Mr. Scandrett's ClassroomOS

Cellular Automata · Lesson 09

Life Lab: The Game of Life

Explore cellular automata through challenge levels, famous patterns, and the story of how Conway's idea changed mathematics, computer science, and AI research.

Simulation Studio

Pick a level, place cells, then run evolution.

Generation: 0

Live Cells: 0

Persistence Peak: 0

Entropy Δ: 0

Beginner: 20 x 20, slower pace for first-time learners.

Tip: Click or drag on the grid to toggle cells before pressing Start.

Learning Console

Read fast, run a task, and collect evidence.

Beginner keeps it short. Advanced reveals deeper terms like universality, information flow, and proof prompts.

History in 3 Moves

Each card: one idea, three bullets, one action.

1940s–1950s: Cellular Automata

Local rules became a new way to study complex systems.

  • Ulam and von Neumann studied grid-based updates.
  • Each cell reads nearby neighbors only.
  • Big idea: local decisions create global behavior.
  • Advanced lens: this is a discrete dynamical system.
  • Challenge: define state space and transition function.
Do this now:

Draw a 3×3 neighborhood and label neighbor counts from 0 to 8.

1970: Conway + Gardner

One rule set produced endless patterns and public excitement.

  • Birth on exactly 3 neighbors (B3).
  • Survive on 2 or 3 neighbors (S23).
  • Martin Gardner popularized it in Scientific American.
  • Glider gun patterns show information-like streams.
  • Challenge: explain why simple rules can be computationally universal.
Do this now:

Predict whether a cell lives or dies for neighbor counts 1, 2, 3, 4.

1970s–Today: Pattern Discovery

Communities mapped still lifes, oscillators, spaceships, and more.

  • Still life: does not change generation to generation.
  • Oscillator: repeats after a fixed period.
  • Spaceship: pattern moves across the grid.
  • Measure period and velocity to classify patterns.
  • Challenge: prove a structure is stable under B3/S23.
Do this now:

Find one oscillator in the simulator and record its period.

Pattern Snapshots

Visual memory tools for fast recognition.

3×3 Neighbors

Center cell reads 8 neighbors.

Block (Still Life)

No changes each generation.

Blinker (2 Frames)

Period 2 oscillator.

Glider (4 Frames)

Moves diagonally over time.

Future + Project Paths

Turn concepts into artifacts you can submit.

Path A (Grades 6–8): Pattern Zoo

Collect, label, and explain behavior patterns.

  • Collect 10 patterns from simulation runs.
  • Sort into still life, oscillator, spaceship.
  • Artifact: screenshot board + one sentence per pattern.
Do this now:

Capture one still life and one oscillator screenshot.

Path B (Grades 8–10): Rule Designer

Compare rule sets and report what changes.

  • Test Classic Life and HighLife for 100 generations.
  • Track population trend and dominant patterns.
  • Artifact: table + short explanation of differences.
  • Challenge: design a rule with long-lived turbulence.
Do this now:

Predict which rule produces more moving structures, then test it.

Path C (Grades 10–12): Model the World

Map automata language onto a real system.

  • Choose traffic, disease spread, or ecosystem change.
  • Define states, neighbors, and update rules.
  • Artifact: two screenshots + 5-sentence reflection.
  • Challenge: justify boundary conditions and sampling limits.
Do this now:

Write what a cell and neighbor represent in your model.

Completion Rubric

  • Completed five task boxes.
  • Submitted two screenshots with labels.
  • Included one period measurement.
  • Wrote a five-sentence reflection.
  • Explained one real-world mapping.

Bonus: discover or design a novel pattern.

Tap a Vocabulary Word

Use this mini glossary while you run experiments.

Select a term to see a one-line definition.