Building Logic Gates and Computers in Conway's Game of Life

Conway's Game of Life is computationally universal, meaning it can simulate any computer program. This remarkable property allows the construction of logic gates, memory units, and even complete computers within the cellular automaton.

Fundamental Logic Elements

Glider Streams as Signals: Information is encoded in the presence or absence of gliders in periodic streams. A glider represents "1" and its absence represents "0".

Basic Gates:

• NOT Gate: The Eater 1 can consume gliders, inverting the signal
• AND Gate: Two glider streams must collide at the right timing
• OR Gate: Multiple input streams merge into one output

Memory and Storage

Flip-flops: Stable configurations that can store one bit of information

Registers: Arrays of flip-flops for multi-bit storage

Memory cells: The OTCA Metapixel serves as a universal memory unit

Clock Signals

Gun-based clocks: Gosper Glider Guns provide regular timing pulses

Synchronized systems: Multiple guns can be phase-locked for complex timing

Advanced Constructions

Universal Turing Machine: The Universal Turing Machine can simulate any computable function

Self-replicators: Gemini demonstrates self-reproduction capabilities

Universal Constructors: Patterns that can build arbitrary configurations from a program

Practical Challenges

Size: Logic gates require hundreds of cells Speed: Operations take hundreds of generations Complexity: Large constructions become difficult to debug

Modern Achievements

Digital clocks: Working timepieces built from Life patterns Calculators: Adding machines that perform arithmetic Game implementations: Life-in-Life and other games

Construction Techniques

Glider synthesis: Precisely timed glider collisions build components

Still life catalysis: Using stable patterns to enable specific reactions

Conduit technology: Herschel tracks and other signal paths