Batch 3 - Class 229 - Game of Life (John Conway)

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Pre-Class Exercise

There are nine cards on a table labeled by numbers 1 through 9. Alice and Bob take turns choosing one card. The player that has collected a set of cards with the property that the sum of numbers on three cards out of total set is 15 wins. There’s a tie if none of the players has a set of cards with this property at the end of the game. Does any of the players have a winning strategy? A non-losing strategy?

Attendance Kabir, Aarkin, Vansh, Advay, Kushagra, Ayush, Rhea, Rohan, Anshi, Vivaan, Rehaan, Angad, Arjun N, Shikher, Aashvi, Nishant

Class puzzles (From Class 56 with additions)

Rules of the game:

There are number of dead squares and a few live ones at beginning of the game
A live square with 0,1 or more than 4 neighbors dies in the next generation due to isolation/crowding. A live square with 2 or 3 neighbors lives on
A dead square with 3 neighbor cells becomes alive in the next generation

Let kids try out the following patterns and what happens. Let kids try out patterns on left, and use a computer program to do the ones on the right. http://gmlive.narod.ru/download/live/version_0_3/gamelive.html You can also download the Life32 simulator http://psoup.math.wisc.edu/Life32.html

Still lifes
Block	https://en.wikipedia.org/wiki/File:Game_of_life_block_with_border.svg
Bee- hive	https://en.wikipedia.org/wiki/File:Game_of_life_beehive.svg
Loaf	https://en.wikipedia.org/wiki/File:Game_of_life_loaf.svg
Boat	https://en.wikipedia.org/wiki/File:Game_of_life_boat.svg
Tub	https://en.wikipedia.org/wiki/File:Game_of_life_flower.svg

Spaceships
Glider
Light- weight spaceship (LWSS)
Middle- weight spaceship (MWSS)
Heavy- weight spaceship (HWSS)

Conway conjectured that all such patterns must be finite, and floated a $50 reward to prove or disprove.

What do you think happened? Try out the Gosper Glider Gun

Applications

People believe one can use this to understand life: In 2010, Andrew Wade created the first life simulator demonstrating two objects "reproducing" a third one, after 34 million steps ("Gemini") https://www.youtube.com/watch?v=A8B5MbHPlH0

Shows that local action and local rules are enough to generate complex behavior, including reproduction
Can be used in robots - specify local rules, and there is no need to have an overview of the world
Think about how we navigate

Universal Turing Machine - https://www.youtube.com/watch?v=My8AsV7bA94 https://www.ics.uci.edu/~welling/teaching/271fall09/Turing-Machine-Life.pdf
Music synthesizer - http://hujackus.altervista.org/conwaymatrix/

Multiplayer Game of Life

Two player game - play with two colors (one for each player) - when new life comes into being, it takes the color of majority of cells around it. On each turn, a player must kill one enemy cell, and must change one empty cell to a cell of their color. A player is eliminated when they lose all cells of their color.
Play here for multiple players (each representing a form of life that competes) http://lifecompetes.com/.

Homework:

(Moscow - 197) A complete set of dominos is as shown below. If you place all the 28 tiles in a continuous chain (adjacent ends of the tiles must match) so that 5 dots are at one end, how many dots will be at the other end?

References:

The Moscow Puzzles, by Boris A. Kordemsky

Game of Life android app (on Play Store)