart
- 8 zero positions; 8 one positions
Construct decoder and verify all cuts
- Stack order≠lookup sort order
- One entry per cyclic start
- Test all 16 cuts
Give complete construction failure diagnostics
- Graph →tour →cycle →cards →decoder
- Report the first specific failure
- Never silently repair the protocol
Companion export challenge and retrieval
- Export stack, lookup and rules
- All checks tied to the same data
- Next: larger alphabets
Companion interactive
Planned
Produce a complete 16-card preparation and decoder with all checks passing.
The interactive for this lecture is being built and will appear here.
Notes
Written notes for this lecture will appear here.
Sources
- Magical Mathematics, pp. 20–24
How these sources were used
- Euler construction; explicit implementation and alternate 16-cycle are checked teaching developments.