Conway’s Game of Life

Introduction

The Rules

  1. Any live cell with fewer than two live neighbors dies, as if by underpopulation.
  2. Any live cell with two or three live neighbors lives on to the next generation.
  3. Any live cell with more than three live neighbors dies, as if by overpopulation.
  4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.
Blinker
  • Cell ‘a’ is dead. Since it does not have exactly 3 live neighbors (rule 4), it remains dead.
  • Cell ‘b’ is also dead. Since it has 3 live neighbors (rule 4), it becomes alive.
  • Cell ‘c’ is alive. Since it has fewer than 2 live neighbors (rule 1), it dies of underpopulation.
  • Cell ‘d’ is alive. Since it has 2 live neighbors (rule 2), it lives on to the next generation.

Classification

  • Still Lifes: In Conway’s Game of Life, still life is a pattern that does not change from one generation to the next. The most common still life (i.e., that most likely to be generated from a random initial state) is the block. The second most common still life is the hive (or beehive).
Block
Hive
  • Oscillators: An oscillator is a pattern that repeats itself after a fixed number of generations (known as its period). One of the fascinating oscillators is ‘Dinner Table,’ discovered by Robert Wainwright. It is a period-12 oscillator where it seems like dinner is being passed among four individuals around the table.
Dinner Table
  • Spaceships: A spaceship is a finite pattern that returns to its initial state after several generations but in a different location. The four smallest spaceships in life, the glider, lightweight spaceship, middleweight spaceship, and heavyweight spaceship, were all found by hand in 1970.
    Gliders were probably the most unexpected characteristic of Conway’s Game of Life and, in the end, the one responsible for its great complexity and utility. Conway quickly realized that gliders were the substitute for von Neumann’s wires as the mechanism for transporting information from one place to another in the Life field.
Glider
Glider Gun

Logic Gates

  • Input electric pulse -> Gliders
  • Wires to transmit input -> Gliders’ movement trajectory
  • Process input and compute a boolean result -> Glider collisions
  • Output -> Collision of gliders with immobile patterns
Glider Collision
Eater
Eater consuming glider
NOT Gate ( A — 0, Output 1)
NOT Gate (A — 1, Output — 0)
AND Gate (A — 1, B — 0, Output — 0)
AND Gate (A — 1, B — 1, Output — 1)
AND Gate (A — 0, B — 1, Output — 0)
OR (A — 1, B — 0, Output — 1)
OR (A — 1, B — 1, Output — 1)
OR (A — 0, B — 0, Output — 0)

Turing Machine

Turing Machine

Other Insane Achievements

Nicolas Loizeau’s 8-bit programmable computer

Digital Clock

Digital Clock

Life Inside Life

Life in Life

Free Will

Conclusion

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I am a Computer Engineer graduated from Kathmandu University, Nepal. The existence is a program, we are here to add our part of code. Website: sbasnet.com.np

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Subash Basnet

I am a Computer Engineer graduated from Kathmandu University, Nepal. The existence is a program, we are here to add our part of code. Website: sbasnet.com.np