A journey through patterns, logic and intuition with a mad patternologist.
An entry to #SoME1.
โ ๐๐ฑ๐ฑ๐ถ๐๐ถ๐ผ๐ป๐ฎ๐น ๐ฐ๐ผ๐ป๐๐ฒ๐ป๐
ยท Python code that counts max-complexity patterns:
https://github.com/zz-zye/patterns
ยท Full process of finding all max-complexity patterns in a 3ร3 grid:
https://drive.google.com/drive/folders/1oHTxjipJ-VdSXGqzaZXxvgR7LRXxRlHi?usp=sharing
โ ๐ฅ๐ฒ๐ณ๐ฒ๐ฟ๐ฒ๐ป๐ฐ๐ฒ
ยท 3Blue1Brown, ๐๐ฉ๐บ ๐ช๐ด ๐ฑ๐ช ๐ฉ๐ฆ๐ณ๐ฆ? ๐๐ฏ๐ฅ ๐ธ๐ฉ๐บ ๐ช๐ด ๐ช๐ต ๐ด๐ฒ๐ถ๐ข๐ณ๐ฆ๐ฅ? ๐ ๐จ๐ฆ๐ฐ๐ฎ๐ฆ๐ต๐ณ๐ช๐ค ๐ข๐ฏ๐ด๐ธ๐ฆ๐ณ ๐ต๐ฐ ๐ต๐ฉ๐ฆ ๐๐ข๐ด๐ฆ๐ญ ๐ฑ๐ณ๐ฐ๐ฃ๐ญ๐ฆ๐ฎ,
https://youtu.be/d-o3eB9sfls/
ยท Mathologer, ๐๐ถ๐ญ๐ฆ๐ณโ๐ด ๐๐ช ๐๐ณ๐ช๐ฎ๐ฆ ๐๐ณ๐ฐ๐ฅ๐ถ๐ค๐ต ๐ข๐ฏ๐ฅ ๐๐ช๐ฆ๐ฎ๐ข๐ฏ๐ฏโ๐ด ๐ก๐ฆ๐ต๐ข ๐๐ถ๐ฏ๐ค๐ต๐ช๐ฐ๐ฏ,
https://youtu.be/LFwSIdLSosI/
ยท Paulo Coelho, ๐๐ฉ๐ฆ ๐๐ญ๐ค๐ฉ๐ฆ๐ฎ๐ช๐ด๐ต
ยท Zoltan Puskas(sinustrom), ๐๐ฏ๐ฅ๐ณ๐ฐ๐ช๐ฅ ๐ถ๐ฏ๐ญ๐ฐ๐ค๐ฌ ๐ฑ๐ข๐ต๐ต๐ฆ๐ณ๐ฏ ๐ด๐ฆ๐ค๐ถ๐ณ๐ช๐ต๐บ ๐ข๐ฏ๐ข๐ญ๐บ๐ด๐ช๐ด,
https://sinustrom.info/2012/05/21/android-unlock-pattern-security-analysis/
ยท Summoning Salt's videos, https://www.youtube.com/c/SummoningSalt
ยท jan Misali's videos, https://www.youtube.com/user/HBMmaster8472
ยท The patterns of this video were animated with Manim! It's a python library for math animations. Check it on https://www.manim.community/
โ ๐ ๐๐๐ถ๐ฐ
(๐ฆ๐ผ๐ฟ๐๐ฒ๐ฑ ๐ฏ๐ ๐๐ต๐ฒ ๐ณ๐ถ๐ฟ๐๐ ๐ฎ๐ฝ๐ฝ๐ฒ๐ฎ๐ฟ๐ฎ๐ป๐ฐ๐ฒ ๐ผ๐ณ ๐ฒ๐ฎ๐ฐ๐ต ๐บ๐๐๐ถ๐ฐ ๐ถ๐ป ๐๐ต๐ฒ ๐๐ถ๐ฑ๐ฒ๐ผ)
Home - We're Finally Landing (00:00)
Asher Fulero - Lukewarm Hazy (00:57)
Home - Pyxis (01:27)
Toby Fox - Can You Really Call This A Hotel, I Didn't Receive A Mint On My Pillow Or Anything (02:35)
Toby Fox - Hotel (04:06 and all the Try It Yourselfs)
Home - Nosebleed (05:22)
C418 - Beton (06:57)
Toby Fox - Snowdin Town (08:46)
Cheel - Soft Feeling (18:49)
Home - Before The Night (20:44)
C418 - AMS (21:58)
โ Try It Yourself! #3 HINT : sวษฏฤฑษนdoษ
โ There was a mistake in 2:53, the written definition only applies to 3x3 patterns because it only checks if there exists a dot in the 'middle' of the current dot and the next dot. The correct way would be to check if there are any dots in the line segment of the current dot and the next dot.
โ ๐ง๐ถ๐บ๐ฒ๐น๐ถ๐ป๐ฒ
00:00 - Intro
01:22 - 1. Define
02:58 - 2. Find It
06:07 - 3. Find All
09:23 - 4. Generalize
15:17 - 5. Number Theory
20:41 - 6. Find Everywhere