CONWAYยท3D

time is the third dimension

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Conway's Game of Life

A zero-player game invented by mathematician John Conway in 1970: draw a starting pattern, and everything unfolds on its own โ€” no input, no randomness, just four rules.

Every generation, each cell counts its 8 neighbors:

  • Loneliness โ€” a live cell with fewer than 2 neighbors dies
  • Survival โ€” a live cell with 2 or 3 neighbors lives on
  • Overcrowding โ€” a live cell with more than 3 neighbors dies
  • Birth โ€” a dead cell with exactly 3 neighbors comes alive

Here the grid is the floor and every generation stacks on top of the last, so height = time: gliders trace diagonal ribbons, oscillators grow repeating columns, and dying patterns leave towers that simplyโ€ฆ stop.

โ–ถ Watch Veritasium explain the Game of Life

ืžืฉื—ืง ื”ื—ื™ื™ื ืฉืœ ืงื•ื ื•ื•ื™ื™

ืžืฉื—ืง ืฉืœ ืืคืก ืฉื—ืงื ื™ื ืฉื”ืžืฆื™ื ื”ืžืชืžื˜ื™ืงืื™ ื’'ื•ืŸ ืงื•ื ื•ื•ื™ื™ ื‘-1970: ืžืฆื™ื™ืจื™ื ืชื‘ื ื™ืช ืคืชื™ื—ื” ืขืœ ื”ืœื•ื—, ื•ืžื›ืืŸ ื”ื›ื•ืœ ื ืงื‘ืข ืžืขืฆืžื• โ€” ื‘ืœื™ ืงืœื˜, ื‘ืœื™ ืืงืจืื™ื•ืช, ืจืง ืืจื‘ืขื” ื—ื•ืงื™ื.

ื‘ื›ืœ ื“ื•ืจ, ื›ืœ ืชื ืกื•ืคืจ ืืช 8 ืฉื›ื ื™ื•:

  • ื‘ื“ื™ื“ื•ืช โ€” ืชื ื—ื™ ืขื ืคื—ื•ืช ืž-2 ืฉื›ื ื™ื ืžืช
  • ื”ื™ืฉืจื“ื•ืช โ€” ืชื ื—ื™ ืขื 2 ืื• 3 ืฉื›ื ื™ื ืžืžืฉื™ืš ืœื—ื™ื•ืช
  • ืฆืคื™ืคื•ืช โ€” ืชื ื—ื™ ืขื ื™ื•ืชืจ ืž-3 ืฉื›ื ื™ื ืžืช
  • ืœื™ื“ื” โ€” ืชื ืžืช ืขื ื‘ื“ื™ื•ืง 3 ืฉื›ื ื™ื ืงื ืœืชื—ื™ื™ื”

ื›ืืŸ ื”ืœื•ื— ื”ื•ื ื”ืจืฆืคื”, ื•ื›ืœ ื“ื•ืจ ื ืขืจื ืžืขืœ ืงื•ื“ืžื• โ€” ื’ื•ื‘ื” = ื–ืžืŸ: ื’ืœื™ื™ื“ืจื™ื ืžืฆื™ื™ืจื™ื ืกืจื˜ื™ื ืืœื›ืกื•ื ื™ื™ื, ืžืชื ื“ื™ื ื‘ื•ื ื™ื ืขืžื•ื“ื™ื ืžื—ื–ื•ืจื™ื™ื, ื•ืชื‘ื ื™ื•ืช ืฉื’ื•ื•ืขื•ืช ืžืฉืื™ืจื•ืช ืžื’ื“ืœ ืฉืคืฉื•ื˜โ€ฆ ื ืขืฆืจ.

ืœืฆืคื™ื™ื” ื‘ื”ืกื‘ืจ ืฉืœ Veritasium ืขืœ ืžืฉื—ืง ื”ื—ื™ื™ื โ—€