What Is The Most Complicated Lock Pattern?

A journey through patterns, logic and intuition with a mad patternologist.
An entry to #SoME1.


● 𝗔𝗱𝗱𝗶𝘁𝗶𝗼𝗻𝗮𝗹 𝗰𝗼𝗻𝘁𝗲𝗻𝘁
· Python code that counts max-complexity patterns:
https://github.com/zz-zye/patterns
· Full process of finding all max-complexity patterns in a 3×3 grid:
https://drive.google.com/drive/folder...

● 𝗥𝗲𝗳𝗲𝗿𝗲𝗻𝗰𝗲
· 3Blue1Brown, 𝘞𝘩𝘺 𝘪𝘴 𝘱𝘪 𝘩𝘦𝘳𝘦? 𝘈𝘯𝘥 𝘸𝘩𝘺 𝘪𝘴 𝘪𝘵 𝘴𝘲𝘶𝘢𝘳𝘦𝘥? 𝘈 𝘨𝘦𝘰𝘮𝘦𝘵𝘳𝘪𝘤 𝘢𝘯𝘴𝘸𝘦𝘳 𝘵𝘰 𝘵𝘩𝘦 𝘉𝘢𝘴𝘦𝘭 𝘱𝘳𝘰𝘣𝘭𝘦𝘮,
   • Why is pi here?  And why is it square...  
· Mathologer, 𝘌𝘶𝘭𝘦𝘳’𝘴 𝘗𝘪 𝘗𝘳𝘪𝘮𝘦 𝘗𝘳𝘰𝘥𝘶𝘤𝘵 𝘢𝘯𝘥 𝘙𝘪𝘦𝘮𝘢𝘯𝘯’𝘴 𝘡𝘦𝘵𝘢 𝘍𝘶𝘯𝘤𝘵𝘪𝘰𝘯,
   • Euler’s Pi Prime Product  and Riemann...  
· Paulo Coelho, 𝘛𝘩𝘦 𝘈𝘭𝘤𝘩𝘦𝘮𝘪𝘴𝘵
· Zoltan Puskas(sinustrom), 𝘈𝘯𝘥𝘳𝘰𝘪𝘥 𝘶𝘯𝘭𝘰𝘤𝘬 𝘱𝘢𝘵𝘵𝘦𝘳𝘯 𝘴𝘦𝘤𝘶𝘳𝘪𝘵𝘺 𝘢𝘯𝘢𝘭𝘺𝘴𝘪𝘴,
https://sinustrom.info/2012/05/21/and...
· Summoning Salt's videos,    / summoningsalt  
· jan Misali's videos,    / hbmmaster8472  
· The patterns of this video were animated with Manim! It's a python library for math animations. Check it on https://www.manim.community/

● 𝗠𝘂𝘀𝗶𝗰
(𝗦𝗼𝗿𝘁𝗲𝗱 𝗯𝘆 𝘁𝗵𝗲 𝗳𝗶𝗿𝘀𝘁 𝗮𝗽𝗽𝗲𝗮𝗿𝗮𝗻𝗰𝗲 𝗼𝗳 𝗲𝗮𝗰𝗵 𝗺𝘂𝘀𝗶𝗰 𝗶𝗻 𝘁𝗵𝗲 𝘃𝗶𝗱𝗲𝗼)
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)

● Try It Yourself! #3 HINT : sǝɯıɹdoɔ

● 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.

● 𝗧𝗶𝗺𝗲𝗹𝗶𝗻𝗲
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